Номер 8, страница 28, часть 2 - гдз по физике 9 класс учебник Белага, Воронцова

Авторы: Белага В. В., Воронцова Н. И., Ломаченков И. А., Панебратцев Ю. А.

Тип: Учебник

Издательство: Просвещение

Год издания: 2024 - 2026

Уровень обучения: углублённый

Часть: 2

Цвет обложки: голубой

ISBN: 978-5-09-121759-9

Часть 2. Глава 7. Звук. Параграф 68. Решение задач. Задачи для самостоятельного решения - номер 8, страница 28.

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" => 1506624
    "created_at" => "2026-04-10 13:58:26"
    "updated_at" => null
    "field_page_start" => "28"
    "field_page_end" => null
    "field_url" => "/9-klass/fizika/belaga-uchebnik/68zadach-8"
    "field_display_title" => "8"
    "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: []
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          #attributeCastCache: []
          #dateFormat: null
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          #dispatchesEvents: []
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          #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 {#1046
      #items: array:1 [
        0 => App\Models\Branch {#1045
          #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" => 1505926
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => null
            "field_branch_order" => "2"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050
              #items: array:1 [
                0 => App\Models\Term {#1047
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
                    "id" => 31
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Часть"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => "1"
                    "field_short_name" => "ч."
                  ]
                  #original: array:7 [
                    "id" => 31
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Часть"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => "1"
                    "field_short_name" => "ч."
                  ]
                  #changes: []
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                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
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                    0 => "*"
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              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "6"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
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            "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 {#1084
              #items: array:1 [
                0 => App\Models\Book {#1049
                  #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" => 1652
                    "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 {#1051
                      #items: array:1 [
                        0 => App\Models\Term {#1048
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6493
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Физика"
                            "field_abbreviated_name" => null
                            "field_cases" => array:6 [ …6]
                            "field_foreign_lang_name" => null
                            "field_short_name" => null
                            "field_subject_type" => "technical_subject"
                            "field_translit" => "fizika"
                          ]
                          #original: array:10 [
                            "id" => 6493
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Физика"
                            "field_abbreviated_name" => null
                            "field_cases" => array:6 [ …6]
                            "field_foreign_lang_name" => null
                            "field_short_name" => null
                            "field_subject_type" => "technical_subject"
                            "field_translit" => "fizika"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1052
                      #items: array:1 [
                        0 => App\Models\Term {#1053
                          #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: []
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                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054
                      #items: array:1 [
                        0 => App\Models\Term {#1055
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
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                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 5153
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Просвещение"
                            "field_cases" => null
                            "field_translit" => "prosveschenie"
                          ]
                          #original: array:6 [
                            "id" => 5153
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Просвещение"
                            "field_cases" => null
                            "field_translit" => "prosveschenie"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1056
                      #items: array:4 [
                        0 => App\Models\Term {#1057
                          #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" => 3824
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Белага"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Виктория"
                            "field_patronymic" => "Владимировна"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 3824
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Белага"
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                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Виктория"
                            "field_patronymic" => "Владимировна"
                            "field_surname_rp" => null
                          ]
                          #changes: []
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                          #dateFormat: null
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                          #hidden: []
                          #visible: []
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                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                        1 => App\Models\Term {#1058
                          #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" => 4049
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Воронцова"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Наталия"
                            "field_patronymic" => "Игоревна"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 4049
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Воронцова"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Наталия"
                            "field_patronymic" => "Игоревна"
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
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                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                        2 => App\Models\Term {#1059
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
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                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 5014
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Ломаченков"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Иван"
                            "field_patronymic" => "Алексеевич"
                            "field_surname_rp" => null
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                          #original: array:12 [
                            "id" => 5014
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Ломаченков"
                            "field_bio" => null
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                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Иван"
                            "field_patronymic" => "Алексеевич"
                            "field_surname_rp" => null
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                          #changes: []
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                            0 => "*"
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                        }
                        3 => App\Models\Term {#1060
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
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                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 5412
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Панебратцев"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Юрий"
                            "field_patronymic" => "Анатольевич"
                            "field_surname_rp" => "Панебратцева"
                          ]
                          #original: array:12 [
                            "id" => 5412
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
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                            "field_foreign_lang_patronymic" => null
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                            "field_name" => "Юрий"
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                            "field_surname_rp" => "Панебратцева"
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                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1061
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062
                      #items: array:1 [
                        0 => App\Models\Term {#1063
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
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                          #withCount: []
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                          #attributes: array:10 [
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                            "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
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                          ]
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                            "id" => 6671
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
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                            "field_plural_form" => null
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                    "field_country" => Illuminate\Database\Eloquent\Collection {#1064
                      #items: array:1 [
                        0 => App\Models\Term {#1065
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
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                            "created_at" => "2026-04-10 13:58:26"
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                            "name" => "Россия"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "rossiya"
                          ]
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                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Россия"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "rossiya"
                          ]
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                      ]
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                    }
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1066
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                        0 => App\Models\Term {#1067
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
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                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "moskva"
                          ]
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                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "moskva"
                          ]
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                          ]
                        }
                      ]
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                    }
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1068
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                      #escapeWhenCastingToString: false
                    }
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1069
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070
                      #items: array:1 [
                        0 => App\Models\Term {#1071
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
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                          +exists: true
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                          #attributes: array:6 [
                            "id" => 39
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "углублённый"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "uglublennyy"
                          ]
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                            "id" => 39
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "углублённый"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "uglublennyy"
                          ]
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                          #dateFormat: null
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                          #hidden: []
                          #visible: []
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                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1072
                      #items: array:1 [
                        0 => App\Models\Term {#1073
                          #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" => 25
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "ФГОС (новый)"
                            "field_cases" => array:6 [ …6]
                            "field_color" => "красный"
                            "field_end_year" => "2027"
                            "field_start_year" => "2023"
                            "field_translit" => "fgos"
                            "field_type" => "новый"
                          ]
                          #original: array:10 [
                            "id" => 25
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "ФГОС (новый)"
                            "field_cases" => array:6 [ …6]
                            "field_color" => "красный"
                            "field_end_year" => "2027"
                            "field_start_year" => "2023"
                            "field_translit" => "fgos"
                            "field_type" => "новый"
                          ]
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                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
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                          #relations: []
                          #touches: []
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                          #visible: []
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                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publication_number" => "2"
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1074
                      #items: array:1 [
                        0 => App\Models\Term {#1075
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 33
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "стереотипное"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "stereotipnoe"
                          ]
                          #original: array:6 [
                            "id" => 33
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "стереотипное"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "stereotipnoe"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1076
                      #items: array:1 [
                        0 => App\Models\Term {#1060}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2024"
                    "field_publication_year_until" => null
                    "field_part" => "1, 2"
                    "field_part_writing" => "Часть"
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное издание"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "919"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_09/belaga-u/"
                    "field_isbn" => "978-5-09-121759-9"
                    "field_cover" => array:2 [
                      0 => "/media/fizika_09/belaga-u/covers/cover1.webp?ts=1761256721"
                      1 => "/media/fizika_09/belaga-u/covers/cover2.webp?ts=1761256721"
                    ]
                    "field_cover_alts" => array:2 [
                      0 => ""
                      1 => ""
                    ]
                    "field_covers" => array:2 [
                      0 => array:4 [
                        "path" => "/media/fizika_09/belaga-u/covers/cover1.webp?ts=1761256721"
                        "alt" => ""
                        "width" => "2322"
                        "height" => "3039"
                      ]
                      1 => array:4 [
                        "path" => "/media/fizika_09/belaga-u/covers/cover2.webp?ts=1761256721"
                        "alt" => ""
                        "width" => "2308"
                        "height" => "3035"
                      ]
                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1077
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1078
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1079
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_url" => "/9-klass/fizika/belaga-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1080
                      #items: array:1 [
                        0 => App\Models\Term {#1081
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
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                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 52
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "голубой"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "goluboy"
                          ]
                          #original: array:6 [
                            "id" => 52
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "голубой"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "goluboy"
                          ]
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                          #dateFormat: null
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                          #relations: []
                          #touches: []
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                          #hidden: []
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                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_metatags_title" => null
                    "field_metatags_description" => null
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                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 380
                      "subject" => 556
                      "class_subject" => 493
                    ]
                  ]
                  #original: array:50 [
                    "id" => 1652
                    "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 {#1051}
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1052}
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054}
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1056}
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1061}
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062}
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1064}
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1066}
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1068}
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1069}
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1072}
                    "field_publication_number" => "2"
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1074}
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1076}
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2024"
                    "field_publication_year_until" => null
                    "field_part" => "1, 2"
                    "field_part_writing" => "Часть"
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное издание"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "919"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_09/belaga-u/"
                    "field_isbn" => "978-5-09-121759-9"
                    "field_cover" => array:2 [
                      0 => "/media/fizika_09/belaga-u/covers/cover1.webp?ts=1761256721"
                      1 => "/media/fizika_09/belaga-u/covers/cover2.webp?ts=1761256721"
                    ]
                    "field_cover_alts" => array:2 [
                      0 => ""
                      1 => ""
                    ]
                    "field_covers" => array:2 [
                      0 => array:4 [
                        "path" => "/media/fizika_09/belaga-u/covers/cover1.webp?ts=1761256721"
                        "alt" => ""
                        "width" => "2322"
                        "height" => "3039"
                      ]
                      1 => array:4 [
                        "path" => "/media/fizika_09/belaga-u/covers/cover2.webp?ts=1761256721"
                        "alt" => ""
                        "width" => "2308"
                        "height" => "3035"
                      ]
                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1077}
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1078}
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1079}
                    "field_url" => "/9-klass/fizika/belaga-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1080}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
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                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 380
                      "subject" => 556
                      "class_subject" => 493
                    ]
                  ]
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                  #touches: []
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                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1082
              #items: []
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1505926
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => null
            "field_branch_order" => "2"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050}
            "field_page_start" => "6"
            "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 {#1084}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1082}
          ]
          #changes: []
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          #attributeCastCache: []
          #dateFormat: null
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          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1117
      #items: array:4 [
        0 => App\Models\Branch {#1127
          #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" => 1505926
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => null
            "field_branch_order" => "2"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1128
              #items: array:1 [
                0 => App\Models\Term {#1047}
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "6"
            "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 {#1129
              #items: array:1 [
                0 => App\Models\Book {#1049}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130
              #items: []
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1505926
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => null
            "field_branch_order" => "2"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1128}
            "field_page_start" => "6"
            "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 {#1129}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130}
          ]
          #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 {#1131
          #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" => 1505927
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Звук"
            "field_branch_order" => "7"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135
              #items: array:1 [
                0 => App\Models\Term {#1132
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #original: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #changes: []
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                  #attributeCastCache: []
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                  #touches: []
                  +timestamps: true
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                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "6"
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            "field_h1" => null
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            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1134
              #items: array:1 [
                0 => App\Models\Book {#1049}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133
              #items: array:1 [
                0 => App\Models\Branch {#1045}
              ]
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            }
          ]
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            "id" => 1505927
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            "field_display_title" => "Звук"
            "field_branch_order" => "7"
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            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135}
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            0 => "*"
          ]
        }
        2 => App\Models\Branch {#1136
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
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          #attributes: array:24 [
            "id" => 1505946
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
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              #items: array:1 [
                0 => App\Models\Term {#1137
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
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                  #withCount: []
                  +preventsLazyLoading: false
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                  #attributes: array:7 [
                    "id" => 32
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Параграф"
                    "field_cases" => array:6 [ …6]
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                  ]
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                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Параграф"
                    "field_cases" => array:6 [ …6]
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                  ]
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                    0 => "*"
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                }
              ]
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              ]
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            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148
              #items: array:1 [
                0 => App\Models\Branch {#1147
                  #connection: "mysql"
                  #table: "branches"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
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                    "book" => Illuminate\Database\Eloquent\Collection {#1150 …2}
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                  ]
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                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1149 …2}
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                    0 => "*"
                  ]
                }
              ]
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            "field_display_title" => "Решение задач"
            "field_branch_order" => "68"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1140}
            "field_page_start" => "26"
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            "book" => Illuminate\Database\Eloquent\Collection {#1139}
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          ]
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            0 => "*"
          ]
        }
        3 => App\Models\Branch {#1141
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
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          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 1505947
            "created_at" => "2026-04-10 13:58:26"
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            "field_branch_order" => null
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            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1138
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "28"
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            "book" => Illuminate\Database\Eloquent\Collection {#1144
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                0 => App\Models\Book {#1049}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1157
              #items: array:1 [
                0 => App\Models\Branch {#1156
                  #connection: "mysql"
                  #table: "branches"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
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                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1158 …2}
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                    "book" => Illuminate\Database\Eloquent\Collection {#1159 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1160 …2}
                  ]
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                    "id" => 1505946
                    "created_at" => "2026-04-10 13:58:26"
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                    "field_display_title" => "Решение задач"
                    "field_branch_order" => "68"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1158 …2}
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                    "book" => Illuminate\Database\Eloquent\Collection {#1159 …2}
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                  ]
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                  ]
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              ]
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          #original: array:24 [
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            "field_branch_order" => null
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            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1138}
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            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "content" => Illuminate\Database\Eloquent\Collection {#1038
      #items: array:2 [
        0 => App\Models\Element {#1108
          #connection: "mysql"
          #table: "elements"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
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          #attributes: array:7 [
            "id" => 1803593
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1100
              #items: array:1 [
                0 => App\Models\Edition {#1092
                  #connection: "mysql"
                  #table: "editions"
                  #primaryKey: "id"
                  #keyType: "int"
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                  #attributes: array:21 [
                    "id" => 6617
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
                    "field_order" => "1"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1107 …2}
                    "field_content_type" => "free"
                    "field_content_mode" => "text, image"
                    "field_page_content_mode" => "image"
                    "field_content_text_checked" => "0"
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Автор"
                    "field_moderator" => "stas"
                    "field_edition_type" => "statement"
                    "field_root_dir" => "0-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1104 …2}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1105 …2}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1102 …2}
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                  ]
                  #original: array:21 [
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                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
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                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1107 …2}
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              ]
              #escapeWhenCastingToString: false
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            "task" => array:2 [
              "refs" => "1506624"
              "type" => "task"
            ]
            "text" => "<p><strong>8.</strong> Спасательный самолёт летит горизонтально с постоянной скоростью в поисках терпящей бедствие лодки. Когда самолёт находится прямо над лодкой, люди на лодке подают звуковой сигнал. К тому времени, когда звуковой датчик самолёта принимает звук сигнала, самолёт преодолел расстояние, равное половине его высоты над водоёмом. Определите скорость самолёта и его высоту, если известно, что звук достиг самолёта через 2 с с момента подачи сигнала. Скорость звука в воздухе примите равной 335 м/с.</p>"
            "img" => array:1 [
              0 => array:5 [
                "name" => "8-1.jpg"
                "alt" => null
                "width" => "1962"
                "height" => 506
                "path" => "/media/fizika_09/belaga-u/0-68zadach/8-1.webp?ts=1762277355"
              ]
            ]
          ]
          #original: array:7 [
            "id" => 1803593
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1100}
            "task" => array:2 [
              "refs" => "1506624"
              "type" => "task"
            ]
            "text" => "<p><strong>8.</strong> Спасательный самолёт летит горизонтально с постоянной скоростью в поисках терпящей бедствие лодки. Когда самолёт находится прямо над лодкой, люди на лодке подают звуковой сигнал. К тому времени, когда звуковой датчик самолёта принимает звук сигнала, самолёт преодолел расстояние, равное половине его высоты над водоёмом. Определите скорость самолёта и его высоту, если известно, что звук достиг самолёта через 2 с с момента подачи сигнала. Скорость звука в воздухе примите равной 335 м/с.</p>"
            "img" => array:1 [
              0 => array:5 [
                "name" => "8-1.jpg"
                "alt" => null
                "width" => "1962"
                "height" => 506
                "path" => "/media/fizika_09/belaga-u/0-68zadach/8-1.webp?ts=1762277355"
              ]
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            "text" => "<p><strong>Дано:</strong></p><p>Время распространения звука, $t = 2$ с</p><p>Скорость звука в воздухе, $v_з = 335$ м/с</p><p>Горизонтальное расстояние, пройденное самолетом, $s = h/2$, где $\text{h}$ - высота самолета</p><p>Все данные представлены в системе СИ.</p><p><strong>Найти:</strong></p><p>Скорость самолёта $v_c$ - ?</p><p>Высота самолёта $\text{h}$ - ?</p><p><strong>Решение:</strong></p><p>Когда самолёт находится прямо над лодкой, люди на лодке подают звуковой сигнал. Пока звуковой сигнал движется от лодки к самолёту, самолёт продолжает лететь горизонтально с постоянной скоростью $v_c$.</p><p>За время $\text{t}$, пока звук доходит до самолёта, самолёт пролетает горизонтальное расстояние $\text{s}$. Это расстояние можно выразить через скорость самолёта и время:</p><p>$s = v_c \cdot t$</p><p>За это же время $\text{t}$ звук, распространяясь со скоростью $v_з$, проходит расстояние $\text{d}$ от лодки до нового положения самолёта:</p><p>$d = v_з \cdot t$</p><p>Рассчитаем это расстояние:</p><p>$d = 335 \text{ м/с} \cdot 2 \text{ с} = 670 \text{ м}$</p><p>В момент приёма сигнала положение лодки, начальное положение самолёта (точка прямо над лодкой) и конечное положение самолёта образуют прямоугольный треугольник. Катетами этого треугольника являются высота полёта самолёта $\text{h}$ и горизонтальное расстояние $\text{s}$, которое он пролетел. Гипотенузой является расстояние $\text{d}$, которое преодолел звуковой сигнал.</p><p>Согласно теореме Пифагора:</p><p>$d^2 = h^2 + s^2$</p><p>Из условия задачи известно, что самолёт преодолел расстояние, равное половине его высоты над водоёмом: $s = \frac{h}{2}$.</p><p>Подставим это соотношение в уравнение теоремы Пифагора:</p><p>$d^2 = h^2 + (\frac{h}{2})^2 = h^2 + \frac{h^2}{4} = \frac{4h^2 + h^2}{4} = \frac{5h^2}{4}$</p><p>Теперь мы можем найти высоту $\text{h}$, используя вычисленное значение $\text{d}$:</p><p>$(670 \text{ м})^2 = \frac{5h^2}{4}$</p><p>$h^2 = \frac{4 \cdot (670 \text{ м})^2}{5}$</p><p>$h = \sqrt{\frac{4 \cdot 448900}{5}} = \sqrt{4 \cdot 89780} = \sqrt{359120} \approx 599.27 \text{ м}$</p><p>Округлим значение высоты до целого числа: $h \approx 599 \text{ м}$.</p><p>Теперь, зная высоту, мы можем найти горизонтальное расстояние $\text{s}$, пройденное самолётом:</p><p>$s = \frac{h}{2} = \frac{599.27 \text{ м}}{2} \approx 299.63 \text{ м}$</p><p>Наконец, определим скорость самолёта $v_c$:</p><p>$v_c = \frac{s}{t} = \frac{299.63 \text{ м}}{2 \text{ с}} \approx 149.82 \text{ м/с}$</p><p>Округлим значение скорости до целого числа: $v_c \approx 150 \text{ м/с}$.</p><p><strong>Ответ:</strong> скорость самолёта составляет приблизительно 150 м/с, а его высота — приблизительно 599 м.</p>"
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            "task" => array:2 [
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            "text" => "<p><strong>Дано:</strong></p><p>Время распространения звука, $t = 2$ с</p><p>Скорость звука в воздухе, $v_з = 335$ м/с</p><p>Горизонтальное расстояние, пройденное самолетом, $s = h/2$, где $\text{h}$ - высота самолета</p><p>Все данные представлены в системе СИ.</p><p><strong>Найти:</strong></p><p>Скорость самолёта $v_c$ - ?</p><p>Высота самолёта $\text{h}$ - ?</p><p><strong>Решение:</strong></p><p>Когда самолёт находится прямо над лодкой, люди на лодке подают звуковой сигнал. Пока звуковой сигнал движется от лодки к самолёту, самолёт продолжает лететь горизонтально с постоянной скоростью $v_c$.</p><p>За время $\text{t}$, пока звук доходит до самолёта, самолёт пролетает горизонтальное расстояние $\text{s}$. Это расстояние можно выразить через скорость самолёта и время:</p><p>$s = v_c \cdot t$</p><p>За это же время $\text{t}$ звук, распространяясь со скоростью $v_з$, проходит расстояние $\text{d}$ от лодки до нового положения самолёта:</p><p>$d = v_з \cdot t$</p><p>Рассчитаем это расстояние:</p><p>$d = 335 \text{ м/с} \cdot 2 \text{ с} = 670 \text{ м}$</p><p>В момент приёма сигнала положение лодки, начальное положение самолёта (точка прямо над лодкой) и конечное положение самолёта образуют прямоугольный треугольник. Катетами этого треугольника являются высота полёта самолёта $\text{h}$ и горизонтальное расстояние $\text{s}$, которое он пролетел. Гипотенузой является расстояние $\text{d}$, которое преодолел звуковой сигнал.</p><p>Согласно теореме Пифагора:</p><p>$d^2 = h^2 + s^2$</p><p>Из условия задачи известно, что самолёт преодолел расстояние, равное половине его высоты над водоёмом: $s = \frac{h}{2}$.</p><p>Подставим это соотношение в уравнение теоремы Пифагора:</p><p>$d^2 = h^2 + (\frac{h}{2})^2 = h^2 + \frac{h^2}{4} = \frac{4h^2 + h^2}{4} = \frac{5h^2}{4}$</p><p>Теперь мы можем найти высоту $\text{h}$, используя вычисленное значение $\text{d}$:</p><p>$(670 \text{ м})^2 = \frac{5h^2}{4}$</p><p>$h^2 = \frac{4 \cdot (670 \text{ м})^2}{5}$</p><p>$h = \sqrt{\frac{4 \cdot 448900}{5}} = \sqrt{4 \cdot 89780} = \sqrt{359120} \approx 599.27 \text{ м}$</p><p>Округлим значение высоты до целого числа: $h \approx 599 \text{ м}$.</p><p>Теперь, зная высоту, мы можем найти горизонтальное расстояние $\text{s}$, пройденное самолётом:</p><p>$s = \frac{h}{2} = \frac{599.27 \text{ м}}{2} \approx 299.63 \text{ м}$</p><p>Наконец, определим скорость самолёта $v_c$:</p><p>$v_c = \frac{s}{t} = \frac{299.63 \text{ м}}{2 \text{ с}} \approx 149.82 \text{ м/с}$</p><p>Округлим значение скорости до целого числа: $v_c \approx 150 \text{ м/с}$.</p><p><strong>Ответ:</strong> скорость самолёта составляет приблизительно 150 м/с, а его высота — приблизительно 599 м.</p>"
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№8 (с. 28)
Условие. №8 (с. 28)
скриншот условия
Физика, 9 класс Учебник, авторы: Белага Виктория Владимировна, Воронцова Наталия Игоревна, Ломаченков Иван Алексеевич, Панебратцев Юрий Анатольевич, издательство Просвещение, Москва, 2024, голубого цвета, Часть 2, страница 28, номер 8, Условие

8. Спасательный самолёт летит горизонтально с постоянной скоростью в поисках терпящей бедствие лодки. Когда самолёт находится прямо над лодкой, люди на лодке подают звуковой сигнал. К тому времени, когда звуковой датчик самолёта принимает звук сигнала, самолёт преодолел расстояние, равное половине его высоты над водоёмом. Определите скорость самолёта и его высоту, если известно, что звук достиг самолёта через 2 с с момента подачи сигнала. Скорость звука в воздухе примите равной 335 м/с.

Решение. №8 (с. 28)

Дано:

Время распространения звука, $t = 2$ с

Скорость звука в воздухе, $v_з = 335$ м/с

Горизонтальное расстояние, пройденное самолетом, $s = h/2$, где $\text{h}$ - высота самолета

Все данные представлены в системе СИ.

Найти:

Скорость самолёта $v_c$ - ?

Высота самолёта $\text{h}$ - ?

Решение:

Когда самолёт находится прямо над лодкой, люди на лодке подают звуковой сигнал. Пока звуковой сигнал движется от лодки к самолёту, самолёт продолжает лететь горизонтально с постоянной скоростью $v_c$.

За время $\text{t}$, пока звук доходит до самолёта, самолёт пролетает горизонтальное расстояние $\text{s}$. Это расстояние можно выразить через скорость самолёта и время:

$s = v_c \cdot t$

За это же время $\text{t}$ звук, распространяясь со скоростью $v_з$, проходит расстояние $\text{d}$ от лодки до нового положения самолёта:

$d = v_з \cdot t$

Рассчитаем это расстояние:

$d = 335 \text{ м/с} \cdot 2 \text{ с} = 670 \text{ м}$

В момент приёма сигнала положение лодки, начальное положение самолёта (точка прямо над лодкой) и конечное положение самолёта образуют прямоугольный треугольник. Катетами этого треугольника являются высота полёта самолёта $\text{h}$ и горизонтальное расстояние $\text{s}$, которое он пролетел. Гипотенузой является расстояние $\text{d}$, которое преодолел звуковой сигнал.

Согласно теореме Пифагора:

$d^2 = h^2 + s^2$

Из условия задачи известно, что самолёт преодолел расстояние, равное половине его высоты над водоёмом: $s = \frac{h}{2}$.

Подставим это соотношение в уравнение теоремы Пифагора:

$d^2 = h^2 + (\frac{h}{2})^2 = h^2 + \frac{h^2}{4} = \frac{4h^2 + h^2}{4} = \frac{5h^2}{4}$

Теперь мы можем найти высоту $\text{h}$, используя вычисленное значение $\text{d}$:

$(670 \text{ м})^2 = \frac{5h^2}{4}$

$h^2 = \frac{4 \cdot (670 \text{ м})^2}{5}$

$h = \sqrt{\frac{4 \cdot 448900}{5}} = \sqrt{4 \cdot 89780} = \sqrt{359120} \approx 599.27 \text{ м}$

Округлим значение высоты до целого числа: $h \approx 599 \text{ м}$.

Теперь, зная высоту, мы можем найти горизонтальное расстояние $\text{s}$, пройденное самолётом:

$s = \frac{h}{2} = \frac{599.27 \text{ м}}{2} \approx 299.63 \text{ м}$

Наконец, определим скорость самолёта $v_c$:

$v_c = \frac{s}{t} = \frac{299.63 \text{ м}}{2 \text{ с}} \approx 149.82 \text{ м/с}$

Округлим значение скорости до целого числа: $v_c \approx 150 \text{ м/с}$.

Ответ: скорость самолёта составляет приблизительно 150 м/с, а его высота — приблизительно 599 м.

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