Question

the speed that a tsunami can travel is modeled by the equation $s = 356\sqrt{d}$, 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?

3.17 km
0.75 km
1.12 km
0.32 km

Explanation:

Step1: Substitute S = 200 into the equation

We have the equation \( S = 356\sqrt{d} \), and we know that \( S = 200 \). So we substitute \( S \) with 200 in the equation:
\( 200 = 356\sqrt{d} \)

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

To solve for \(\sqrt{d}\), we divide both sides of the equation by 356:
\( \sqrt{d}=\frac{200}{356} \)
Simplify the right - hand side: \( \frac{200}{356}\approx0.5618 \)

Step3: Solve for d

To find \( d \), we square both sides of the equation \( \sqrt{d}\approx0.5618 \):
\( d = (\frac{200}{356})^2=\frac{200^2}{356^2}=\frac{40000}{126736}\approx0.316 \approx 0.32\)

Answer:

0.32 km