51 A tennis player tosses a tennis ball straight up and then

Each problem below refers to triangle ABC In each case find the area of the tri angle Round to three significant digits 1 a 50 centimeters b 70 centimeters C 60 2 a 10 centimeters b 12 centimeters C 120 3 a 41 meters c 34 meters B 151 5 4 a 76 3 meters c 42 8 meters B 16 3 5 b 0 923 kilometers c 0 387 kilometers A 43 20

Verify that the function satisfies the three hypotheses of Rolle s Theorem on the given interval Then find all numbers that satisfy the conclusion of Belle s Theorem Enter your answers as a comma separated 1 12 22 12x 1 0 4

11 a 4 inches b 6 inches c 8 inches Remember Solve for the largest angle first and round to the nearest tenth of a degree

Find the volume of the solid formed by rotating the region enclosed by about the y axis Volume I y e 5 y 0 x 0 x 0 8

The area of the region between the graph of y x x 20 and the x axis is

Find the volume of the solid formed by rotating the region enclosed by about the x axis Answer x 0 x 1 y 0 y 7 x

Two catalysts may be used in a batch chemical process Twelve batches were prepared using catalyst 1 resulting in an average yield of 86 and a sample standard deviation of 3 Fifteen batches were prepared using catalyst 2 and they resulted in an average yield of 89 with a standard deviation of 2 Assume that yield measurements are approximately normally distributed with the same standard deviation a Is there evidence to support a claim that catalyst 2 produces a higher mean yield than catalyst 1 Use a 0 01 b Find a 99 confidence interval on the difference in mean yields that can be used to test the claim in part a

9x Suppose G x f t dt 8 G x G z

Find the flow of the velocity field F x y i x y j along each of the following paths from 1 0 to 1 0 in the xy plane a The upper half of the circle x y 1 b The line segment from 1 0 to 1 0 c The line segment from 1 0 to 0 1 followed by the line segment from 0 1 to 1 0 a The flow of the velocity field is Type an exact answer

The tank shown below is full of water Using the fact that the weight of water is 62 5 lb ft find the work in ft lbs required to pump the water out of the outlet Make sure your answer is correct to within ten ft lbs 5 ft Work ft lbs hemisphere