Find the gradient field of the function.f(x, y, z) = (x7y2 - y6z3)e-z2
A. ?f = 7x6y2e-z2i + (2x7y - 6y5z3)e-z2j + y2ze- z2[y4z(2z2 - 3) - 2x7]k
B. ?f = 7x6i + (6y5 - 2y)j + 2z4e-z2k
C. ?f = 7x6y2e-z2i + (2x7y - 6y5z3)e-z2j + (3 - 2z2)y6z2e-z2k
D. ?f = 7x6y2i + (6y5z3 - 2x7y)j + (2z2 - 3)y6z2k
Answer: A
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Solve the problem.Newton's Law of Cooling states that the temperature of a heated object decreases exponentially over time toward the temperature of the surrounding medium. Suppose that a coffee is served at a temperature of 150°F and placed in a room whose temperature is 70°F. The temperature ? (in °F) of the coffee at time t (in minutes) can be modeled by ?(t) = 70 + 80e-0.06t. When will the temperature be 105°F?
A. 13.8 minutes B. 6.9 minutes C. 5.9 minutes D. 6.2 minutes
Use the Integral Test to determine whether the series is convergent or divergent.
Provide an appropriate response.Suppose that the accompanying table shows the velocity of a car every second for 8 seconds. Use the Trapezoidal Rule to approximate the distance traveled by the car in the 8 seconds.
A. 221.5 feet B. 145.5 feet C. 291 feet D. 162 feet
Solve the problem.The distance d, in feet, a bomb falls in t seconds is given by d = . How many seconds are required for a bomb released at 6000 feet to reach its target? (If necessary, round your answer to two decimal places.)
A. 1076.66 seconds B. 67.29 seconds C. 326.35 seconds D. 33.65 seconds