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2 years ago

10

This is 50 points plz help ( no links ) EXPLAIN YOU ANSWER plz

1 answer:

fomenos2 years ago

8 0

Answer: 1,920

Explanation:

1. Divide the figure into two separate rectangular prisms.

2. Find the volume of each prism (Volume = Length*Width*Height), then add. Don’t forget to multiply by 2 because of the other bookend.

Here are some ways you can divide the bookend.

Method A:

Figure 1: 8*8*10
Figure 2: 4*8*10
Result: 960
Volume: 1,920 (don’t forget to multiply 960 by 2 due to the other bookend)

Method B:

Figure 1: (8+8)*10*4
Figure 2: 10*8*4
Result: 960
Volume: 1,920 (don’t forget to multiply 960 by 2 due to the other bookend)

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A water tank has the shape of an inverted right circular cone with base radius 3 meters and height 6 meters. Water is being pump

Ivan

Answer:

the rate of change is 3.8m/s

Step-by-step explanation:

The volume of the right circular cone is

$V= \frac{\pi*r^2h}{3}.$

The rate of change of volume is

$\frac{dV}{dt} =\frac{d}{dt}( \frac{\pi*r^2h}{3})=\frac{\pi}{3} \frac{d}{dt}(r^2h)=\frac{\pi}{3}(2rh\frac{dr}{dt}+r^2\frac{dh}{dt})$

In order to proceed further we have to define r in terms of h so tht we can compute the derivative above.

The ratio between h and r is

$\frac{h}{r}=\frac{6}{3} =2$

Therefore $r=\frac{h}{2}$ .

We plug that into the derivative above and get:

$2rh\frac{dr}{dt}+r^2\frac{dh}{dt}=\frac{h^2}{2}\frac{dh}{dt}+\frac{h^2}{4}\frac{dh}{dt}=\frac{3h^2}{4}\frac{dh}{dt}.$

Thus

$\frac{dV}{dt}=\frac{\pi}{3}\frac{3h^2}{4}\frac{dh}{dt}$

Now for the numerical part.

The rate of change of volume $\frac{dV}{dt}$ is $12\frac{m^3}{s}$ , so when the water is 2 meters deep $h=2$ , therefore:

$12=\frac{\pi*3*2^2}{4*3} \frac{dh}{dt} \\\\\therefore \boxed{ \frac{dh}{dt}=3.8m/s.}$

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2 years ago

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Vesna [10]

Answer:

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3 years ago

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3 years ago

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Answer:

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