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A box has a width of 12 cm and a length of 9 cm. the volume of the box is decreasing at a rate of 541 cubic cm per second, with the width and length being held constant. what is the rate of change of the height, in cm per second, when the height is 6 cm?

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ayune

With the width and length being held constant, the height of the box decreases at rate  5 cm/s

Let:

l = length

w = wide

h = height

Then, the volume of the box is given by:

V = l . w. h

The length and the width are assumed to be constant. Hence, the derivative with respect to time is:

dV/dt = l . w dh/dt

Parameters given:

dV/dt = - 541 cm³/dt

l = 9 cm

w = 12 cm

Plug these parameters into the formula:

-541 = 12 . 9 . dh/dt

dh/dt = 5 cm/s

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