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Question : The amplitude of an alternating voltage V = V(t) is sometimes indicated : 2151796

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by the curves.

1) y = x + 1, y = 0, x = -1, x = 6

A) 49π

B) (343/3)π

C) (7/2)π

D) 24π

2) f(x) = √(x), y = 0, x = 1, x = 10

A) 50π

B) 99π

C) 49.5π

D) 4.5π

3) f(x) = x^{2}, y = 0, x = 1, x = 13

A) 74,258.4π

B) 732.00π

C) 371,292π

D) 74,258.6π

4) f(x) = 2x + 5, y = 0, x = 0, x = 10

A) 2583.33π

B) 150π

C) 5166.66π

D) 2604.17π

5) f(x) = √(4x + 9) , y = 0, x = 1, x = 5

A) 132π

B) 84π

C) 132

D) 84

6) f(x) = (1/√(x + 9)), y = 0, x = -8, x = 12 Give your answer in exact form.

A) 2π (√(21) - 1)

B) π (ln21 - 1)

C)ln21

D) πln21

7) y = (1/√(x)), y = 0, x = 1, x = 4 Give your answer in exact form.

A) (1/2)πln4

B) (1/4)π

C) 2π

D) πln4

8) y = (1/x), y = 0, x = 1, x = 9

A) (8/9)π

B) (1/9)π

C) πln9

D) (4/9)π

9) y = e^{x}, y = 0, x = -5, x = 3 Give your answer in exact form.

A) π^{2}(e^{3} - e^{-5})

B) (π/2)(e^{6} - e^{-10})

C) π(e^{6} - e^{-10})

D) (π/2)(e^{3} - e^{-5})

10) y = √(49 - x^{2}), y = 0, x = 0, x = 7

A) 196π

B) 14π

C) (1372/3)π

D) (686/3)π

Find the average value of the function on the given interval.

11) f(x) = 3x^{2} - 4; [0, 15]

A) (221/3)

B) 221

C) 225

D) 222

12) f(x) = ex/2; [0, 10]

A) 7.37

B) 29.67

C) 14.73

D) 29.48

13) f(x) = √(x + 2); [1, 19]

A) 3.459

B) 5.058

C) 3.194

D) 3.372

14) f(x) = x + 4; [1, 17]

A) 22.031

B) 13.281

C) 12.235

D) 13

15) f(x) = 4 - x^{2}; [1, 18]

A) -339

B) -104.204

C) -110.333

D) -110.118

16) f(x) = x^{3} - 6x^{2} + 12x - 8; [0, 4]

A) 8

B) 4

C) 16

D) 0

17) f(x) = (2x + 1)^{1/2} ; [0, 4]

A) (13/2)π

B) 5

C) (26/3)

D) (13/6)

18) f(x) = x^{2}e^{5x}; [0, 3] Give your answer in exact form.

A) (197/125)e^{15} - (2/125)

B) (197/375)e^{15}

C) (197/375)e^{15} - (2/375)

D) (5/3)e^{15} - (2/3)

19) f(x) = 7xlnx; [1, e^{2}] Give your answer in exact form.

A) (7/4)((3e^{4} - 1)/(e^{2} + 1))

B) (7/4)((3e^{2} + 1)/(e^{2} - 1))

C) (7/4)((4e^{4} + 1)/(e^{2} - 1))

D) (7/4)((3e^{4} + 1)/(e^{2} - 1))

Solve the problem.

20) The amplitude of an alternating voltage V = V(t) is sometimes indicated by giving the rms (root mean square) voltage, which is the square root of the average value of V2. Find the rms voltage if V(t) = 28,800t over the period t = 0 to t = 1/60 s.

A) 160.0 V

B) 25,600.0 V

C) 0.1 V

D) 277.1 V

21) Suppose the number of items a new worker on an assembly line produces daily after t days on the job is given by 25 + 2t. Find the average number of items produced daily in the first 10 days.

A) 38

B) 350

C) 35

D) 40

22) The voltage v (in volts) induced in a tape head is given by v = t^{2}e^{3t}, where t is the time (in seconds). Find the average value of v over the interval from t = 0 to t = 2. Round to the nearest volt.

A) 194 volts

B) 1564 volts

C) 6 volts

D) 40 volts

23) Suppose the number of items a new worker on an assembly line produces daily after t days on the job is given by 25 + 2t. Find the average number of items produced daily in the first 20 days.

A) 45

B) 900

C) 40

D) 48

24) The design of an electric power generating station depends on both the peak and the average power that it must produce. If a community uses 112 + 48t - 2t^{2} megawatts at time t (in hours) during the period t = 0 to t = 24, find the average level of power consumption for that day.

A) 688 MW

B) 304 MW

C) 7296 MW

D) 16,512 MW

25) The price per share of a stock can be approximated by the function S(t) = t(24 - 4t) + 28, where t is time (in years) since the stock was purchased. Find the average price of the stock over the first 8 years.

A) $38.00

B) $57.87

C) $309.33

D) $38.67

26) The intensity of the reaction to a certain drug, in appropriate units, is given by R(t) = te^{-0.05t}, where t is time (in hours) after the drug is administered. Find the average intensity during the 4th hour.

A) 480e^{-0.2} - 500e^{-0.25}

B) 460e^{-0.15} - 480e^{-0.2}

C) 460e^{-0.15} + 400e^{-0.2}

D) -0.85e^{-0.15} - 480e^{-0.2}

27) Find the volume of a right circular cone with a height of 10 meters and a base radius of 4 meters.

A) (40/3)π cubic m

B) (160/3)π cubic m

C) 37π cubic m

D) (160/3) cubic m

28) An auxiliary fuel tank for a helicopter is shaped like the surface generated by revolving the curve y = 1 - (x^{2}/16), -4 ≤ x ≤ 4, about the x-axis (dimensions are in feet). How many cubic feet of fuel will the tank hold to the nearest cubic foot?

A) 17 cubic ft

B) 13 cubic ft

C) 7 cubic ft

D) 4 cubic ft

29) An auxiliary fuel tank for a helicopter is shaped like the surface generated by revolving the curve y = 1 - (x^{2}/9), -3 ≤ x ≤ 3, about the x-axis (dimensions are in feet). If a cubic foot holds 7.481 gallons and the helicopter gets 3 miles to the gallon, how many additional miles will the helicopter be able to fly once the tank is installed (to the nearest mile)?

A) 56 mi

B) 75 mi

C) 226 mi

D) 113 mi