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Ilya [14]
3 years ago
15

A conical (cone shaped) water tower has a height of 12 ft and a radius of 3 ft. Water is pumped into the tank at a rate of 4 ft^

3/min. How fast is the water level rising when the water level is 6 ft?
Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
5 0

Answer:

The water rises at a rate of 16/(9π) ft/min or approximately 0.566 ft/min.

Step-by-step explanation:

Volume of a cone is:

V = ⅓ π r² h

Using similar triangles, we can relate the radius and height of the water to the radius and height of the tank.

r / h = R / H

r / h = 3 / 12

r = ¼ h

Substitute:

V = ⅓ π (¼ h)² h

V = ¹/₄₈ π h³

Take derivative with respect to time:

dV/dt = ¹/₁₆ π h² dh/dt

Plug in values:

4 = ¹/₁₆ π (6)² dh/dt

dh/dt = 16 / (9π)

dh/dt ≈ 0.566

The water rises at a rate of 16/(9π) ft/min or approximately 0.566 ft/min.

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KIM [24]

Answer:

A. a) 24

A. b) 4

B. a) 40320

B. b) 576

Step-by-step explanation:

General formula for Permutations:

P(n,r) = \frac{n!}{(n - r)!}

A. Concert seats:  2 couple --- total of 4 persons.

a) without restrictions

Since there are no restrictions, but that the order is important (John, Mary, Paul, Michelle isn't the  same as Michelle, Mary, Paul, John), it's a permutation calculation.

Then we calculate the permutations of 4, out of 4, so...

P(4,4) = \frac{4!}{(4 - 4)!} = 4! = 24

24 different ways for them to sit.

b) couples together

Now, we can see the problem as having 2 levels of permutations, first the couples, then inside the couples.

There are 2 ways for the first level or order... couples AB or BA, so 2 possibilities.

Inside each couple, man then woman (MW) or woman then man (WM), so 2 possibilities there too on 2nd level.

Overall 2 * 2 = 4 ways to sit by couple.

B) Single file

a) without restrictions

Again, order is important, so another permutation, not a combination.  And since we have no restriction, it can be any sequence.

We then have to calculate the number of permutations of 8 out of 8...

P(8,8) = \frac{8!}{(8 - 8)!} = 8! = 40320

There are 40,320 ways these 8 kids can pass the door.

b) girls first.

So, the four girls have to enter first.... and these four girls can be in any order.. how many permutations? P(4,4)... so 24 as calculated above.

For the four boys, how many permutations?  Yes, again P(4,4)... so 24 again.

Overall, we need to multiply the two... 24 x 24 = 576 ways if the girls enter first, followed by the boys.

8 0
3 years ago
A point (-7, -6) is rotated counterclockwise about the origin to map onto (-6, 7). The
Ierofanga [76]

Option D, 270 is the answer

3 0
3 years ago
Whitch of the following options have the same value of 15 % of 20​
Gemiola [76]

Answer:

15% of 20 is 3

Step-by-step explanation:

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USPshnik [31]

Answer:

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Step-by-step explanation:

\sqrt{16} = 4

So, the answer is 4 mm.

<h2><u><em>Please mark as Brainliest!!!</em></u></h2>
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Answer:

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Step-by-step explanation:

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