The value of $\mathrm{x}$ which satisfies the equation $8 \cos x+3=0$ on the domain $\frac{\pi}{2} \leq x \leq \pi$ correct to the nearest hundredth of a radian is

Step 1 ：The given equation is \(8 \cos x+3=0\). We need to find the value of \(x\) that satisfies this equation on the domain \(\frac{\pi}{2} \leq x \leq \pi\).

Step 2 ：First, we isolate \(\cos x\) in the equation. This gives us \(\cos x = -0.375\).

Step 3 ：Then, we use the inverse cosine function to find the value of \(x\). This gives us \(x = 1.96\).

Step 4 ：The value of \(x\) that we calculated falls within the given domain, so it is the solution to the equation.

Step 5 ：Final Answer: The value of \(x\) which satisfies the equation \(8 \cos x+3=0\) on the domain \(\frac{\pi}{2} \leq x \leq \pi\) correct to the nearest hundredth of a radian is \(\boxed{1.96}\).