Exam 8: Further Applications of Integration

A steady wind blows a kite due west.The kite's height above ground from horizontal position to ft is given by Find the distance traveled by the kite.Give yourAnswer rounded to two decimal places.

Find the centroid of the region bounded by the graphs of the given equations.

Use Simpson's Rule with n = 6 to estimate the length of the curve Round yourAnswer to six decimal places.

The manager of a fast-food restaurant determines that the average time that her customers wait for service is 2 minutes.The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger.But she doesn't want to give away free hamburgers to more than of her customers.What value of must she use in the advertisement "if you aren't served within minutes, you get a free hamburger"?

Use the arc length formula to find the length of the curve.

Select the correct Answer: for each question. -Find the area of the surface obtained by rotating the circle about the line

Select the correct Answer for each question. -Find the area of the surface obtained by revolving the given curve about the x-axis.

Boxes are labeled as containing 500 g of cereal.The machine filling the boxes produces weights that are normally distributed with standard deviation 12 g.If the target weight is 500 g, what is the probability that the machine produces a box with less than of cereal? Round yourAnswer to four decimal places.

Find the centroid of the region bounded by the graphs of the given equations.

You are given the shape of the vertical ends of a trough that is completely filled with water.Find the force exerted by the water on one end of the trough.(The weight density of water is

A large tank is designed with ends in the shape of the region between the curves and measured in feet.Find the hydrostatic force on one end of the tank if it is filled to a depth of ft with gasoline.(Assume that the density of the gasoline is Select the correct Answer

Dye dilution is a method of measuring cardiac output.If A mg of dye is used and c(t) is the concentration of the dye at time t, then the cardiac output over the time interval [0, T ] is given by Find the cardiac output over the time interval [0, 15] if the dye dilution method is used with mg of dye and the dye concentration, in mg/L, is modeled by where t is measured in seconds.

A movie theater has been charging per person and selling about tickets on a typical weeknight.After surveying their customers, the theater estimates that for every that they lower the price, the number of moviegoers will increase by per night.Find the demand function and calculate the consumer surplus when the tickets are priced at

Find the centroid of the region bounded by the graphs of the given equations.

A cylindrical drum of diameter 2 ft and length 5 ft is lying on its side, submerged in water 17 ft deep.Find the force exerted by the water on one end of the drum to the nearest pound.(The weight density of water is

Select the correct Answer for each question. -Find the length of the curve.

The mass are located at the points Find the moments and and the center of mass of the system.

Find the arc length of the graph of the given equation on the specified interval.

Write an integral giving the arc length of the graph of the equation from to

Select the correct Answer for each question. -The masses are located at the points Find the moments and and the center of mass of the system.