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Номер 216, страница 68 - гдз по алгебре 9 класс учебник Солтан, Солтан
Авторы: Солтан Г. Н., Солтан А. Е., Жумадилова А. Ж.
Тип: Учебник
Издательство: Кокшетау
Год издания: 2019 - 2026
ISBN: 978-601-317-424-2
Рекомендовано Министерством образования и науки Республики Казахстан
Популярные ГДЗ в 9 классе
II. Элементы комбинаторики. 7. Основные понятия и правила комбинаторики - номер 216, страница 68.
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" => 1107919 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-216" "field_display_title" => "216" "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 {#1071 #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" => 1107646 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "II. Элементы комбинаторики" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "62" "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" => 4298 "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 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_standart_of_education" => 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"field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4298 "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 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1047 …2} 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"field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1068 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107646 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "II. 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"field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4298 "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 {#1074 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1078 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1080 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" 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"field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1101 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107646 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "II. Элементы комбинаторики" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1072} "field_page_start" => "62" "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 {#1070} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1101} ] #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 {#1102 #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" => 1107647 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7. Основные понятия и правила комбинаторики" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1103 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "63" "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 {#1104 #items: array:1 [ 0 => App\Models\Book {#1105 #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" => 4298 "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 {#1106 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4298 "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 {#1106 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1133 #items: array:1 [ 0 => App\Models\Branch {#1134 #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" => 1107646 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "II. Элементы комбинаторики" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_page_start" => "62" "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 {#1136 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1137 …2} ] #original: array:24 [ "id" => 1107646 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "II. Элементы комбинаторики" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_page_start" => "62" "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 {#1136 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1137 …2} ] #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" => 1107647 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7. Основные понятия и правила комбинаторики" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1103} "field_page_start" => "63" "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 {#1104} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133} ] #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 {#1156 #items: array:3 [ 0 => App\Models\Element {#1166 #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" => 1276571 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1175 #items: array:1 [ 0 => App\Models\Edition {#1167 #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" => 4953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1169 …2} "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" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_content_source" => null ] #original: array:21 [ "id" => 4953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1169 …2} "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" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1172 …2} "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" => "1107919" "type" => "task" ] "text" => "<p><strong>216.</strong> Известно, что скорость вращения Земли вокруг Солнца равна 40 247 км/ч, а скорость вращения Луны вокруг Земли - 8568 км/ч. Представьте числа, выражающие эти скорости, в виде суммы наименьшего количества степеней числа 2 с неотрицательными целыми показателями.</p><p><svg width="300" height="200" viewBox="0 0 300 200"><!-- Background --><rect x="0" y="0" width="300" height="200" fill="black"/><!-- Earth --><circle cx="150" cy="100" r="40" fill="#87CEEB" stroke="black" stroke-width="1"/><!-- Simplified landmasses --><path d="M140 90 Q145 80 150 90 T160 100 Q155 110 150 100 T140 90" fill="#32CD32"/><path d="M160 80 Q165 70 170 80 T180 90 Q175 100 170 90 T160 80" fill="#32CD32"/><path d="M130 110 Q135 120 140 110 T150 100 Q145 90 140 100 T130 110" fill="#32CD32"/><!-- Earth's Axis (red line) --><line x1="150" y1="50" x2="150" y2="150" stroke="red" stroke-width="1" transform="rotate(-23.5 150 100)"/><text x="145" y="45" fill="white" font-size="10" transform="rotate(-23.5 150 100)">N</text><text x="145" y="155" fill="white" font-size="10" transform="rotate(-23.5 150 100)">S</text><text x="135" y="60" fill="white" font-size="10" transform="rotate(-23.5 150 100)">Ось</text><!-- Celestial Equator (white dashed line) --><line x1="90" y1="100" x2="210" y2="100" stroke="white" stroke-dasharray="3 2" transform="rotate(-23.5 150 100)"/><text x="95" y="115" fill="white" font-size="10" transform="rotate(-23.5 150 100)">Небесный экватор</text><!-- Implied Ecliptic Plane (horizontal reference line) --><line x1="20" y1="100" x2="280" y2="100" stroke="lightgray" stroke-dasharray="1 3"/><!-- Earth's Tilt Angle (23.5°) reference lines and text --><path d="M220 100 L210 100 A10 10 0 0 1 207 108 L220 108" fill="none" stroke="white" stroke-width="1"/><line x1="210" y1="100" x2="210" y2="130" stroke="white"/><text x="215" y="125" fill="white" font-size="10">23.5°</text><!-- Moon's Orbit (white dashed ellipse, tilted 5 degrees relative to ecliptic) --><ellipse cx="150" cy="100" rx="90" ry="45" fill="none" stroke="white" stroke-dasharray="2 2" transform="rotate(5 150 100)"/><!-- Moon (small lightgray circle) --><circle cx="60" cy="100" r="7" fill="lightgray" stroke="white" transform="rotate(5 150 100)"/><text x="40" y="95" fill="white" font-size="10" transform="rotate(5 150 100)">Луна</text><!-- Moon's Orbit Direction Arrow (red arrow on ellipse) --><path d="M230 100 L225 95 M230 100 L225 105" stroke="red" fill="none" transform="rotate(5 150 100)"/><!-- Earth's Rotation Arrow (blue curl near S pole) --><path d="M145 140 A 10 10 0 1 0 155 140" fill="none" stroke="blue" stroke-width="1"/><path d="M155 140 L152 143 M155 140 L158 143" stroke="blue" fill="none"/><!-- Moon's Self-Rotation/Precession Arrow (blue curl near Moon) --><path d="M55 110 A 5 5 0 1 0 65 110" fill="none" stroke="blue" stroke-width="1" transform="rotate(5 150 100)"/><path d="M65 110 L62 113 M65 110 L68 113" stroke="blue" fill="none" transform="rotate(5 150 100)"/><!-- Angle 5° (Moon's orbit inclination to ecliptic, red lines and text) --><line x1="220" y1="100" x2="220" y2="90" stroke="red"/><line x1="220" y1="90" x2="200" y2="90" stroke="red"/><text x="225" y="85" fill="white" font-size="10">5°</text><!-- Angle 1.5° (near Moon, red lines and text) --><line x1="50" y1="110" x2="50" y2="120" stroke="red"/><line x1="50" y1="120" x2="70" y2="120" stroke="red"/><text x="40" y="125" fill="white" font-size="10">1.5°</text></svg></p><p><em>Вращение Луны вокруг Земли</em></p>" "img" => array:1 [ 0 => array:5 [ "name" => "216-1.jpg" "alt" => null "width" => "1573" "height" => 694 "path" => "/media/algebra_09/soltan-u19/0-1/216-1.webp?ts=1752834264" ] ] ] #original: array:7 [ "id" => 1276571 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1175} "task" => array:2 [ "refs" => "1107919" "type" => "task" ] "text" => "<p><strong>216.</strong> Известно, что скорость вращения Земли вокруг Солнца равна 40 247 км/ч, а скорость вращения Луны вокруг Земли - 8568 км/ч. Представьте числа, выражающие эти скорости, в виде суммы наименьшего количества степеней числа 2 с неотрицательными целыми показателями.</p><p><svg width="300" height="200" viewBox="0 0 300 200"><!-- Background --><rect x="0" y="0" width="300" height="200" fill="black"/><!-- Earth --><circle cx="150" cy="100" r="40" fill="#87CEEB" stroke="black" stroke-width="1"/><!-- Simplified landmasses --><path d="M140 90 Q145 80 150 90 T160 100 Q155 110 150 100 T140 90" fill="#32CD32"/><path d="M160 80 Q165 70 170 80 T180 90 Q175 100 170 90 T160 80" fill="#32CD32"/><path d="M130 110 Q135 120 140 110 T150 100 Q145 90 140 100 T130 110" fill="#32CD32"/><!-- Earth's Axis (red line) --><line x1="150" y1="50" x2="150" y2="150" stroke="red" stroke-width="1" transform="rotate(-23.5 150 100)"/><text x="145" y="45" fill="white" font-size="10" transform="rotate(-23.5 150 100)">N</text><text x="145" y="155" fill="white" font-size="10" transform="rotate(-23.5 150 100)">S</text><text x="135" y="60" fill="white" font-size="10" transform="rotate(-23.5 150 100)">Ось</text><!-- Celestial Equator (white dashed line) --><line x1="90" y1="100" x2="210" y2="100" stroke="white" stroke-dasharray="3 2" transform="rotate(-23.5 150 100)"/><text x="95" y="115" fill="white" font-size="10" transform="rotate(-23.5 150 100)">Небесный экватор</text><!-- Implied Ecliptic Plane (horizontal reference line) --><line x1="20" y1="100" x2="280" y2="100" stroke="lightgray" stroke-dasharray="1 3"/><!-- Earth's Tilt Angle (23.5°) reference lines and text --><path d="M220 100 L210 100 A10 10 0 0 1 207 108 L220 108" fill="none" stroke="white" stroke-width="1"/><line x1="210" y1="100" x2="210" y2="130" stroke="white"/><text x="215" y="125" fill="white" font-size="10">23.5°</text><!-- Moon's Orbit (white dashed ellipse, tilted 5 degrees relative to ecliptic) --><ellipse cx="150" cy="100" rx="90" ry="45" fill="none" stroke="white" stroke-dasharray="2 2" transform="rotate(5 150 100)"/><!-- Moon (small lightgray circle) --><circle cx="60" cy="100" r="7" fill="lightgray" stroke="white" transform="rotate(5 150 100)"/><text x="40" y="95" fill="white" font-size="10" transform="rotate(5 150 100)">Луна</text><!-- Moon's Orbit Direction Arrow (red arrow on ellipse) --><path d="M230 100 L225 95 M230 100 L225 105" stroke="red" fill="none" transform="rotate(5 150 100)"/><!-- Earth's Rotation Arrow (blue curl near S pole) --><path d="M145 140 A 10 10 0 1 0 155 140" fill="none" stroke="blue" stroke-width="1"/><path d="M155 140 L152 143 M155 140 L158 143" stroke="blue" fill="none"/><!-- Moon's Self-Rotation/Precession Arrow (blue curl near Moon) --><path d="M55 110 A 5 5 0 1 0 65 110" fill="none" stroke="blue" stroke-width="1" transform="rotate(5 150 100)"/><path d="M65 110 L62 113 M65 110 L68 113" stroke="blue" fill="none" transform="rotate(5 150 100)"/><!-- Angle 5° (Moon's orbit inclination to ecliptic, red lines and text) --><line x1="220" y1="100" x2="220" y2="90" stroke="red"/><line x1="220" y1="90" x2="200" y2="90" stroke="red"/><text x="225" y="85" fill="white" font-size="10">5°</text><!-- Angle 1.5° (near Moon, red lines and text) --><line x1="50" y1="110" x2="50" y2="120" stroke="red"/><line x1="50" y1="120" x2="70" y2="120" stroke="red"/><text x="40" y="125" fill="white" font-size="10">1.5°</text></svg></p><p><em>Вращение Луны вокруг Земли</em></p>" "img" => array:1 [ 0 => array:5 [ "name" => "216-1.jpg" "alt" => null "width" => "1573" "height" => 694 "path" => "/media/algebra_09/soltan-u19/0-1/216-1.webp?ts=1752834264" ] ] ] #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 {#1173 #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" => 1277862 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1183 #items: array:1 [ 0 => App\Models\Edition {#1174 #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" => 4954 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_content_source" => null ] #original: array:21 [ "id" => 4954 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1180 …2} "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" => "1107919" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "216-1.jpg" "alt" => null "width" => "1413" "height" => 554 "path" => "/media/algebra_09/soltan-u19/1-1/216-1.webp?ts=1752830955" ] ] ] #original: array:6 [ "id" => 1277862 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1183} "task" => array:2 [ "refs" => "1107919" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "216-1.jpg" "alt" => null "width" => "1413" "height" => 554 "path" => "/media/algebra_09/soltan-u19/1-1/216-1.webp?ts=1752830955" ] ] ] #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\Element {#1181 #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" => 1553817 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1191 #items: array:1 [ 0 => App\Models\Edition {#1182 #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" => 5665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1185 …2} "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" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1187 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1188 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1185 …2} "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" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1187 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1188 …2} "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" => "1107919" "type" => "task" ] "text" => "<p><strong>Скорость вращения Земли вокруг Солнца</strong></p><p>Чтобы представить число 40 247 в виде суммы наименьшего количества степеней числа 2 с неотрицательными целыми показателями, нужно разложить это число по степеням двойки. Это эквивалентно переводу числа из десятичной системы счисления в двоичную. Мы будем последовательно находить наибольшую степень двойки, не превосходящую текущее число, и вычитать ее, пока не получим ноль.</p><p><strong>1.</strong> Наибольшая степень двойки, меньшая или равная 40 247, это $2^{15} = 32768$.<br>Остаток: $40247 - 32768 = 7479$.</p><p><strong>2.</strong> Для остатка 7479 наибольшая степень двойки — это $2^{12} = 4096$.<br>Остаток: $7479 - 4096 = 3383$.</p><p><strong>3.</strong> Для остатка 3383 наибольшая степень двойки — это $2^{11} = 2048$.<br>Остаток: $3383 - 2048 = 1335$.</p><p><strong>4.</strong> Для остатка 1335 наибольшая степень двойки — это $2^{10} = 1024$.<br>Остаток: $1335 - 1024 = 311$.</p><p><strong>5.</strong> Для остатка 311 наибольшая степень двойки — это $2^8 = 256$.<br>Остаток: $311 - 256 = 55$.</p><p><strong>6.</strong> Для остатка 55 наибольшая степень двойки — это $2^5 = 32$.<br>Остаток: $55 - 32 = 23$.</p><p><strong>7.</strong> Для остатка 23 наибольшая степень двойки — это $2^4 = 16$.<br>Остаток: $23 - 16 = 7$.</p><p><strong>8.</strong> Для остатка 7 наибольшая степень двойки — это $2^2 = 4$.<br>Остаток: $7 - 4 = 3$.</p><p><strong>9.</strong> Для остатка 3 наибольшая степень двойки — это $2^1 = 2$.<br>Остаток: $3 - 2 = 1$.</p><p><strong>10.</strong> Остаток 1 равен $2^0$.</p><p>Собрав все найденные степени двойки, получаем итоговую сумму.</p><p><strong>Ответ:</strong> $40247 = 2^{15} + 2^{12} + 2^{11} + 2^{10} + 2^8 + 2^5 + 2^4 + 2^2 + 2^1 + 2^0$</p><p><strong>Скорость вращения Луны вокруг Земли</strong></p><p>Аналогично представим число 8568 в виде суммы степеней двойки.</p><p><strong>1.</strong> Наибольшая степень двойки, меньшая или равная 8568, это $2^{13} = 8192$.<br>Остаток: $8568 - 8192 = 376$.</p><p><strong>2.</strong> Для остатка 376 наибольшая степень двойки — это $2^8 = 256$.<br>Остаток: $376 - 256 = 120$.</p><p><strong>3.</strong> Для остатка 120 наибольшая степень двойки — это $2^6 = 64$.<br>Остаток: $120 - 64 = 56$.</p><p><strong>4.</strong> Для остатка 56 наибольшая степень двойки — это $2^5 = 32$.<br>Остаток: $56 - 32 = 24$.</p><p><strong>5.</strong> Для остатка 24 наибольшая степень двойки — это $2^4 = 16$.<br>Остаток: $24 - 16 = 8$.</p><p><strong>6.</strong> Остаток 8 равен $2^3$.</p><p>Собрав все найденные степени двойки, получаем итоговую сумму.</p><p><strong>Ответ:</strong> $8568 = 2^{13} + 2^8 + 2^6 + 2^5 + 2^4 + 2^3$</p>" ] #original: array:6 [ "id" => 1553817 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1191} "task" => array:2 [ "refs" => "1107919" "type" => "task" ] "text" => "<p><strong>Скорость вращения Земли вокруг Солнца</strong></p><p>Чтобы представить число 40 247 в виде суммы наименьшего количества степеней числа 2 с неотрицательными целыми показателями, нужно разложить это число по степеням двойки. Это эквивалентно переводу числа из десятичной системы счисления в двоичную. Мы будем последовательно находить наибольшую степень двойки, не превосходящую текущее число, и вычитать ее, пока не получим ноль.</p><p><strong>1.</strong> Наибольшая степень двойки, меньшая или равная 40 247, это $2^{15} = 32768$.<br>Остаток: $40247 - 32768 = 7479$.</p><p><strong>2.</strong> Для остатка 7479 наибольшая степень двойки — это $2^{12} = 4096$.<br>Остаток: $7479 - 4096 = 3383$.</p><p><strong>3.</strong> Для остатка 3383 наибольшая степень двойки — это $2^{11} = 2048$.<br>Остаток: $3383 - 2048 = 1335$.</p><p><strong>4.</strong> Для остатка 1335 наибольшая степень двойки — это $2^{10} = 1024$.<br>Остаток: $1335 - 1024 = 311$.</p><p><strong>5.</strong> Для остатка 311 наибольшая степень двойки — это $2^8 = 256$.<br>Остаток: $311 - 256 = 55$.</p><p><strong>6.</strong> Для остатка 55 наибольшая степень двойки — это $2^5 = 32$.<br>Остаток: $55 - 32 = 23$.</p><p><strong>7.</strong> Для остатка 23 наибольшая степень двойки — это $2^4 = 16$.<br>Остаток: $23 - 16 = 7$.</p><p><strong>8.</strong> Для остатка 7 наибольшая степень двойки — это $2^2 = 4$.<br>Остаток: $7 - 4 = 3$.</p><p><strong>9.</strong> Для остатка 3 наибольшая степень двойки — это $2^1 = 2$.<br>Остаток: $3 - 2 = 1$.</p><p><strong>10.</strong> Остаток 1 равен $2^0$.</p><p>Собрав все найденные степени двойки, получаем итоговую сумму.</p><p><strong>Ответ:</strong> $40247 = 2^{15} + 2^{12} + 2^{11} + 2^{10} + 2^8 + 2^5 + 2^4 + 2^2 + 2^1 + 2^0$</p><p><strong>Скорость вращения Луны вокруг Земли</strong></p><p>Аналогично представим число 8568 в виде суммы степеней двойки.</p><p><strong>1.</strong> Наибольшая степень двойки, меньшая или равная 8568, это $2^{13} = 8192$.<br>Остаток: $8568 - 8192 = 376$.</p><p><strong>2.</strong> Для остатка 376 наибольшая степень двойки — это $2^8 = 256$.<br>Остаток: $376 - 256 = 120$.</p><p><strong>3.</strong> Для остатка 120 наибольшая степень двойки — это $2^6 = 64$.<br>Остаток: $120 - 64 = 56$.</p><p><strong>4.</strong> Для остатка 56 наибольшая степень двойки — это $2^5 = 32$.<br>Остаток: $56 - 32 = 24$.</p><p><strong>5.</strong> Для остатка 24 наибольшая степень двойки — это $2^4 = 16$.<br>Остаток: $24 - 16 = 8$.</p><p><strong>6.</strong> Остаток 8 равен $2^3$.</p><p>Собрав все найденные степени двойки, получаем итоговую сумму.</p><p><strong>Ответ:</strong> $8568 = 2^{13} + 2^8 + 2^6 + 2^5 + 2^4 + 2^3$</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" => "1107920" "type" => "task" ] "previous" => array:2 [ "refs" => "1107918" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1195 #items: array:1 [ 0 => App\Models\Book {#1163 #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" => 4298 "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 {#1148 #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:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #original: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #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 {#1149 #items: array:1 [ 0 => App\Models\Term {#1154 #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" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #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 {#1153 #items: array:1 [ 0 => App\Models\Term {#1152 #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" => 7002 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кокшетау" "field_cases" => array:6 [ …6] "field_translit" => "Kokshetau" ] #original: array:6 [ "id" => 7002 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кокшетау" "field_cases" => array:6 [ …6] "field_translit" => "Kokshetau" ] #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 {#1150 #items: array:3 [ 0 => App\Models\Term {#1151 #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" => 7003 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Генадий" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 7003 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Генадий" "field_patronymic" => "Николаевич" "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 => "*" ] } 1 => App\Models\Term {#1140 #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" => 7004 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алла" "field_patronymic" => "Евгеньевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 7004 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алла" "field_patronymic" => "Евгеньевна" "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 => "*" ] } 2 => 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:12 [ "id" => 7005 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумадилова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Аманбала" "field_patronymic" => "Жумадиловна" "field_surname_rp" => null ] #original: array:12 [ "id" => 7005 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумадилова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Аманбала" "field_patronymic" => "Жумадиловна" "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 {#1139 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Term {#1145 #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 [ …6] "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 [ …6] "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 {#1144 #items: array:1 [ 0 => App\Models\Term {#1142 #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" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ …6] "field_translit" => "kazakhstan" ] #original: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ …6] "field_translit" => "kazakhstan" ] #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 {#1143 #items: array:1 [ 0 => App\Models\Term {#1157 #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" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ …6] "field_translit" => "almaty" ] #original: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ …6] "field_translit" => "almaty" ] #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 {#1155 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1162 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1164 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1160 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1158 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1161 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1159 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1189 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1190 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1192 #items: [] #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" => 380 "subject" => 542 "class_subject" => 386 ] ] #original: array:50 [ "id" => 4298 "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 {#1148} "field_class" => Illuminate\Database\Eloquent\Collection {#1149} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1153} "field_author" => Illuminate\Database\Eloquent\Collection {#1150} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1139} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1146} "field_country" => Illuminate\Database\Eloquent\Collection {#1144} "field_city" => Illuminate\Database\Eloquent\Collection {#1143} "field_series" => Illuminate\Database\Eloquent\Collection {#1155} "field_umk" => Illuminate\Database\Eloquent\Collection {#1162} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1164} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1160} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1158} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1161} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1159} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1189} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1190} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1192} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1200 #items: array:1 [ 0 => App\Models\BookPage {#1199 #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" => 1097810 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/page-68" "field_display_title" => "68" "field_folder" => "folder1" "field_image_name" => "68" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1201 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1202 #items: array:1 [ 0 => App\Models\Book {#1163} ] #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 {#1203 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1213 #items: array:1 [ 0 => App\Models\Element {#1212 #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" => 1260961 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1260961 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #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" => "1097811" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1097809" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1370 #items: array:8 [ 0 => App\Models\Task {#1384 #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" => 1107912 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-209" "field_display_title" => "209" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1385 …2} "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 {#1386 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1387 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1388 …2} "content" => Illuminate\Database\Eloquent\Collection {#1398 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1405 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1107912 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-209" "field_display_title" => "209" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1385 …2} "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 {#1386 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1387 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1388 …2} "content" => Illuminate\Database\Eloquent\Collection {#1398 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1405 …2} "page" => array:2 [ …2] ] #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 {#1389 #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" => 1107913 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-210" "field_display_title" => "210" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1391 …2} "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 {#1390 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1396 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1395 …2} "content" => Illuminate\Database\Eloquent\Collection {#1403 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1419 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1107913 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-210" "field_display_title" => "210" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1391 …2} "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 {#1390 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1396 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1395 …2} "content" => Illuminate\Database\Eloquent\Collection {#1403 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1419 …2} "page" => array:2 [ …2] ] #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 {#1394 #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" => 1107914 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-211" "field_display_title" => "211" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1393 …2} "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 {#1392 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1402 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1406 …2} "content" => Illuminate\Database\Eloquent\Collection {#1417 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1433 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1107914 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-211" "field_display_title" => "211" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1393 …2} "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 {#1392 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1402 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1406 …2} "content" => Illuminate\Database\Eloquent\Collection {#1417 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1433 …2} "page" => array:2 [ …2] ] #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 {#1404 #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" => 1107915 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-212" "field_display_title" => "212" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1397 …2} "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 {#1399 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1416 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1420 …2} "content" => Illuminate\Database\Eloquent\Collection {#1431 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1447 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1107915 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-212" "field_display_title" => "212" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1397 …2} "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 {#1399 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1416 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1420 …2} "content" => Illuminate\Database\Eloquent\Collection {#1431 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1447 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true 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№216 (с. 68)
Условие. №216 (с. 68)
скриншот условия
216. Известно, что скорость вращения Земли вокруг Солнца равна 40 247 км/ч, а скорость вращения Луны вокруг Земли - 8568 км/ч. Представьте числа, выражающие эти скорости, в виде суммы наименьшего количества степеней числа 2 с неотрицательными целыми показателями.
Вращение Луны вокруг Земли
Решение. №216 (с. 68)
Решение 2 (rus). №216 (с. 68)
Скорость вращения Земли вокруг Солнца
Чтобы представить число 40 247 в виде суммы наименьшего количества степеней числа 2 с неотрицательными целыми показателями, нужно разложить это число по степеням двойки. Это эквивалентно переводу числа из десятичной системы счисления в двоичную. Мы будем последовательно находить наибольшую степень двойки, не превосходящую текущее число, и вычитать ее, пока не получим ноль.
1. Наибольшая степень двойки, меньшая или равная 40 247, это $2^{15} = 32768$.
Остаток: $40247 - 32768 = 7479$.
2. Для остатка 7479 наибольшая степень двойки — это $2^{12} = 4096$.
Остаток: $7479 - 4096 = 3383$.
3. Для остатка 3383 наибольшая степень двойки — это $2^{11} = 2048$.
Остаток: $3383 - 2048 = 1335$.
4. Для остатка 1335 наибольшая степень двойки — это $2^{10} = 1024$.
Остаток: $1335 - 1024 = 311$.
5. Для остатка 311 наибольшая степень двойки — это $2^8 = 256$.
Остаток: $311 - 256 = 55$.
6. Для остатка 55 наибольшая степень двойки — это $2^5 = 32$.
Остаток: $55 - 32 = 23$.
7. Для остатка 23 наибольшая степень двойки — это $2^4 = 16$.
Остаток: $23 - 16 = 7$.
8. Для остатка 7 наибольшая степень двойки — это $2^2 = 4$.
Остаток: $7 - 4 = 3$.
9. Для остатка 3 наибольшая степень двойки — это $2^1 = 2$.
Остаток: $3 - 2 = 1$.
10. Остаток 1 равен $2^0$.
Собрав все найденные степени двойки, получаем итоговую сумму.
Ответ: $40247 = 2^{15} + 2^{12} + 2^{11} + 2^{10} + 2^8 + 2^5 + 2^4 + 2^2 + 2^1 + 2^0$
Скорость вращения Луны вокруг Земли
Аналогично представим число 8568 в виде суммы степеней двойки.
1. Наибольшая степень двойки, меньшая или равная 8568, это $2^{13} = 8192$.
Остаток: $8568 - 8192 = 376$.
2. Для остатка 376 наибольшая степень двойки — это $2^8 = 256$.
Остаток: $376 - 256 = 120$.
3. Для остатка 120 наибольшая степень двойки — это $2^6 = 64$.
Остаток: $120 - 64 = 56$.
4. Для остатка 56 наибольшая степень двойки — это $2^5 = 32$.
Остаток: $56 - 32 = 24$.
5. Для остатка 24 наибольшая степень двойки — это $2^4 = 16$.
Остаток: $24 - 16 = 8$.
6. Остаток 8 равен $2^3$.
Собрав все найденные степени двойки, получаем итоговую сумму.
Ответ: $8568 = 2^{13} + 2^8 + 2^6 + 2^5 + 2^4 + 2^3$
Другие задания:
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