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lesya692 [45]
3 years ago
11

A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rate of 10

cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep.

Mathematics
1 answer:
just olya [345]3 years ago
3 0

Answer:

\frac{dh}{dt}≅0.286\frac{ft^{3} }{min}

Step-by-step explanation:

V=\frac{\pi }{3}r^{2}h; rate of change \frac{dV}{dt}=10\frac{ft^{3} }{min}, we must find the rate of change of the depth \frac{dh}{dt} =?;h=8ft

5h=12r; V=\frac{\pi }{3}\({\((5h}/12} )} ^{2}h=\frac{\pi }{3}(\frac{25h^{2} }{144})h; V=\frac{25\pi h^{3}}{432}; deriving \frac{dV}{dt} = \frac{25\pi }{432}(3h^{2})\frac{dh}{dt} → 10=\frac{25\pi h^{2}}{144} \frac{dh}{dt} → h=8 then \frac{dh}{dt}=\frac{1440}{25\pi 64}=\frac{9}{10\pi}≅ 0.286\frac{ft^{3} }{min}

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3 years ago
How do I solve this?
maksim [4K]

Answer:

Answer A represents this

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Step-by-step explanation:

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This inequality is represented by shading the left section of the number line starting at x = -3 (make sure you draw a SOLID dot to mae clear that the point x = -3 is also included in your drawing.

The other inequality:

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4 0
3 years ago
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Start with

-3|2x+6|=-12

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Answer:

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Step-by-step explanation:

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x-y=-11

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In order to find the y coordinate of the solution we must first find the solution to this system of equations. We first start by solving one of the given equations and then substitute the answer of that into the second equation and further solve to get the final answers.

x=y=-11

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