57. CONSERVATION Water collected in a rain barrel can be used to water plants and reduce city water use. Water flowing from an open rain barrel has velocity $$ v=8 h^{\frac{1}{2}} $$, where $$ v $$ is in feet per second and $$ h $$ is the height of the water in feet. Find the height of the water if it is flowing at 16 feet per second.

Question

UpStudy AI · Accepted Answer

To determine the height $$ h $$ of the water when the velocity $$ v $$ is 16 feet per second, follow these steps:

1. **Given Equation:**
   $$
   v = 8 h^{\frac{1}{2}}
   $$
   where:
   - $$ v $$ is the velocity in feet per second,
   - $$ h $$ is the height of the water in feet.

2. **Plug in the Known Velocity:**
   $$
   16 = 8 h^{\frac{1}{2}}
   $$

3. **Solve for $$ h^{\frac{1}{2}} $$:**
   $$
   h^{\frac{1}{2}} = \frac{16}{8} = 2
   $$

4. **Square Both Sides to Solve for $$ h $$:**
   $$
   h = (h^{\frac{1}{2}})^2 = 2^2 = 4
   $$

**Conclusion:**
The height of the water in the rain barrel is **4 feet** when the velocity is 16 feet per second.
The height of the water is 4 feet when the velocity is 16 feet per second.

CONSERVATION Water collected in a rain barrel can be used to
water plants and reduce city water use. Water flowing from
an open rain barrel has velocity , where is in feet per
second and is the height of the water in feet. Find the height
of the water if it is flowing at 16 feet per second.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions

CONSERVATION Water collected in a rain barrel can be used to water plants and reduce city water use. Water flowing from an open rain barrel has velocity , where is in feet per second and is the height of the water in feet. Find the height of the water if it is flowing at 16 feet per second.