July 23, 2017

Minimum cost. From a tract of land, a developer plans to fence a rectangular region and

then divide it into two identical rectangular lots by putting a fence down the middle.

Suppose that the fence for the outside boundary costs per foot and the fence for the

middle costs per foot. If each lot contains square feet, find the dimensions of

each lot that yield the minimum cost for the fence.

A) Dimensions are 48.07 ft for the side parallel to the divider and 85.29 ft for the other

side.

B) Dimensions are 85.29 ft for the side parallel to the divider and 48.07 ft for the other

side.

C) Dimensions are 64.03 ft for the side parallel to the divider and 64.03 ft for the other

side.

D) Dimensions are 60.37 ft for the side parallel to the divider and 67.91 ft for the other

side.

E) Dimensions are 67.91 ft for the side parallel to the divider and 60.37 ft for the other

side.

Determine the open intervals on which the graph of is concave

downward or concave upward.

A) concave downward on

B) concave downward on ; concave upward on

C) concave upward on ; concave downward on

D) concave downward on ; concave upward on

E) concave upward on ; concave downward on

Find the dimensions of the rectangle of maximum area bounded by the x-axis and y-axis

and the graph of .

A) length 0.75; width 0.625

B) length 1; width 0.5

C) length 0.25; width 0.875

D) length 0.5; width 0.75

E) none of the above

Use Lagrange multipliers to find the given extremum. In each case, assume that

and are positive.

Maximize Constraints

A)

B)

C)

D)

E)

The graph shows the number of visitors V to a national park in hundreds of thousands

during a one-year period, where t = 1 represents January. Estimate the rate of change of

V over the interval . Round your answer to the nearest hundred thousand visitors

per year.

A) 176.92 hundred thousand visitors per year

B) 328.57 hundred thousand visitors per year

C) 166.67 hundred thousand visitors per year

D) 383.33 hundred thousand visitors per year

E) 766.67 hundred thousand visitors per year

Find given the probability distribution.

A) 0.440

B) 1.000

C) 0.790

D) 0.650

E) 0.250

A wooden beam has a rectangular cross section of height h and width w (see figure).

The strength S of the beam is directly proportional to the width and the square of the

height. What are the dimensions of the strongest beam that can be cut from a round log

of diameter d = 23 inches? Round your answers to two decimal places. [Hint:

where is the proportionality constant.]

A) w = 13.28 inches and h = 18.78 inches

B) w = 7.67 inches and h = 21.68 inches

C) w = 19.92 inches and h = 11.50 inches

D) w = 16.26 inches and h = 16.27 inches

E) w = 18.78 inches and h = 13.28 inches

Use separation of variables to find the general solution of the differential equation.

A)

B)

C)

D)

E)

Find the derivative of the function.

A)

B)

C)

D)

E)

Complete the table and use the result to estimate the limit.

x

f(x)

A) 0.142857

B) 0.642857

C) 0.517857

D) 0.767857

E) "0.232143

If find and

A)

B)

C)

D)

E)

Find of , .

A)

B)

C)

D)

E) none of these choices

Medication. The number of milligrams x of a medication in the bloodstream t hours

after a dose is taken can be modeled by . Find the maximum value of

x. Round your answer to two decimal places.

A) 2.65 mg

B) 755.93 mg

C) 1663.04 mg

D) 8.20 mg

E) 1500.40 mg

An employee of a delivery company earns 22.50 per hour driving a delivery van in an

area where gasoline costs 2.50 per gallon. When the van is driven at a constant speed

s (in miles per hour, with ), the van gets miles per gallon. Determine

the most economical speed s for a 100-mile trip on an interstate highway.

A) The most economical speed is 47.0 mph.

B) The most economical speed is 43.0 mph.

C) The most economical speed is 22.5 mph.

D) The most economical speed is 45.0 mph.

E) The most economical speed is 48.0 mph.

Volume. A rectangular box with a square base is to be formed from a square piece of

metal with 36-inch sides. If a square piece with side x is cut from each corner of the

metal and the sides are folded up to form an open box, the volume of the box is

What value of x will maximize the volume of the box?

A) 18

B) 1

C) 6

D) 15

E) 9

Which of the following is the correct graph of ?

A)

B)

C)

D)

E)

Find the third derivative of the function .

A)

B)

C)

D)

E)

Write the following expression as a logarithm of a single quantity.

A)

B)

C)

D)

E) none of the above

Find the particular solution of the differential equation that satisfies the

initial condition y = 8 when x = 3, where is the general solution.

A)

B)

C)

D)

E)

Find the general solution of the first-order linear differential equation.

A)

B)

C)

D)

E)

Use a table of integrals to find the indefinite integral .

A)

B)

C)

D)

E)

For the function , use a graphing utility to complete the table and

estimate the limit as x approaches infinity.

x 100 101 102 103 104 105 106

f(x)

A) 0.6

B) 1.666667

C) 2.666667

D) 1.6

E) "0.4

Use integration by parts to evaluate .

A)

B)

C)

D)

E)

For the probability density function on the interval , find the

probability that . Round your answer to the nearest thousandth.

A) 0.088

B) 0.245

C) 0.224

D) 0.250

E) 0.264

An airplane flying at an altitude of 5 miles passes directly over a radar antenna. When

the airplane is 25 miles away (s = 25), the radar detects that the distance s is changing at

a rate of 250 miles per hour. What is the speed of the airplane? Round your answer to

the nearest integer.

A) 255 mi/hr

B) 236 mi/hr

C) 510 mi/hr

D) 128 mi/hr

E) 118 mi/hr

Solve the differential equation to find velocity v as a function of time t if when

The differential equation models the motion of two people on a toboggan after

consideration of the forces of gravity, friction, and air resistance.

A)

B)

C)

D)

E)

Find an equation of the graph that passes through the point and has the specified slope.

Then graph the equation. Point: , Slope:

A)

B)

C)

D)

E) None of the Above

Assume that the median sales prices of existing one family homes sold (in thousands of

dollars) in the United States from 1990 through 2005 are as given in the following

figure. Use the following figure to estimate the percent increase in the value of existing

one-family homes from 1997 to 1998.

A) 0.021%

B) 0.058%

C) 2.06%

D) 55.5%

E) 5.8%

Use the function to find

A)

B)

C)

D)

E)

Find the value for the function .

A) 734,208

B) 430,080

C) 221,185

D) 430,081

E) 3,403,776

Determine whether is a solution of the differential equation .

A)

B)

C)

D)

E)

Production. Suppose that the total number of units produced by a worker in t hours of

an 8-hour shift can be modeled by the production function

. Find the number of hours before the rate of production

is maximized. That is, find the point of diminishing returns.

A)

B)

C)

D)

E)