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Номер 6, страница 458 - гдз по физике 10 класс учебник Касьянов
Авторы: Касьянов В. А.
Тип: Учебник
Издательство: Просвещение
Год издания: 2021 - 2026
Уровень обучения: углублённый
Цвет обложки: белый самолет и молнии изображены
ISBN: 978-5-09-103621-3
Популярные ГДЗ в 10 классе
Лабораторные работы. 7. Изучение капиллярных явлений, обусловленных поверхностным натяжением жидкости - номер 6, страница 458.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1390622 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab07-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "426" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 #items: array:1 [ 0 => App\Models\Term {#1042 …30} ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\Term {#1044 …30} ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ 0 => App\Models\Term {#1046 …30} ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:1 [ 0 => App\Models\Term {#1048 …30} ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1051 …30} ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:1 [ 0 => App\Models\Term {#1059 …30} ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 …30} ] #escapeWhenCastingToString: false } "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 …30} ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ 0 => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" "alt" => "" "width" => "1604" "height" => "2397" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 …30} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #original: array:50 [ "id" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045} "field_author" => Illuminate\Database\Eloquent\Collection {#1047} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_country" => Illuminate\Database\Eloquent\Collection {#1052} "field_city" => Illuminate\Database\Eloquent\Collection {#1054} "field_series" => Illuminate\Database\Eloquent\Collection {#1056} "field_umk" => Illuminate\Database\Eloquent\Collection {#1057} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ 0 => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" "alt" => "" "width" => "1604" "height" => "2397" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "426" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:2 [ 0 => App\Models\Branch {#1116 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1117 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "426" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1150 #items: array:1 [ 0 => App\Models\Book {#1118 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1120 #items: array:1 [ 0 => App\Models\Term {#1119 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:1 [ 0 => App\Models\Term {#1122 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #original: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Term {#1124 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Term {#1126 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4566 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Касьянов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Валерий" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4566 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Касьянов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Валерий" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1127 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\Term {#1129 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Term {#1131 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1132 #items: array:1 [ 0 => App\Models\Term {#1133 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1134 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1135 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1136 #items: array:1 [ 0 => App\Models\Term {#1137 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 39 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "углублённый" "field_cases" => array:6 [ "field_accusative_case" => "углубленный" "field_creative_case" => "углубленным" "field_dative_case" => "углубленному" "field_genitive_case" => "углубленного" "field_nominative_case" => "углубленный" "field_prepositional_case" => "углубленном" ] "field_translit" => "uglublennyy" ] #original: array:6 [ "id" => 39 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "углублённый" "field_cases" => array:6 [ "field_accusative_case" => "углубленный" "field_creative_case" => "углубленным" "field_dative_case" => "углубленному" "field_genitive_case" => "углубленного" "field_nominative_case" => "углубленный" "field_prepositional_case" => "углубленном" ] "field_translit" => "uglublennyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1138 #items: array:1 [ 0 => App\Models\Term {#1139 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ 0 => App\Models\Term {#1141 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "stereotipnoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ 0 => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" "alt" => "" "width" => "1604" "height" => "2397" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1143 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Term {#1147 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "field_translit" => "belyy" ] #original: array:6 [ "id" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "field_translit" => "belyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #original: array:50 [ "id" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1120} "field_class" => Illuminate\Database\Eloquent\Collection {#1121} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1123} "field_author" => Illuminate\Database\Eloquent\Collection {#1125} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1127} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1128} "field_country" => Illuminate\Database\Eloquent\Collection {#1130} "field_city" => Illuminate\Database\Eloquent\Collection {#1132} "field_series" => Illuminate\Database\Eloquent\Collection {#1134} "field_umk" => Illuminate\Database\Eloquent\Collection {#1135} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1136} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1138} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1140} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ 0 => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" "alt" => "" "width" => "1604" "height" => "2397" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1143} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1117} "field_page_start" => "426" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1150} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1149 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1389661 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7. Изучение капиллярных явлений, обусловленных поверхностным натяжением жидкости" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1151 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "457" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1152 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389661 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7. Изучение капиллярных явлений, обусловленных поверхностным натяжением жидкости" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1151} "field_page_start" => "457" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1152} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:2 [ 0 => App\Models\Element {#1099 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1641052 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ 0 => App\Models\Edition {#1097 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5810 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1095 #items: array:1 [ 0 => App\Models\Term {#1098 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1096 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1093 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1094 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5810 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1095} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1096} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1093} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1094} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1390622" "type" => "task" ] "text" => "<p><strong>6.</strong> Запишите значение диаметра капилляров с учётом абсолютной погрешности измерения: $D_1 \pm \Delta D_1, D_2 \pm \Delta D_2.$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "6-1.jpg" "alt" => null "width" => "1691" "height" => 289 "path" => "/media/fizika_10/kasyanov-u/0-lab07/6-1.webp?ts=1757958251" ] ] ] #original: array:7 [ "id" => 1641052 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1089} "task" => array:2 [ "refs" => "1390622" "type" => "task" ] "text" => "<p><strong>6.</strong> Запишите значение диаметра капилляров с учётом абсолютной погрешности измерения: $D_1 \pm \Delta D_1, D_2 \pm \Delta D_2.$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "6-1.jpg" "alt" => null "width" => "1691" "height" => 289 "path" => "/media/fizika_10/kasyanov-u/0-lab07/6-1.webp?ts=1757958251" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1092 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1693634 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1083 #items: array:1 [ 0 => App\Models\Edition {#1091 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1087 #items: array:1 [ 0 => App\Models\Term {#1090 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1087} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1088} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1085} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1390622" "type" => "task" ] "text" => "<p>Вопрос требует записать результаты измерений диаметров двух капилляров в стандартном виде, включающем среднее значение и абсолютную погрешность. Общий вид такой записи: $X = \langle X \rangle \pm \Delta X$, где $\langle X \rangle$ — наилучшая оценка измеряемой величины (обычно среднее арифметическое), а $\Delta X$ — абсолютная погрешность измерения.</p><p>Поскольку в самом вопросе не предоставлены данные измерений, для демонстрации полного решения приведём гипотетический пример с расчётами.</p><p><strong>Дано:</strong></p><p>Проведены измерения диаметров двух капилляров с помощью микрометра, цена деления которого составляет $c = 0.01$ мм. Для каждого капилляра было сделано по $n=5$ измерений.</p><p>Результаты измерений для первого капилляра ($d_1$, мм): 1.52, 1.54, 1.53, 1.55, 1.51.</p><p>Результаты измерений для второго капилляра ($d_2$, мм): 0.88, 0.85, 0.89, 0.87, 0.86.</p><p><strong>Найти:</strong></p><p>Записать значения диаметров капилляров $D_1$ и $D_2$ с учётом абсолютной погрешности.</p><p><strong>Решение:</strong></p><p>Абсолютная погрешность состоит из приборной и случайной составляющих. Приборная погрешность $\Delta D_{пр}$ для микрометра принимается равной половине цены деления:</p><p>$\Delta D_{пр} = \frac{c}{2} = \frac{0.01 \text{ мм}}{2} = 0.005 \text{ мм}$.</p><p><em>Расчёт для первого капилляра ($D_1$):</em></p><p><strong>1.</strong> Найдём среднее значение диаметра, которое является наилучшей оценкой $D_1$:</p><p>$D_1 = \langle d_1 \rangle = \frac{1.52 + 1.54 + 1.53 + 1.55 + 1.51}{5} = \frac{7.65}{5} = 1.53 \text{ мм}$.</p><p><strong>2.</strong> Рассчитаем случайную погрешность измерения $\Delta D_{1,сл}$ как стандартную ошибку среднего. Для этого сначала найдём сумму квадратов отклонений от среднего:</p><p>$\sum_{i=1}^{5} (d_{1,i} - D_1)^2 = (1.52-1.53)^2 + (1.54-1.53)^2 + (1.53-1.53)^2 + (1.55-1.53)^2 + (1.51-1.53)^2$</p><p>$= 0.0001 + 0.0001 + 0 + 0.0004 + 0.0004 = 0.0010 \text{ мм}^2$.</p><p>Тогда случайная погрешность:</p><p>$\Delta D_{1,сл} = \sqrt{\frac{\sum(d_{1,i} - D_1)^2}{n(n-1)}} = \sqrt{\frac{0.0010}{5(5-1)}} = \sqrt{\frac{0.0010}{20}} = \sqrt{0.00005} \approx 0.00707 \text{ мм}$.</p><p><strong>3.</strong> Найдём полную абсолютную погрешность $\Delta D_1$ как сумму случайной и приборной погрешностей:</p><p>$\Delta D_1 = \Delta D_{1,сл} + \Delta D_{пр} \approx 0.00707 + 0.005 = 0.01207 \text{ мм}$.</p><p><strong>4.</strong> Округлим результат. Абсолютную погрешность следует округлить до одной значащей цифры: $\Delta D_1 \approx 0.01 \text{ мм}$. Среднее значение $D_1 = 1.53 \text{ мм}$ округляем до того же знака после запятой, что и погрешность (до сотых). В данном случае оно уже имеет нужную точность.</p><p><em>Расчёт для второго капилляра ($D_2$):</em></p><p><strong>1.</strong> Найдём среднее значение диаметра $D_2$:</p><p>$D_2 = \langle d_2 \rangle = \frac{0.88 + 0.85 + 0.89 + 0.87 + 0.86}{5} = \frac{4.35}{5} = 0.87 \text{ мм}$.</p><p><strong>2.</strong> Рассчитаем случайную погрешность $\Delta D_{2,сл}$. Сумма квадратов отклонений:</p><p>$\sum_{i=1}^{5} (d_{2,i} - D_2)^2 = (0.88-0.87)^2 + (0.85-0.87)^2 + (0.89-0.87)^2 + (0.87-0.87)^2 + (0.86-0.87)^2$</p><p>$= 0.0001 + 0.0004 + 0.0004 + 0 + 0.0001 = 0.0010 \text{ мм}^2$.</p><p>Случайная погрешность:</p><p>$\Delta D_{2,сл} = \sqrt{\frac{\sum(d_{2,i} - D_2)^2}{n(n-1)}} = \sqrt{\frac{0.0010}{5(5-1)}} = \sqrt{\frac{0.0010}{20}} \approx 0.00707 \text{ мм}$.</p><p><strong>3.</strong> Найдём полную абсолютную погрешность $\Delta D_2$:</p><p>$\Delta D_2 = \Delta D_{2,сл} + \Delta D_{пр} \approx 0.00707 + 0.005 = 0.01207 \text{ мм}$.</p><p><strong>4.</strong> Округлим результат. Абсолютную погрешность округляем до одной значащей цифры: $\Delta D_2 \approx 0.01 \text{ мм}$. Среднее значение $D_2 = 0.87 \text{ мм}$ уже имеет требуемую точность (до сотых).</p><p><strong>$D_1 \pm \Delta D_1$</strong></p><p><strong>Ответ:</strong> $D_1 = (1.53 \pm 0.01) \text{ мм}$.</p><p><strong>$D_2 \pm \Delta D_2$</strong></p><p><strong>Ответ:</strong> $D_2 = (0.87 \pm 0.01) \text{ мм}$.</p>" ] #original: array:6 [ "id" => 1693634 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1083} "task" => array:2 [ "refs" => "1390622" "type" => "task" ] "text" => "<p>Вопрос требует записать результаты измерений диаметров двух капилляров в стандартном виде, включающем среднее значение и абсолютную погрешность. Общий вид такой записи: $X = \langle X \rangle \pm \Delta X$, где $\langle X \rangle$ — наилучшая оценка измеряемой величины (обычно среднее арифметическое), а $\Delta X$ — абсолютная погрешность измерения.</p><p>Поскольку в самом вопросе не предоставлены данные измерений, для демонстрации полного решения приведём гипотетический пример с расчётами.</p><p><strong>Дано:</strong></p><p>Проведены измерения диаметров двух капилляров с помощью микрометра, цена деления которого составляет $c = 0.01$ мм. Для каждого капилляра было сделано по $n=5$ измерений.</p><p>Результаты измерений для первого капилляра ($d_1$, мм): 1.52, 1.54, 1.53, 1.55, 1.51.</p><p>Результаты измерений для второго капилляра ($d_2$, мм): 0.88, 0.85, 0.89, 0.87, 0.86.</p><p><strong>Найти:</strong></p><p>Записать значения диаметров капилляров $D_1$ и $D_2$ с учётом абсолютной погрешности.</p><p><strong>Решение:</strong></p><p>Абсолютная погрешность состоит из приборной и случайной составляющих. Приборная погрешность $\Delta D_{пр}$ для микрометра принимается равной половине цены деления:</p><p>$\Delta D_{пр} = \frac{c}{2} = \frac{0.01 \text{ мм}}{2} = 0.005 \text{ мм}$.</p><p><em>Расчёт для первого капилляра ($D_1$):</em></p><p><strong>1.</strong> Найдём среднее значение диаметра, которое является наилучшей оценкой $D_1$:</p><p>$D_1 = \langle d_1 \rangle = \frac{1.52 + 1.54 + 1.53 + 1.55 + 1.51}{5} = \frac{7.65}{5} = 1.53 \text{ мм}$.</p><p><strong>2.</strong> Рассчитаем случайную погрешность измерения $\Delta D_{1,сл}$ как стандартную ошибку среднего. Для этого сначала найдём сумму квадратов отклонений от среднего:</p><p>$\sum_{i=1}^{5} (d_{1,i} - D_1)^2 = (1.52-1.53)^2 + (1.54-1.53)^2 + (1.53-1.53)^2 + (1.55-1.53)^2 + (1.51-1.53)^2$</p><p>$= 0.0001 + 0.0001 + 0 + 0.0004 + 0.0004 = 0.0010 \text{ мм}^2$.</p><p>Тогда случайная погрешность:</p><p>$\Delta D_{1,сл} = \sqrt{\frac{\sum(d_{1,i} - D_1)^2}{n(n-1)}} = \sqrt{\frac{0.0010}{5(5-1)}} = \sqrt{\frac{0.0010}{20}} = \sqrt{0.00005} \approx 0.00707 \text{ мм}$.</p><p><strong>3.</strong> Найдём полную абсолютную погрешность $\Delta D_1$ как сумму случайной и приборной погрешностей:</p><p>$\Delta D_1 = \Delta D_{1,сл} + \Delta D_{пр} \approx 0.00707 + 0.005 = 0.01207 \text{ мм}$.</p><p><strong>4.</strong> Округлим результат. Абсолютную погрешность следует округлить до одной значащей цифры: $\Delta D_1 \approx 0.01 \text{ мм}$. Среднее значение $D_1 = 1.53 \text{ мм}$ округляем до того же знака после запятой, что и погрешность (до сотых). В данном случае оно уже имеет нужную точность.</p><p><em>Расчёт для второго капилляра ($D_2$):</em></p><p><strong>1.</strong> Найдём среднее значение диаметра $D_2$:</p><p>$D_2 = \langle d_2 \rangle = \frac{0.88 + 0.85 + 0.89 + 0.87 + 0.86}{5} = \frac{4.35}{5} = 0.87 \text{ мм}$.</p><p><strong>2.</strong> Рассчитаем случайную погрешность $\Delta D_{2,сл}$. Сумма квадратов отклонений:</p><p>$\sum_{i=1}^{5} (d_{2,i} - D_2)^2 = (0.88-0.87)^2 + (0.85-0.87)^2 + (0.89-0.87)^2 + (0.87-0.87)^2 + (0.86-0.87)^2$</p><p>$= 0.0001 + 0.0004 + 0.0004 + 0 + 0.0001 = 0.0010 \text{ мм}^2$.</p><p>Случайная погрешность:</p><p>$\Delta D_{2,сл} = \sqrt{\frac{\sum(d_{2,i} - D_2)^2}{n(n-1)}} = \sqrt{\frac{0.0010}{5(5-1)}} = \sqrt{\frac{0.0010}{20}} \approx 0.00707 \text{ мм}$.</p><p><strong>3.</strong> Найдём полную абсолютную погрешность $\Delta D_2$:</p><p>$\Delta D_2 = \Delta D_{2,сл} + \Delta D_{пр} \approx 0.00707 + 0.005 = 0.01207 \text{ мм}$.</p><p><strong>4.</strong> Округлим результат. Абсолютную погрешность округляем до одной значащей цифры: $\Delta D_2 \approx 0.01 \text{ мм}$. Среднее значение $D_2 = 0.87 \text{ мм}$ уже имеет требуемую точность (до сотых).</p><p><strong>$D_1 \pm \Delta D_1$</strong></p><p><strong>Ответ:</strong> $D_1 = (1.53 \pm 0.01) \text{ мм}$.</p><p><strong>$D_2 \pm \Delta D_2$</strong></p><p><strong>Ответ:</strong> $D_2 = (0.87 \pm 0.01) \text{ мм}$.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390623" "type" => "task" ] "previous" => array:2 [ "refs" => "1390621" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1102 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\BookPage {#1104 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1391106 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_url" => "/10-klass/fizika/kasyanov-uchebnik/page-458" "field_display_title" => "458" "field_folder" => "1" "field_image_name" => "458" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1080 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1111 #items: array:1 [ 0 => App\Models\Element {#1115 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1641606 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1109 #items: array:1 [ 0 => App\Models\Edition {#1097} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1391106" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "458-1.jpg" "alt" => null "width" => "1868" "height" => 2533 "path" => "/media/fizika_10/kasyanov-u/0-1/458-1.webp?ts=1757958810" ] ] ] #original: array:6 [ "id" => 1641606 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1109} "book_page" => array:2 [ "refs" => "1391106" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "458-1.jpg" "alt" => null "width" => "1868" "height" => 2533 "path" => "/media/fizika_10/kasyanov-u/0-1/458-1.webp?ts=1757958810" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1391107" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1391105" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:6 [ 0 => App\Models\Task {#1255 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1390617 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab07-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1256 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1257 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1258 #items: array:1 [ 0 => App\Models\Branch {#1116} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1259 #items: array:2 [ 0 => App\Models\Branch {#1116} 1 => App\Models\Branch {#1149} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1261 #items: array:2 [ 0 => App\Models\Element {#1270 …30} 1 => App\Models\Element {#1272 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390618" "type" => "task" ] "previous" => array:2 [ "refs" => "1390616" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1267 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391106" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390617 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab07-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1256} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1257} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1258} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1259} "content" => Illuminate\Database\Eloquent\Collection {#1261} "next" => array:2 [ "refs" => "1390618" "type" => "task" ] "previous" => array:2 [ "refs" => "1390616" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1267} "page" => array:2 [ "refs" => "1391106" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1262 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1390618 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab07-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1260 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1269 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1265 #items: array:1 [ 0 => App\Models\Branch {#1116} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1263 #items: array:2 [ 0 => App\Models\Branch {#1116} 1 => App\Models\Branch {#1149} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1264 #items: array:2 [ 0 => App\Models\Element {#1282 …30} 1 => App\Models\Element {#1284 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390619" "type" => "task" ] "previous" => array:2 [ "refs" => "1390617" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1279 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391106" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390618 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab07-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1260} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1269} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1265} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1263} "content" => Illuminate\Database\Eloquent\Collection {#1264} "next" => array:2 [ "refs" => "1390619" "type" => "task" ] "previous" => array:2 [ "refs" => "1390617" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1279} "page" => array:2 [ "refs" => "1391106" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1274 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1390619 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab07-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1266 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1281 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1277 #items: array:1 [ 0 => App\Models\Branch {#1116} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1275 #items: array:2 [ 0 => App\Models\Branch {#1116} 1 => App\Models\Branch {#1149} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1276 #items: array:2 [ 0 => App\Models\Element {#1294 …30} 1 => App\Models\Element {#1296 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390620" "type" => "task" ] "previous" => array:2 [ "refs" => "1390618" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1291 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391106" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390619 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab07-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1266} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1281} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1277} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1275} "content" => Illuminate\Database\Eloquent\Collection {#1276} "next" => array:2 [ "refs" => "1390620" "type" => "task" ] "previous" => array:2 [ "refs" => "1390618" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1291} "page" => array:2 [ "refs" => "1391106" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1286 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1390620 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab07-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1278 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1293 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1289 #items: array:1 [ 0 => App\Models\Branch {#1116} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1287 #items: array:2 [ 0 => App\Models\Branch {#1116} 1 => App\Models\Branch {#1149} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1288 #items: array:2 [ 0 => App\Models\Element {#1306 …30} 1 => App\Models\Element {#1308 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390621" "type" => "task" ] "previous" => array:2 [ "refs" => "1390619" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1303 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391106" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390620 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab07-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1278} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1293} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1289} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1287} "content" => Illuminate\Database\Eloquent\Collection {#1288} "next" => array:2 [ "refs" => "1390621" "type" => "task" ] "previous" => array:2 [ "refs" => "1390619" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1303} "page" => array:2 [ "refs" => "1391106" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1298 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1390621 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab07-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1290 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1305 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1301 #items: array:1 [ 0 => App\Models\Branch {#1116} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1299 #items: array:2 [ 0 => App\Models\Branch {#1116} 1 => App\Models\Branch {#1149} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1300 #items: array:2 [ 0 => App\Models\Element {#1318 …30} 1 => App\Models\Element {#1320 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390622" "type" => "task" ] "previous" => array:2 [ "refs" => "1390620" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1315 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391106" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390621 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab07-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1290} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1305} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1301} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1299} "content" => Illuminate\Database\Eloquent\Collection {#1300} "next" => array:2 [ "refs" => "1390622" "type" => "task" ] "previous" => array:2 [ "refs" => "1390620" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1315} "page" => array:2 [ "refs" => "1391106" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1310 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1390622 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab07-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1302 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1317 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1313 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1311 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1314 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390623" "type" => "task" ] "previous" => array:2 [ "refs" => "1390621" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1312 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391106" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390622 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab07-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1302} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1317} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1313} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1311} "content" => Illuminate\Database\Eloquent\Collection {#1314} "next" => array:2 [ "refs" => "1390623" "type" => "task" ] "previous" => array:2 [ "refs" => "1390621" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1312} "page" => array:2 [ "refs" => "1391106" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1391106 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_url" => "/10-klass/fizika/kasyanov-uchebnik/page-458" "field_display_title" => "458" "field_folder" => "1" "field_image_name" => "458" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1084} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1082} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1080} "content" => Illuminate\Database\Eloquent\Collection {#1111} "next" => array:2 [ "refs" => "1391107" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1391105" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1243} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1390622 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "458" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab07-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1108} "content" => Illuminate\Database\Eloquent\Collection {#1071} "next" => array:2 [ "refs" => "1390623" "type" => "task" ] "previous" => array:2 [ "refs" => "1390621" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1102} "page" => array:2 [ "refs" => "1391106" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№6 (с. 458)
Условие. №6 (с. 458)
скриншот условия
6. Запишите значение диаметра капилляров с учётом абсолютной погрешности измерения: $D_1 \pm \Delta D_1, D_2 \pm \Delta D_2.$
Решение. №6 (с. 458)
Вопрос требует записать результаты измерений диаметров двух капилляров в стандартном виде, включающем среднее значение и абсолютную погрешность. Общий вид такой записи: $X = \langle X \rangle \pm \Delta X$, где $\langle X \rangle$ — наилучшая оценка измеряемой величины (обычно среднее арифметическое), а $\Delta X$ — абсолютная погрешность измерения.
Поскольку в самом вопросе не предоставлены данные измерений, для демонстрации полного решения приведём гипотетический пример с расчётами.
Дано:
Проведены измерения диаметров двух капилляров с помощью микрометра, цена деления которого составляет $c = 0.01$ мм. Для каждого капилляра было сделано по $n=5$ измерений.
Результаты измерений для первого капилляра ($d_1$, мм): 1.52, 1.54, 1.53, 1.55, 1.51.
Результаты измерений для второго капилляра ($d_2$, мм): 0.88, 0.85, 0.89, 0.87, 0.86.
Найти:
Записать значения диаметров капилляров $D_1$ и $D_2$ с учётом абсолютной погрешности.
Решение:
Абсолютная погрешность состоит из приборной и случайной составляющих. Приборная погрешность $\Delta D_{пр}$ для микрометра принимается равной половине цены деления:
$\Delta D_{пр} = \frac{c}{2} = \frac{0.01 \text{ мм}}{2} = 0.005 \text{ мм}$.
Расчёт для первого капилляра ($D_1$):
1. Найдём среднее значение диаметра, которое является наилучшей оценкой $D_1$:
$D_1 = \langle d_1 \rangle = \frac{1.52 + 1.54 + 1.53 + 1.55 + 1.51}{5} = \frac{7.65}{5} = 1.53 \text{ мм}$.
2. Рассчитаем случайную погрешность измерения $\Delta D_{1,сл}$ как стандартную ошибку среднего. Для этого сначала найдём сумму квадратов отклонений от среднего:
$\sum_{i=1}^{5} (d_{1,i} - D_1)^2 = (1.52-1.53)^2 + (1.54-1.53)^2 + (1.53-1.53)^2 + (1.55-1.53)^2 + (1.51-1.53)^2$
$= 0.0001 + 0.0001 + 0 + 0.0004 + 0.0004 = 0.0010 \text{ мм}^2$.
Тогда случайная погрешность:
$\Delta D_{1,сл} = \sqrt{\frac{\sum(d_{1,i} - D_1)^2}{n(n-1)}} = \sqrt{\frac{0.0010}{5(5-1)}} = \sqrt{\frac{0.0010}{20}} = \sqrt{0.00005} \approx 0.00707 \text{ мм}$.
3. Найдём полную абсолютную погрешность $\Delta D_1$ как сумму случайной и приборной погрешностей:
$\Delta D_1 = \Delta D_{1,сл} + \Delta D_{пр} \approx 0.00707 + 0.005 = 0.01207 \text{ мм}$.
4. Округлим результат. Абсолютную погрешность следует округлить до одной значащей цифры: $\Delta D_1 \approx 0.01 \text{ мм}$. Среднее значение $D_1 = 1.53 \text{ мм}$ округляем до того же знака после запятой, что и погрешность (до сотых). В данном случае оно уже имеет нужную точность.
Расчёт для второго капилляра ($D_2$):
1. Найдём среднее значение диаметра $D_2$:
$D_2 = \langle d_2 \rangle = \frac{0.88 + 0.85 + 0.89 + 0.87 + 0.86}{5} = \frac{4.35}{5} = 0.87 \text{ мм}$.
2. Рассчитаем случайную погрешность $\Delta D_{2,сл}$. Сумма квадратов отклонений:
$\sum_{i=1}^{5} (d_{2,i} - D_2)^2 = (0.88-0.87)^2 + (0.85-0.87)^2 + (0.89-0.87)^2 + (0.87-0.87)^2 + (0.86-0.87)^2$
$= 0.0001 + 0.0004 + 0.0004 + 0 + 0.0001 = 0.0010 \text{ мм}^2$.
Случайная погрешность:
$\Delta D_{2,сл} = \sqrt{\frac{\sum(d_{2,i} - D_2)^2}{n(n-1)}} = \sqrt{\frac{0.0010}{5(5-1)}} = \sqrt{\frac{0.0010}{20}} \approx 0.00707 \text{ мм}$.
3. Найдём полную абсолютную погрешность $\Delta D_2$:
$\Delta D_2 = \Delta D_{2,сл} + \Delta D_{пр} \approx 0.00707 + 0.005 = 0.01207 \text{ мм}$.
4. Округлим результат. Абсолютную погрешность округляем до одной значащей цифры: $\Delta D_2 \approx 0.01 \text{ мм}$. Среднее значение $D_2 = 0.87 \text{ мм}$ уже имеет требуемую точность (до сотых).
$D_1 \pm \Delta D_1$
Ответ: $D_1 = (1.53 \pm 0.01) \text{ мм}$.
$D_2 \pm \Delta D_2$
Ответ: $D_2 = (0.87 \pm 0.01) \text{ мм}$.
Другие задания:
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