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