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Giải Bài 5 trang 22 SGK Toán 8 tập 2 – Chân trời sáng tạo

Gọi (C) và (r) lần lượt là chu vi và bán kính của một đường tròn. Hãy chứng tỏ (C) là một hàm số bậc nhất theo biến số (r). Tìm hệ số (a,b) của hàm số này.

෴Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Gọi \(C\) và \(r\) lần lượt là chu vi và bán kính của một đường tròn. Hãy chứng tỏ \(C\) là một hàm số bậc nhất theo biến số \(r\). Tìm hệ số \(a,b\) của hàm số này.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

- Công thức tính chu vi đường tròn: \(C = \pi .d = \pi .2r\) (đơn vị độ dài) - Hàm số bậc nhất là hàm số được cho bởi công thức \(y = ax + b\) với \(a,b\) là các số cho trước và \(a \ne 0\).

Lời giải chi tiết

Công thức tính chu vi đường tròn: \(C = \pi .d = \pi .2r\) (đơn vị độ dài) Trong đó, \(C\) là chu vi đường tròn; \(r\) là bán kính đường tròn; \(d\) là đường kính đường tròn. Vì \(C = 2\pi .r\) nên \(C\) là hàm số bậc nhất theo biến \(r\) vì có dạng \(C = a.r + b\). Ta có: \(C = 2\pi .r\) nên \(a = 2\pi ;b = 0\). Vậy C là một hàm số bậc nhất theo biến \(r\) với \(a = 2\pi ;b = 0\).

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