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Giải bài 6.2 trang 6 sách bài tập toán 9 - Kết nối tri thức tập 2

Cầu treo Sunshine Skyway bắc qua Vịnh Tampa ở bang Florida (Mỹ) được hỗ trợ bởi 21 dây cáp làm bằng thép, mỗi dây có đường kính 9inch. Khối lượng mà mỗi dây cáp có thể chịu được là (w = 8{d^2}) (tấn), trong đó d là đường kính của dây cáp (tính bằng inch) (Theo Algebra 2, NXB McGraw-Hill, 2018). a) Tính khối lượng tối đa mà cây cầu treo có thể chịu đựng được. b) Nếu muốn cây cầu treo có thể chịu được khối lượng là 15 162 tấn thì đường kính của dây cáp phải là bao nhiêu?

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Cầu treo Sunshine Skyway bắc qua Vịnh Tampa ở bang Florida (Mỹ) được hỗ trợ bởi 21 dây cáp làm bằng thép, mỗi dây có đường kính 9inch. Khối lượng mà mỗi dây cáp có thể chịu được là \(w = 8{d^2}\) (tấn), trong đó d là đường kính của dây cáp (tính bằng inch) (Theo Algebra 2, NXB McGraw-Hill, 2018).

a) Tính khối lượng tối đa mà cây cầu treo có thể chịu đựng được. b) Nếu muốn cây cầu treo có thể chịu được khối lượng là 15 162 tấn thì đường kính của dây cáp phải là bao nhiêu?

Phương pháp giải - Xem chi tiết

a) Cây cầu gồm 21 dây cáp nên khối lượng cầu có thể chịu được là \(w = 21.8{d^2}\). Thay \(d = 9\) vào công thức 21\(w = 21.8{d^2}\) ta tính được khối lượng tối đa mà cây cầu treo có thể chịu đựng được. b) Thay \(w = 15{\rm{ }}162\) vào công thức 21\(w = 21.8{d^2}\), ta tính được d, từ đó tính được đường kính của dây cáp.

Lời giải chi tiết

a) Khối lượng tối đa mà cây cầu treo có thể chịu đựng được là: \(21w = {21.8.9^2} = 13\;608\) (tấn). Khối lượng tối đa mà cây cầu treo có thể chịu đựng được là 13 608 tấn. b) Để cây cầu treo có thể chịu được khối lượng là 15 162 tấn thì: \(15\;162 = 21.8.{d^2}\) nên \(d = \sqrt {\frac{{15\;162}}{{168}}}  = 9,5\left( {inch} \right)\) (do \(d > 0\)). Vậy muốn cây cầu treo có thể chịu được khối lượng là 15 162 tấn thì đường kính của dây cáp bằng 9,5inch.

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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