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alexira [117]
3 years ago
15

Can a cold front warm air moves which direction

Chemistry
1 answer:
Katena32 [7]3 years ago
6 0
East is the cold front
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An inverted pyramid is being filled with water at a constant rate of 45 cubic centimeters per second. The pyramid, at the top, h
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13.20 cm/s is the rate at which the water level is rising when the water level is 4 cm.

Explanation:

Length of the base = l

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Volume of the pyramid = V=\frac{1}{3}lwh

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Rate at which water is filled in cube = \frac{dV}{dt}= 45 cm^3/s

Square based pyramid:

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Volume of the square based pyramid = V

V=\frac{1}{3}\times l^2\times h

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l=\frac{6h}{13}

V=\frac{1}{3}\times (\frac{6h}{13})^2\times h

V=\frac{12}{169}h^3

Differentiating V with respect to dt:

\frac{dV}{dt}=\frac{d(\frac{12}{169}h^3)}{dt}

\frac{dV}{dt}=3\times \frac{12}{169}h^2\times \frac{dh}{dt}

45 cm^3/s=3\times \frac{12}{169}h^2\times \frac{dh}{dt}

\frac{dh}{dt}=\frac{45 cm^3/s\times 169}{3\times 12\times h^2}

Putting, h = 4 cm

\frac{dh}{dt}=\frac{45 cm^3/s\times 169}{3\times 12\times (4 cm)^2}

=13.20 cm/s

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