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Giải bài tập 6.6 trang 5 SGK Toán 9 tập 2 - Cùng khám phá

Khối lượng tối da L (tấn) mà một loại dây có thể chịu được phụ thuộc vào đường kính d (inch) của dây theo hàm số L = ad2 (1 inch \( \approx \) 2,54 cm). a) Tìm hệ số a, biết sợi dây có đường kính 1,5 inch chịu được khối lượng tối đa 18 tấn. b) Một sợi dây có đường kính 26 mm sẽ chịu được khối lượng tối đa bao nhiêu tấn (làm tròn kết quả đến hàng phần trăm)?

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

Toán - Văn - Anh
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Đề bài

Khối lượng tối da L (tấn) mà một loại dây có thể chịu được phụ thuộc vào đường kính d (inch) của dây theo hàm số L = ad2 (1 inch \( \approx \) 2,54 cm).

a) Tìm hệ số a, biết sợi dây có đường kính 1,5 inch chịu được khối lượng tối đa 18 tấn. b) Một sợi dây có đường kính 26 mm sẽ chịu được khối lượng tối đa bao nhiêu tấn (làm tròn kết quả đến hàng phần trăm)?

Phương pháp giải - Xem chi tiết

Tính a dựa vào biết sợi dây có đường kính 1,5 inch chịu được khối lượng tối đa 18 tấn và công thức L = ad2.

Sau đó thay d = 26 mm vào công thức công thức L = ad2 để tìm khối lượng tối da mà dây chịu được.

Lời giải chi tiết

a) Thay d = 1,5 ; L = 18 vào L = ad2 ta có:

\(\begin{array}{l}18 = a.1,{5^2}\\a = 8\end{array}\)

Ta có L = 8d2 .

b) Thay d = 26 mm = 2,6 cm vào L = 8d2 ta có:

L = 8. 2,62 = 54,08 tấn

Vậy một sợi dây có đường kính 26 mm sẽ chịu được khối lượng tối đa 54,08 tấn.

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