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Giải bài 5 trang 27 sách bài tập toán 10 - Cánh diều

Một sân bóng đá có dạng hình chữ nhật với chiều dài và chiều rộng của sân lần lượt là 105 m và 68 m. Khoảng cách xa nhất giữa hai vị trí trên sân đúng bằng độ dài đường chéo của sân. Tìm một giá trị gần đúng (theo đơn vị mét) của độ dài đường chéo sân và tìm độ chính xác, sai số tương đối của số gần đúng đó.

🍸Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Cánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Một sân bóng đá có dạng hình chữ nhật với chiều dài và chiều rộng của sân lần lượt là 105 m và 68 m. Khoảng cách xa nhất giữa hai vị trí trên sân đúng bằng độ dài đường chéo của sân. Tìm một giá trị gần đúng (theo đơn vị mét) của độ dài đường chéo sân và tìm độ chính xác, sai số tương đối của số gần đúng đó.

Phương pháp giải - Xem chi tiết

Gọi \(x\) là độ dài đường chéo của sân bóng. Tính \(x\) và tìm độ chính xác, sai số tương đối của \(x\)

Lời giải chi tiết

Gọi \(x\) là độ dài đường chéo của sân bóng. Áp dụng định lý Pytago, ta có:\(x = \sqrt {{{105}^2} + {{68}^2}}  = \sqrt {15.649}  = 125,09596...\)Lấy một giá trị gần đúng của \(x\) là 125,1, ta có: \(125,09 < x < 125,1\)\( \Rightarrow \left| {x - 125,1} \right| < \left| {125,09 - 125,1} \right| = 0,01\)Vậy độ dài sân bóng có thể lấy bằng 125,1 với độ chính xác \(d = 0,01\)Sai số tương đối của 125,1 là \({\delta _{125,1}} = \frac{{{\Delta _{125,1}}}}{{\left| {125,1} \right|}} < \frac{{0,01}}{{125,1}} \approx 0,08\% \)

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