# A cube of ice is melting and the volume is decreasing at a rate of 3 cubic m/s. How fast is the height decreasing when the cube is 6 inches in height?

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To find the rate at which the height is decreasing when the cube is 6 inches in height, you can use related rates. Since the cube is melting, its volume is decreasing at a rate of 3 cubic meters per second. Let ( V ) represent the volume of the cube and ( h ) represent its height. The volume of a cube is given by ( V = h^3 ). Differentiating both sides with respect to time ( t ), we get ( \frac{dV}{dt} = 3h^2 \frac{dh}{dt} ). Given that ( \frac{dV}{dt} = -3 ) (negative because the volume is decreasing) and when ( h = 6 ), you can solve for ( \frac{dh}{dt} ). Plugging in the values, you'll get ( \frac{dh}{dt} = -\frac{1}{4} ) meters per second.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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