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Занимательные задачи 2, страница 247 - 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
V. Элементы теории вероятностей. 34. Упражнения на повторение раздела «Элементы теории вероятностей» - страница 247.
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=> "девятом" ] "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 {#1036 #items: array:1 [ 0 => App\Models\Term {#1037 #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 [ "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" => "Kokshetau" ] #original: array:6 [ "id" => 7002 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кокшетау" "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" => "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 {#1038 #items: array:3 [ 0 => App\Models\Term {#1039 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] 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Illuminate\Database\Eloquent\Collection {#1055} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1056} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1057} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1058} "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 } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107673 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "V. Элементы теории вероятностей" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1023} "field_page_start" => "229" "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 {#333} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1059} ] #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 {#1060 #items: array:2 [ 0 => App\Models\Branch {#342} 1 => App\Models\Branch {#1061 #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" => 1107677 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "34. Упражнения на повторение раздела «Элементы теории вероятностей»" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "245" "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 {#1063 #items: array:1 [ 0 => App\Models\Book {#1033} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Branch {#1065 #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" => 1107673 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "V. Элементы теории вероятностей" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "229" "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 {#1067 #items: array:1 [ 0 => App\Models\Book {#1068 #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 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1096 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107673 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "V. Элементы теории вероятностей" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1066} "field_page_start" => "229" "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 {#1067} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1096} ] #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" => 1107677 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "34. Упражнения на повторение раздела «Элементы теории вероятностей»" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_page_start" => "245" "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 {#1063} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1064} ] #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 {#1097 #items: array:3 [ 0 => App\Models\Element {#1098 #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" => 1277799 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1099 #items: array:1 [ 0 => App\Models\Edition {#1100 #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 {#1101 #items: array:1 [ 0 => App\Models\Term {#1102 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #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" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1103 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1104 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1105 #items: [] #escapeWhenCastingToString: false } "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 {#1101} "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 {#1103} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1104} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1105} "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" => "1108646" "type" => "task" ] "text" => "<p><strong>2)</strong> Имеется 8 ключей от 8 дверей, к каждой из которых подходит только один ключ. Какое наименьшее количество попыток надо сде-лать, чтобы открыть все эти двери имеющимися ключами наверняка, если неизвестно, к какой двери какой ключ подходит?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1611" "height" => 351 "path" => "/media/algebra_09/soltan-u19/0-zad247/2-1.webp?ts=1752835213" ] ] ] #original: array:7 [ "id" => 1277799 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1099} "task" => array:2 [ "refs" => "1108646" "type" => "task" ] "text" => "<p><strong>2)</strong> Имеется 8 ключей от 8 дверей, к каждой из которых подходит только один ключ. Какое наименьшее количество попыток надо сде-лать, чтобы открыть все эти двери имеющимися ключами наверняка, если неизвестно, к какой двери какой ключ подходит?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1611" "height" => 351 "path" => "/media/algebra_09/soltan-u19/0-zad247/2-1.webp?ts=1752835213" ] ] ] #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 {#1106 #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" => 1278932 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1107 #items: array:1 [ 0 => App\Models\Edition {#1108 #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 {#1109 #items: array:1 [ 0 => App\Models\Term {#1110 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "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 {#1111 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1112 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1113 #items: [] #escapeWhenCastingToString: false } "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 {#1109} "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 {#1111} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1112} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1113} "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" => "1108646" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "885" "height" => 666 "path" => "/media/algebra_09/soltan-u19/1-zad247/2-1.webp?ts=1752832086" ] ] ] #original: array:6 [ "id" => 1278932 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1107} "task" => array:2 [ "refs" => "1108646" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "885" "height" => 666 "path" => "/media/algebra_09/soltan-u19/1-zad247/2-1.webp?ts=1752832086" ] ] ] #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 {#1114 #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" => 1554881 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1115 #items: array:1 [ 0 => App\Models\Edition {#1116 #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 {#1117 #items: array:1 [ 0 => App\Models\Term {#1118 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #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" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1119 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1120 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1121 #items: [] #escapeWhenCastingToString: false } "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 {#1117} "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 {#1119} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1120} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1121} "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" => "1108646" "type" => "task" ] "text" => "<p><strong>1)</strong> Для решения этой задачи нужно определить положение часовой и минутной стрелок в указанный момент времени.</p><p>Изначальное время — 3:00. Нам нужно найти угол между стрелками через сутки и полчаса.</p><p>Через сутки (24 часа) положение стрелок на стандартных механических часах будет точно таким же, как и вначале, поскольку полный цикл для часовой стрелки составляет 12 часов. Таким образом, нам достаточно определить положение стрелок через 30 минут после 3:00, то есть в 3:30.</p><p>Рассчитаем угловые скорости стрелок. Циферблат представляет собой окружность в $360^\circ$.</p><ul><li><p><strong>Минутная стрелка</strong> проходит полный круг ($360^\circ$) за 60 минут. Ее скорость составляет $360^\circ / 60 \text{ мин} = 6^\circ$ в минуту.</p></li><li><p><strong>Часовая стрелка</strong> проходит полный круг ($360^\circ$) за 12 часов (720 минут). Ее скорость составляет $360^\circ / 720 \text{ мин} = 0.5^\circ$ в минуту.</p></li></ul><p>Теперь найдем положение каждой стрелки в 3:30, отсчитывая угол от отметки "12" по часовой стрелке.</p><p><strong>Положение минутной стрелки в 3:30:</strong></p><p>Минутная стрелка будет указывать на 30 минут. Ее угол составит:$30 \text{ мин} \times 6^\circ/\text{мин} = 180^\circ$.</p><p><strong>Положение часовой стрелки в 3:30:</strong></p><p>В 3:00 часовая стрелка находилась на отметке "3". Угол от "12" составляет $3 \times (360^\circ / 12) = 3 \times 30^\circ = 90^\circ$.За последующие 30 минут часовая стрелка сместится еще на некоторый угол. Это смещение равно:$30 \text{ мин} \times 0.5^\circ/\text{мин} = 15^\circ$.Таким образом, итоговое положение часовой стрелки будет:$90^\circ + 15^\circ = 105^\circ$.</p><p><strong>Угол между стрелками:</strong></p><p>Чтобы найти угол между стрелками, нужно найти разницу между их угловыми положениями:$\text{Угол} = |180^\circ - 105^\circ| = 75^\circ$.</p><p><strong>Ответ:</strong> $75^\circ$.</p>" ] #original: array:6 [ "id" => 1554881 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1115} "task" => array:2 [ "refs" => "1108646" "type" => "task" ] "text" => "<p><strong>1)</strong> Для решения этой задачи нужно определить положение часовой и минутной стрелок в указанный момент времени.</p><p>Изначальное время — 3:00. Нам нужно найти угол между стрелками через сутки и полчаса.</p><p>Через сутки (24 часа) положение стрелок на стандартных механических часах будет точно таким же, как и вначале, поскольку полный цикл для часовой стрелки составляет 12 часов. Таким образом, нам достаточно определить положение стрелок через 30 минут после 3:00, то есть в 3:30.</p><p>Рассчитаем угловые скорости стрелок. Циферблат представляет собой окружность в $360^\circ$.</p><ul><li><p><strong>Минутная стрелка</strong> проходит полный круг ($360^\circ$) за 60 минут. Ее скорость составляет $360^\circ / 60 \text{ мин} = 6^\circ$ в минуту.</p></li><li><p><strong>Часовая стрелка</strong> проходит полный круг ($360^\circ$) за 12 часов (720 минут). Ее скорость составляет $360^\circ / 720 \text{ мин} = 0.5^\circ$ в минуту.</p></li></ul><p>Теперь найдем положение каждой стрелки в 3:30, отсчитывая угол от отметки "12" по часовой стрелке.</p><p><strong>Положение минутной стрелки в 3:30:</strong></p><p>Минутная стрелка будет указывать на 30 минут. Ее угол составит:$30 \text{ мин} \times 6^\circ/\text{мин} = 180^\circ$.</p><p><strong>Положение часовой стрелки в 3:30:</strong></p><p>В 3:00 часовая стрелка находилась на отметке "3". Угол от "12" составляет $3 \times (360^\circ / 12) = 3 \times 30^\circ = 90^\circ$.За последующие 30 минут часовая стрелка сместится еще на некоторый угол. Это смещение равно:$30 \text{ мин} \times 0.5^\circ/\text{мин} = 15^\circ$.Таким образом, итоговое положение часовой стрелки будет:$90^\circ + 15^\circ = 105^\circ$.</p><p><strong>Угол между стрелками:</strong></p><p>Чтобы найти угол между стрелками, нужно найти разницу между их угловыми положениями:$\text{Угол} = |180^\circ - 105^\circ| = 75^\circ$.</p><p><strong>Ответ:</strong> $75^\circ$.</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" => "1108647" "type" => "task" ] "previous" => array:2 [ "refs" => "1108645" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1122 #items: array:1 [ 0 => App\Models\Book {#1033} ] #escapeWhenCastingToString: false } "page" => 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Занимательные задачи 2 (с. 247)
Условие. Занимательные задачи 2 (с. 247)
скриншот условия
2) Имеется 8 ключей от 8 дверей, к каждой из которых подходит только один ключ. Какое наименьшее количество попыток надо сде-лать, чтобы открыть все эти двери имеющимися ключами наверняка, если неизвестно, к какой двери какой ключ подходит?
Решение. Занимательные задачи 2 (с. 247)
Решение 2 (rus). Занимательные задачи 2 (с. 247)
1) Для решения этой задачи нужно определить положение часовой и минутной стрелок в указанный момент времени.
Изначальное время — 3:00. Нам нужно найти угол между стрелками через сутки и полчаса.
Через сутки (24 часа) положение стрелок на стандартных механических часах будет точно таким же, как и вначале, поскольку полный цикл для часовой стрелки составляет 12 часов. Таким образом, нам достаточно определить положение стрелок через 30 минут после 3:00, то есть в 3:30.
Рассчитаем угловые скорости стрелок. Циферблат представляет собой окружность в $360^\circ$.
Минутная стрелка проходит полный круг ($360^\circ$) за 60 минут. Ее скорость составляет $360^\circ / 60 \text{ мин} = 6^\circ$ в минуту.
Часовая стрелка проходит полный круг ($360^\circ$) за 12 часов (720 минут). Ее скорость составляет $360^\circ / 720 \text{ мин} = 0.5^\circ$ в минуту.
Теперь найдем положение каждой стрелки в 3:30, отсчитывая угол от отметки "12" по часовой стрелке.
Положение минутной стрелки в 3:30:
Минутная стрелка будет указывать на 30 минут. Ее угол составит:$30 \text{ мин} \times 6^\circ/\text{мин} = 180^\circ$.
Положение часовой стрелки в 3:30:
В 3:00 часовая стрелка находилась на отметке "3". Угол от "12" составляет $3 \times (360^\circ / 12) = 3 \times 30^\circ = 90^\circ$.За последующие 30 минут часовая стрелка сместится еще на некоторый угол. Это смещение равно:$30 \text{ мин} \times 0.5^\circ/\text{мин} = 15^\circ$.Таким образом, итоговое положение часовой стрелки будет:$90^\circ + 15^\circ = 105^\circ$.
Угол между стрелками:
Чтобы найти угол между стрелками, нужно найти разницу между их угловыми положениями:$\text{Угол} = |180^\circ - 105^\circ| = 75^\circ$.
Ответ: $75^\circ$.
Другие задания:
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