ORadicals
Word problem involving radical equations: Basic
Suppose that a wave forms in shallow water. The depth of the water (in
the equation . If a wave forms in water with a depth of 8.8 feet,
what is its velocity?
Round your answer to the nearest tenth.
Explanation feet per second

Question

ORadicals
Word problem involving radical equations: Basic
Suppose that a wave forms in shallow water. The depth

of the water (in
the equation

. If a wave forms in water with a depth of 8.8 feet,
what is its velocity?
Round your answer to the nearest tenth.
Explanation feet per second

UpStudy AI · Accepted Answer

1. The formula for the velocity is given by  
   $$
   v = \sqrt{32d}.
   $$

2. Substitute the depth $$ d = 8.8 $$ feet into the formula:  
   $$
   v = \sqrt{32 \times 8.8}.
   $$

3. Calculate the product inside the square root:  
   $$
   32 \times 8.8 = 281.6.
   $$

4. Now, compute the square root:  
   $$
   v = \sqrt{281.6}.
   $$

5. Using a calculator,  
   $$
   v \approx 16.8 \text{ feet per second}.
   $$

Thus, the velocity of the wave is approximately $$ 16.8 $$ feet per second.
The wave's velocity is approximately 16.8 feet per second.

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