(a) If \(9 \cos x - 7 = 1\) and \(0° \leq x…

Question 1 Report

(a) If \(9 \cos x - 7 = 1\) and \(0° \leq x \leq 90°\), find x.

(b) Given that x is an integer, find the three greatest values of x which satisfy the inequality \(7x < 2x - 13\).

Answer

Answer Details

(a) \(9\cos x-7=1\Rightarrow 9\cos x=8\Rightarrow \cos x=\dfrac{8}{9}=0.8889\).

For \(0^{\circ}\le x\le 90^{\circ}\): \(x=\cos^{-1}(0.8889)\approx \mathbf{27.3^{\circ}}\).

(b) \(7x<2x-13 \Rightarrow 7x-2x<-13 \Rightarrow 5x<-13 \Rightarrow x<-2.6\).

Since \(x\) is an integer, the values are \(\ldots,-5,-4,-3\). The three greatest are \(\mathbf{-3,\ -4,\ -5}\).

(a) If \(9 \cos x - 7 = 1\) and \(0° \leq x \leq 90°\), find x. (b) Given that x is an integer, find the three greatest values of x which satisfy the inequa...