Simplify the following expression.<br><br> 29.718

If a fire is burning a building and it takes 2 hours to put it out using 2000 gal./min., what minimum diameter cylindrical tank

strojnjashka [21]

Answer:

The minimum diameter of the cylindrical tank needed to store the quantity needed to put out the fire is approximately 58.415 feet.

Step-by-step explanation:

A gallon equals 0.134 cubic feet. First, we determine the amount of water ( $Q$ ), measured in cubic feet, needed to put out the fire under the assumption that water is consumed at constant rate:

$Q = \dot Q \cdot \Delta t$ (1)

Where:

$\dot Q$ - Volume rate, measured in feet per minute.

$\Delta t$ - Time, measured in minutes.

If we know that $\dot Q = 2000\,\frac{gal}{min}$ and $\Delta t = 120\,min$ , then the amount of water is:

$Q = \left(2000\,\frac{gal}{min} \right)\cdot (120\,min) \cdot \left(0.134\,\frac{ft^{3}}{gal} \right)$

$Q = 32160\,ft^{3}$

And the diameter of the cylindrical tank based on the capacity found above is determined by volume formula for a cylinder:

$Q = \frac{\pi}{4}\cdot D^{2}\cdot h$ (2)

Where:

$D$ - Diameter, measured in feet.

$h$ - Height, measured in feet.

If we know that $Q = 32160\,ft^{3}$ and $h = 12\,ft$ , then the minimum diameter is:

$D^{2} = \frac{4\cdot Q}{\pi\cdot h}$

$D = 2\cdot \sqrt{\frac{Q}{\pi\cdot h} }$

$D = 2\cdot \sqrt{\frac{32160\,ft^{3}}{\pi\cdot (12\,ft)} }$

$D \approx 58.415\,ft$

The minimum diameter of the cylindrical tank needed to store the quantity needed to put out the fire is approximately 58.415 feet.

8 0

2 years ago

PLEASE HELP ME !!! SOS

kramer

Answer:6x - 2y = 22

Step-by-step explanation:

Just multiplying equation by 2

Can do it with any number

8 0

3 years ago

A person reads a books at a rate of 1 word every 0.0145 seconds. How long will it take to read 3,500 words?

Ludmilka [50]

Answer:

50.75 seconds

Step-by-step explanation:

0.0145 x 3500 = 50.75 sec

I hope this helps! Have a nice day!

4 0

2 years ago

When x is 2, y is 4, p is 0.5, and m is 2. If x varies directly with the product of p and m and inversely with y, which equation

galben [10]

Can you elaborate please? What does p and m mean?

3 0

3 years ago

Read 2 more answers

Can you help me with number 3? Please!!!!

Fantom [35]

Answer:

D

Step-by-step explanation:

Take it step by step.

The area of a rectangle is width times length.

We know the length is 7 since it's given, and we can find the width by adding shared sides of the square and triangle.

So the width is 10 + 14 or 24

That means the area of the rectangle is 7 * 24

The area of the second rectangle is 12 * 14, since they are both given.

Finally, the area of the triangle is 1/2 of the base times height and we can find the height by looking at the shared side and using the definition of a rectangle.

So the area of the triangle is 1/2 of 10 * 12.

3 0

3 years ago

Simplify the following expression. 29.718 - 29.63