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Giải bài 3 trang 70 SGK Toán 10 tập 2 – Chân trời sáng tạo

Để cắt một bảng hiệu quảng cáo hình Elip có trục lớn là 80 cm và trục nhỏ là 40 cm từ một tấm ván ép hình chữ nhật có kích thước là 80 cm x 40 cm, người ta vẽ hình elip đó trên tấm ván ép như hướng dẫn sau:

Tổn♔g hợp đề thi học kì 2 lớp 10 tất cả các môn - Chân𝄹 trời sáng tạo

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Đề bài

Để cắt một bảng hiệu quảng cáo hình Elip có trục lớn là 80 cm và trục nhỏ là 40 cm từ một tấm ván ép hình chữ nhật có kích thước là 80 cm x 40 cm, người ta vẽ hình elip đó trên tấm ván ép như hướng dẫn sau:

Chuẩn bị

- Hai cái đinh, một vòng dây kín không đàn hồi, bút chì.

Thực hiện

- Xác định vị trí (hai tiêu điểm của elip) và ghim hai cái đinh trên 2 điểm đó trên tấm ván.

- Quàng vòng dây qua hai chiếc đinh và kéo căng tại một điểm M nào đó. Tựa đầu bút chì vào trong vòng dây tại điểm M  rồi di chuyển sao cho dây lಌuôn luôn căng. Đầu bút chì vạcꦬh lên tấm bìa một đường elip (Xem minh họa trong hình 15).

Phải ghim hai cái đinh cách các mép tấm bìa bao nhiêu xentimets và lấy vòng dây có độ dài là bao nhiêu?

Phương pháp giải - Xem chi tiết

Bước 1: Từ giả thiết xác định a, c

Bước 2: Xác định vị trí đinh cách mép biết được tính bằng \(a - c\) Bước 3: Xác định chiều dài vòng dây, biết chiều dài vòng dây là \(2a + 2c\)

Lời giải chi tiết

Từ giải thiết ta có: \(2a = 80 \Rightarrow a = 40,2b = 40 \Rightarrow b = 20\)Suy ra, \(c = \sqrt {{a^2} - {b^2}}  = 20\sqrt 3 \)Suy ra vị trí đinh cách mép là \(a - c = 40 - 20\sqrt 3 = 5,36\) cmChiều dài vòng dây là \(2a + 2c = 2.40 + 2.20\sqrt 3 = 149,28\) cmVậy phải ghim hai cái đinh cách các mép tấm bìa 5,36 cm và lấy vòng dây có độ dài là 149,28 cm

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