Exam 8: Further Applications of Integration

A vertical plate is submerged in water (the surface of the water coincides with the x-axis).Find the force exerted by the water on the plate.(The weight density of water is

According to the National Health Survey, the heights of adult males in the United States are (normally distributed with mean) 73 inches, and standard deviation of 2.8 inches.What is the probability that an adult male chosen at random is between inches and inches tall? Select the correct Answer

Find the area of the surface obtained by rotating the curve about the x-axis.

A hawk flying at an altitude of accidentally drops its prey.The parabolic trajectory of the falling prey is described by the equation until it hits the ground, where is its height above the ground and is the horizontal distance traveled in meters.True or False? The distance traveled by the prey from the time it is dropped until the time it hits the ground is approximately

Select the correct Answer: for each question. -The standard deviation for a random variable with probability density function and mean is defined Find the standard deviation for an exponential density function with mean

A hot, wet summer is causing a mosquito population explosion in a lake resort area.The number of mosquitoes is increasing at an estimated rate of per week (where t is measured in weeks).By how much does the mosquito population increase between the 4th and th weeks of summer?

A trough is filled with a liquid of density 855 The ends of the trough are equilateral triangles with sides m long and vertex at the bottom.Find the hydrostatic force on one end of the trough.Select the correct Answer

A vertical plate is submerged in water (the surface of the water coincides with the Find the force exerted by the water on the plate.(The weight density of water is

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 trough is filled with a liquid of density The ends of the trough are equilateral triangles with sides m long and vertex at the bottom.Find the hydrostatic force on one end of the trough.

A trough has vertical ends that are equilateral triangles with sides of le If the trough is filled with water to a depth of 1 ft, find the force exerted by the water on one end of the trough.Round to one decimal place.(The weight density of water is Select the correct Answer

Use the Theorem of Pappus to find the volume of the solid obtained by revolving the region bounded by the graphs of and about the y-axis.Select the correct Answer

Let a) For what value of is probability density function? b) For that value of , find

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 is measured in seconds.

Find the length of the curve for the interval

Find the center of mass of the lamina of the region shown if the density of the circular lamina is six times that of the rectangular lamina.

Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about the x-axis on the interval

Select the correct Answer: for each question. -A gate in an irrigation canal is constructed in the form of a trapezoid ft wide at the bottom, ft wide at the top, and 2 ft high.It is placed vertically in the canal, with the water extending to its top.Find the hydrostatic force on one side of the gate.

Find the area of the surface obtained by rotating the curve about the y-axis.

For a given commodity and pure competition, the number of units produced and the price per unit are determined as the coordinates of the point of intersection of the supply and demand curves.Given the demand curve and the supply curve find the consumer surplus.