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VMariaS [17]
3 years ago
11

The area of a base of a cylindrical water tank is 12π square feet. the volume of water in the tank is dependent on the height of

the water (h) and is represented by the function V(h) = 12π h
part a - find V to the power of -1 (h)
part b - what will the height of the water be when the volume reacher 420π cubic feet
Mathematics
1 answer:
Alex73 [517]3 years ago
8 0

Answer:

Step-by-step explanation:

V^-1(h)is find inverse function=h / 12π

V=12πh=420π

h=420π/12π=35 feet

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The radius of the large sphere is double the radius of the small sphere. How many times does the volume of the large sphere than
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Answer:

8 times larger.

Step-by-step explanation:

The radius of the large sphere is double the radius of the small sphere.

Question asked:

How many times does the volume of the large sphere than the small sphere

Solution:

<u>Let radius of the small sphere = </u>x<u />

<u>As the radius of the large sphere is double the radius of the small sphere:</u>

Then, radius of the large sphere = 2x

To find that how many times is the volume of the large sphere than the small sphere, we will <em><u>divide the volume of large sphere by  volume of small sphere:-</u></em>

For smaller sphere: Radius = x

Volume \ of \ sphere = \frac{4}{3} \pi r^{3}

                             =\frac{4}{3} \pi x^{3}

For larger sphere: Radius = 2x

Volume \ of \ sphere = \frac{4}{3} \pi r^{3}

                             =\frac{4}{3} \pi (2x)^{3}

Now, we will divide volume of the larger by the smaller one:

=\frac{4}{3} \pi (2x)^{3}\div\frac{4}{3} \times\frac{\pi }{1 } \times x^{3}\\  \\ =\frac{4}{3} \pi\times8x^{3} \times\frac{3}{4\pi }\  \times\frac{1}{x^{3} }

\frac{4}{3}\pi\   is \ canceled\  by\  \frac{3}{4\pi } \ and\ also\ x^{3} is\ canceled\ by \ \frac{1}{x^{3} }

<u>Now, we have</u>

= \frac{8}{1}

Therefore, the volume of the large sphere is 8 times larger than the smaller sphere.

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Answer:

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Step-by-step explanation:

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the value of n is both 5 times as much as the value of m and 36 more than the value of m. what are the values of n and m? explai
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We have to find the values of m and n. We know that the value of n is 5 times as much as the value of m : n = 5 m. Also n is 36 more than the value of m : n = m + 36. This is a system of equations. Of we substitute n = 5 m into the second equation: 5 m = m + 36; 5 m - m = 36; 4 m = 36; m = 36 : 4; m = 9. Finally: n = 5 * 9 ; n = 45. Answer: The values are n = 45 and m = 9.
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