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Question : A department store has revenue from the sale of electrical kitchen appliances that is given approximately : 2163393

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

55) ∫(sintcost dt)

Enter your answer in terms of cosine without using parentheses.

56) ∫(sin(3t + 2)dt)

Enter your answer using parentheses around the argument of the function.

57) ∫(sin4t dt)

Enter your answer without parentheses around the argument of the function.

58) ∫(3cos(2x)dx)

Enter your answer using parentheses around the argument of the function.

59) ∫(cos2t dt)

Enter your answer without parentheses.

60) ∫(4sin2t dt)

Enter your answer without parentheses.

61) Evaluate:

Enter just an integer.

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

62) Find the area under the curve y = sin2x from x = 0 to x = (π/4).

A) -1

B) (1/2)

C) 0

D) (4π/3)

E) none of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

63) Find the area under the curve y = sin(3t - π) for (π/3) ≤ t ≤ (2π/3).

Enter just a reduced fraction.

64) Find the area under the curve y = sin2x + cosx for 0 ≤ x ≤ (π/4).

Enter as (√(A) + b/2).

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

65) A department store has revenue from the sale of electrical kitchen appliances that is given approximately by R(t) = 2.2 + 2.2cos(πt/23) for 0 ≤ t ≤ 52, where R(t) is revenue in hundreds of dollars for a week of sales t weeks after January 1. What is the total revenue (to the nearest hundred dollars) earned from t = 10 to t = 16?

A) $1000

B) $1300

C) $1100

D) $300

66) In a large city, the amount of sulfur dioxide pollutant released into the atmosphere due to the burning of coal and oil for heating purposes is given approximately by P(t) = 3 + cos(πt/26) for 0 ≤ t ≤ 104, where P(t) is the amount of sulfur dioxide in tons released during the nth week after January 1. How many tons (to the nearest ton) of pollutants were emitted into the atmosphere from t = 0 to t = 65?

A) 4 tons

B) 203 tons

C) 221 tons

D) 196 tons

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

67) The U.S. Geological Survey estimates that the normal stream flow of the Potomac River (in millions of gallons per day) is given by the function f(t) = 4200 + 3000cos((π/6)t + (5π/12)) where t denotes the number of months after January 1. Determine the maximum and minimum daily stream flows of the Potomac River. Enter your answer exactly as a, b where a represents the maximum and b represents the minimum,both integers separated by a comma, no units or words.

68) The size of an animal population at time t is given by N(t) = 50,000 + 200sin(7πt/48), where t is the number of months from June 1, 1980. At what rate is the animal population changing on June 1, 1981?

Enter your answer as a quotient reduced form (a/B) with π in the numerator (no units).

69) A person's blood pressure P at time t is given by P(t) = 90 + 30sin(7πt/3), where t is measured in seconds. What is the average blood pressure over a time interval of 60 seconds?

Enter just an integer (no units).

70) Suppose in a study of a prarie dog town it is dis covered that the number of prarie dogs at any time t is given by P(t) = 1000 + 500cos((2πt/12)), where t is measured in months from July 1, 1990. What is the average number of prarie dogs living in the town from July 1, 1990 to July 1, 1992?

Enter just an integer.

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

Solve the problem.

71) The velocity of a car is 63cost km/hr on the time interval [0, 2] hours. Calculate the distance the car traveled in that time interval.

A) 126 kilometers

B) 183.286 kilometers

C) 68.714 kilometers

D) 57.286 kilometers

72) The motion of a spring-mass system is described by the equation y = 11sin(πt - (π/4)), where y is the distance in feet from the equilibrium position and t is time in seconds. Find the velocity of the mass at time t = 3/4 seconds. Is the mass moving toward or away from its equilibrium position or neither?

A) -11π feet/second; toward from equilibrium position

B) 0 feet/second; away from equilibrium position

C) 0 feet/second; neither

D) 11π feet/second; away from equilibrium position