Brian R.

Actuarial Sciences Senior at Auburn University

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Physics (Newtonian Mechanics)

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Question:

A ball is thrown up in the air and comes back down. At the top of the motion when the ball stops and comes back down, the acceleration vector is pointed: a) up b) down c) the acceleration is zero at the top of the ball's motion

Brian R.

Answer:

b) down The acceleration of gravity is always pointed downward. The velocity is zero at the top of the motion, but the ball has a constant downward acceleration. This is why it slows down on the way up and speeds up on the way down.

Calculus

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Question:

True or False: The infinite series of 1/n is convergent because the limit as n approaches infinity for 1/n goes to 0.

Brian R.

Answer:

False. The infinite series of 1/n is divergent. Just because a sequence approaches 0, does not mean the series will be convergent. The infinite series of 1/n can be shown to be divergent by the Integral Test.

Calculus

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Question:

A farmer needs to build a build a rectangular fenced-plot to hold his sheep. He needs his pin to be 400 ft^2, and the cost of fencing is $10 per foot. What are the dimensions of the fenced pin that minimize the cost?

Brian R.

Answer:

The width would be 20ft and the length would also be 20ft. You start with two equations for optimization problems. We have C=20w+20l for the cost and 400=w*l for the area. By combining these equations we get C=20(400/l)+20l, simplifying to C=8000/l + 20l. To minimize the cost, we take the derivative of the equation to get dC/dl= -8000/l^2+20. After setting equal to zero, we get l=20ft. Plugging that into 400=w*l, we get w=20ft.

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