#
Question : Assume x and y are functions of t. Evaluate dy/dt. 1) xy + x = 12; dx/dt = -3, x = 2, y = 5 : 2151737

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

Assume x and y are functions of t. Evaluate dy/dt.

1) xy + x = 12; dx/dt = -3, x = 2, y = 5

A) -9

B) 3

C) 9

D) -3

2) x^{3} + y^{3} = 9; dx/dt = -3, x = 1, y = 2

A) - (3/4)

B) - (4/3)

C) (3/4)

D) (4/3)

3) x^{4}/3 + y^{4}/3 = 2; dx/dt = 6, x = 1, y = 1

A) -6

B) 6

C) (1/6)

D) - (1/6)

4) xy^{2} = 4; dx/dt = -5, x = 4, y = 1

A) - (8/5)

B) - (5/8)

C) (8/5)

D) (5/8)

5) (x + y/x - y) = x^{2} + y^{2}; dx/dt = 12, x = 1, y = 0

A) (1/12)

B) - (1/12)

C) -12

D) 12

6) y√(x + 1) = 12; dx/dt = 8, x = 15, y = 3

A) - (3/4)

B) - (4/3)

C) (4/3)

D) (3/4)

7) x^{2} ln y = 1 + xe^{y}; dx/dt = 10, x = 3, y = 1

A) 0

B) 1

C) (10e/3(3 - e))

D) (10e/3 - e)

8) x^{3}e^{y} - y^{3}lnx = 10; dx/dt = 2, x = 1, y = 2

A) (16 - 6e^{2}/e^{2})

B) (16 - 6e^{2}/2)

C) 10

D) (16 + e^{2}/e^{2})

Solve the problem.

9) A company knows that unit cost C and unit revenue R from the production and sale of x units are related by C = (R2/118,000) + 6562. Find the rate of change of revenue per unit when the cost per unit is changing by $8 and the revenue is $2000.

A) $236.00

B) $80.00

C) $656.20

D) $446.10

10) Given the revenue and cost functions R = 34x - 0.3x^{2} and C = 8x + 12, where x is the daily production, find the rate of change of profit with respect to time when 15 units are produced and the rate of change of production is 6 units per day.

A) $150.00 per day

B) $147.00 per day

C) $102.00 per day

D) $152.40 per day

11) A product sells by word of mouth. The company that produces the product has noticed that revenue from sales is given by R(t) = 4√(x), where x is the number of units produced and sold. If the revenue keeps changing at a rate of $100 per month, how fast is the rate of sales changing when 700 units have been made and sold? (Round to the nearest dollar per month.)

A) $661/month

B) $21,166/month

C) $1323/month

D) $2/month

12) The average daily metabolic rate for a hippopotamus living in the wild can be expressed as a function of weight by m = 132.9w^{0.75}, where w is the weight of the hippopotamus (in kg) and m is the metabolic rate (in kcal/day). Determine dm/dt for a 2900-kg hippopotamus that is gaining weight at a rate of 21.75 kg/day.

A) 15,909 kcal/day^{2}

B) 14 kcal/day^{2}

C) 394 kcal/day^{2}

D) 295 kcal/day^{2}

13) The energy cost of a speed burst as a function of the body weight of a dolphin is given by E = 43.5w^{-0.61}, where w is the weight of the dolphin (in kg) and E is the energy expenditure (in kcal/kg/km). Suppose that the weight of a 500-kg dolphin is increasing at a rate of 15 kg/day. Find the rate at which the energy expenditure is changing with respect to time.

A) -8.9854 kcal/kg/km/day

B) -0.018 kcal/kg/km/day

C) -35.2624 kcal/kg/km/day

D) -0.0012 kcal/kg/km/day

14) Water is discharged from a pipeline at a velocity v given by v = 1158p(1/2), where p is the pressure (in psi). If the water pressure is changing at a rate of 0.230 psi/second, find the acceleration (dv/dt) of the water when p = 57 psi.

A) 1005.41 ft/s^{2}

B) 43.71 ft/s^{2}

C) 76.69 ft/s^{2}

D) 17.64 ft/s^{2}

15) A zoom lens in a camera makes a rectangular image on the film that is 8 cm × 5 cm. As the lens zooms in and out, the size of the image changes. Find the rate at which the area of the image begins to change (dA/df) if the length of the frame changes at 0.6cm/s and the width of the frame changes at 0.3 cm/s.

A) 1.08 m^{2}/s

B) (8/5) m^{2}/2

C) 6.3 m^{2}/s

D) 5.4 m^{2}/s

16) One airplane is approaching an airport from the north at 213 km/hr. A second airplane approaches from the east at 270 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 33 km away from the airport and the westbound plane is 25 km from the airport.

A) 116 km/hr

B) 333 km/hr

C) 1559 km/hr

D) 1409 km/hr

17) A container, in the shape of an inverted right circular cone, has a radius of 1 inches at the top and a height of 5 inches. At the instant when the water in the container is 4 inches deep, the surface level is falling at the rate of -1.7 in./s. Find the rate at which water is being drained.

A) -3.26 in.3/s

B) -3.42 in.3/s

C) -15.04 in.3/s

D) -12.82 in.3/s

18) A man 6 ft tall walks at a rate of 2 ft/s away from a lamppost that is 12 ft high. At what rate is the length of his shadow changing when he is 60 ft away from the lamppost?

A) 20 ft/s

B) (2/3) ft/s

C) 2 ft/s

D) (1/3) ft/s

19) Boyle's law states that if the temperature of a gas remains constant, then PV = c, where P is the pressure, V is the volume, and c is a constant. Given a quantity of gas at constant temperature, if V is decreasing at a rate of 10 in.3/s, at what rate is P increasing when P = 60 lb/in.2 and V = 90 in.3?

A) 15 lb/in.2-s

B) (20/3) lb/in.2-s

C) 540 lb/in.2-s

D) (4/9) lb/in.2-s

20) Electrical systems are governed by Ohm's law, which states that V = IR, where V = voltage, I = current, and R = resistance. If the current in an electrical system is decreasing at a rate of 7 A/s while the voltage remains constant at 22 V, at what rate is the resistance increasing when the current is 24 A?

A) (12/77) ohms/s

B) (77/288) ohms/s

C) (539/12) ohms/s

D) (77/12) ohms/s

21) The volume of a sphere is increasing at a rate of 3 cm^{3}/s. Find the rate of change of its surface area when its volume is (4π/3) cm^{3}

A) 2 cm^{2}/s

B) 6 cm^{2}/s

C) (1/3) cm^{2}/s

D) 4 cm^{2}/s