A gutter is to be made from metal sheet where the length of the two of the two sides of the gutter is 4cm and the third side is 5cm. How do you find an angle so that the gutter will carry the maximum amount of water?

Answer 1

Let the angle of the gutter be #theta#

Then the volume of the gutter

#V=1/2xx4xx4xxsinthetaxx5 cm^3#

#=>V=40sinthetacm^3#

Volume #V# will be maximum when #sintheta# is maximum i.e #sintheta=1#

This is possible only when #theta=pi/2#

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Answer 2

To find the angle that maximizes the amount of water carried by the gutter, you can use calculus. First, express the area of the gutter as a function of the angle. Then, find the derivative of the area function with respect to the angle, set it equal to zero, and solve for the angle. This angle will correspond to the maximum area, hence maximizing the amount of water carried by the gutter.

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Answer from HIX Tutor

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.

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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