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Giải bài 6.10 trang 7 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Khoảng cách từ một hành tinh đến Mặt Trời có thể xấp xỉ bằng một hàm số của độ dài năm của hành tinh đó

꧙Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Khoảng cách từ một hành tinh đến Mặt Trời có thể xấp xỉ bằng một hàm số của độ dài năm của hành tinh đó. Công thức của hàm số đó là \(d = \sqrt[3]{{6{t^2}}}\), trong đó  là khoảng cách từ hành tinh đó đến Mặt Trời (tính bằng triệu dặm) và  là độ dài năm của hạnh tinh đó (tính bằng số ngày Trái Đất). (Theo Algebra 2, NXB MacGraw-Hill, 2008). a) Nếu độ dài của một năm trên Sao Hoả là \(687\) ngày Trái Đất thì khoảng cách từ Sao Hoả đến Mặt Trời là bao nhiêu? b) Tính khoảng cách từ Trái Đất đến Mặt Trời (coi một năm trên Trái Đất có 365 ngày). (Kết quả của câu a và câu b tính theo đơn vị triệu dặm và làm tròn đến chữ số thập phân thứ hai).

Phương pháp giải - Xem chi tiết

a) Áp dụng công thức của hàm số đó là \(d = \sqrt[3]{{6{t^2}}}\)với \(t = 687\)      b) Áp dụng công thức của hàm số đó là \(d = \sqrt[3]{{6{t^2}}}\)với \(t = 365\)     

Lời giải chi tiết

a) Thay \(t = 687\) vào công thức ta được khoàng cách từ Sao Hoà đến Mặt Trời là\(d = \sqrt[3]{{6{t^2}}} = \sqrt[3]{{6 \cdot {{687}^2}}} \approx 141,48\) (triệu dặm)b) Thay \(t = 365\) vào công thức ta được khoảng cách từ Trái Đất đến Mặt Trời là:\(d = \sqrt[3]{{6{t^2}}} = \sqrt[3]{{6 \cdot {{365}^2}}} \approx 92,81\) (triệu dặm)

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