Suppose that a wave forms in shallow water The depth d of the water (in feet)and the velocity v of the wave (in feet per second) are related by the equation v=sqrt (32d) If a wave forms in water with a depth of 8.7 feet, what is its velocity? Round your answer to the nearest tenth. square square

To find the velocity \( v \) of the wave, we can use the given equation:<br /><br />\[ v = \sqrt{32d} \]<br /><br />where \( d \) is the depth of the water. Given that the depth \( d \) is 8.7 feet, we substitute this value into the equation:<br /><br />\[ v = \sqrt{32 \times 8.7} \]<br /><br />First, calculate the product inside the square root:<br /><br />\[ 32 \times 8.7 = 278.4 \]<br /><br />Now, take the square root of 278.4:<br /><br />\[ v = \sqrt{278.4} \approx 16.68 \]<br /><br />Rounding to the nearest tenth, the velocity \( v \) is approximately:<br /><br />\[ v \approx 16.7 \]<br /><br />Therefore, the velocity of the wave is approximately 16.7 feet per second.