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Question : The number of cows that can graze on a ranch is approximated by C(x,y) = 9x + 5y - 6 : 2151813

Choose the graph that matches the equation.

16) z = -x^{2} - y^{2}

A)

B)

C)

D)

17) z = 3 - x^{2}

A)

B)

C)

D)

18) z = √(4 - x^{2} - y^{2})

A)

B)

C)

D)

19) z = 4x^{2} + 4y^{2} + 2

A)

B)

C)

D)

20) z = 1 - x - 2y

A)

B)

C)

D)

21) x^{2} + y^{2} + (z - 1)^{2} = 1

A)

B)

C)

D)

Solve the problem.

22) Let f(x, y) = 8x - 3y^{2} - 7

Find (f(x + h, y) - f(x, y)/h)

A) 8x

B) 8 - 6y

C) 8 - 3y^{2} - 7

D) 8

23) Let f(x, y) = 6x - 8y^{2} - 10

Find (f(x, y + h) - f(x, y)/h)

A) 6x - 16y^{2}

B) 6 - 16y^{2}

C) -16y - 10

D) -16y

24) Let f(x, y) = 5 - 4x^{2} + 3y^{3}

Find (f(x + h, y) - f(x, y)/h)

A) -8x - 4h^{2}

B) -8x - 4h + 3y^{3}

C) -8x - 4h

D) -8x^{2} - 4h

25) Let f(x, y) = 5 + 5x^{2} + 9y^{3}

Find (f(x, y + h) - f(x, y)/h)

A) 5x^{2} + 27y^{2} + 27yh + 9h^{2}

B) 9y^{2}h + 27yh + 9h^{2}

C) 27y^{2} + 27yh + 9h^{2}

D) 27y^{2}h + 27yh + 27h^{2}

26) Production of television sets is given by P(x,y) = 100((2/3)x^{-2/3} + (2/5)y^{-1/3})^{-3}, where x is work hours and y is the amount of capital. If 8 work hours and 27 units of capital are used, what is the production output?

A) 3704

B) 270

C) 37

D) 27,000

27) The number of cows that can graze on a ranch is approximated by C(x,y) = 9x + 5y - 6, where x is the number of acres of grass and y the number of acres of alfalfa. If the ranch has 30 acres of alfalfa and 75 acres of grass, how many cows may graze?

A) 825 cows

B) 819 cows

C) 645 cows

D) 639 cows

28) The surface area of a human body (in square meters) is approximated by A = 0.202W(0.425)H(0.725), where W is the weight of the person in kilograms and H is the height in meters. Find A if W = 62 and H = 1.61. Round your answer to two decimal places.

A) 1.53 m^{2}

B) 1.65 m^{2}

C) 1.88 m^{2}

D) 1.64 m^{2}

29) The multiplier function M = ((1 + i)^{n}(1 - t) + t/[1 + (1 - t)i]^{n}) compares the growth of an Individual Retirement Account (IRA) with the growth of the same deposit in a regular savings account. The function M depends on the three variables n, i, and t, where n represents the number of years an amount is left at interest, i represents the interest rate in both types of accounts, and t represents the income tax rate. Values of M > 1 indicate that the IRA grows faster than the savings account. Find the multiplier when funds are left for 20 years at 8% interest and the income tax rate is 26%.

A) 1.174

B) 29.706

C) 1.526

D) 1.383

30) The volume of a flower pot is given by V = (1/3)πhwhere r_{1}is the major radius and r_{2}is the minor radius and h is the height of the pot (see figure below).

If the dimensions of the pot are r_{1}= 6 inches, r_{2}= 4 inches and h = 8 inches, find the volume of potting soil required to fill the pot to the top. Round to the nearest cubic inch.

A) 637 in^{3}

B) 648 in^{3}

C) 1245 in^{3}

D) 285 in^{3}

31) The price-earnings ratio of a stock is given by R(P, E) = (P/E), where P is the price per share of a stock, and E is the earnings per share of the same stock. If the price per share of a given stock is $280, and the earnings per share of the same stock are $30.75, what is the price-earnings ratio of the stock? Give decimal notation to the nearest tenth.

A) 9.1

B) 310.8

C) 0.1

D) 8610.0

32) The yield of a stock is given by Y(D, P) = (D/P), where D is the dividends per share of a stock, and P is the price per share of the stock. If the price per share of a stock is $105, and the dividends per share of the same stock are $2.45, then what is the yield of the stock to the nearest tenth of a percent?

A) 1.2%

B) 42.9%

C) 2.3%

D) 257.3%

33) The sum of all the forces acting on an object can be described mathematically by F(m, a) = ma, where m is the mass of the object (in kg) and a is the acceleration felt by the object (in m/s^{2}) as a result of the forces (in newtons, N) acting on it. What is the force required to accelerate a 7 kg object at 14 m/s^{2}?

A) 98 N

B) 7 N

C) 196 N

D) 21 N

34) Newton's Universal Law of Gravitation states that the attractive force exerted on one spherically symmetric object of mass M by a second spherically symmetric object of mass m is given by F = G(mM/r^{2}), where r is the distance between the centers of the two objects and G is a constant equal to 6.67 × 10^{-11} Nm^{2}/kg^{2} when F is in newtons (N), M and m are in kilograms (kg), and r is in meters (m). What is the magnitude of the gravitational force exerted on an object of mass 50 kg by an object of mass 1 × 10^{12} kg if the objects are 19 m apart?

A) 9.2 N

B) 92.4 N

C) 175.5 N

D) 31,682.5 N

35) The intelligence quotient in psychology is given by

Q(m, c) = 100 ? (m/c),

where m is a person's mental age, and c is his or her chronological, or actual, age. Find Q(23, 19) and round your answer to the nearest whole number.

A) 100

B) 83

C) 12

D) 121