Question

the speed that a tsunami can travel is modeled by the equation $s = 358sqrt{d}$, where $s$ is the speed in kilometers per hour and $d$ is the average depth of the water in kilometers. what is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?

○ 0.32 km
○ 0.75 km
○ 1.12 km
○ 3.17 km

Explanation:

Step1: Substitute S with 200

We know the equation \( S = 358\sqrt{d} \), and we are given that \( S = 200 \). So we substitute \( S \) in the equation: \( 200 = 358\sqrt{d} \).

Step2: Solve for \(\sqrt{d}\)

Divide both sides of the equation by 358: \( \sqrt{d}=\frac{200}{358}\approx0.55866 \).

Step3: Solve for d

Square both sides of the equation to solve for \( d \): \( d = (\frac{200}{358})^2=\frac{40000}{128164}\approx0.312 \approx 0.32 \).

Answer:

0.32 km