A yam is put into a hot oven, maintained at a constant temperature of 200'C.At time t = 30 minutes, the temperature T of the yam is 120°C and is increasingat an instantaneous rate of 2 degrees per minute. Newton's Law of Cooling(or, in this case, warming) implies that the temperature at time t is given byT(t) = 200 – aebt.%3DFind a and b.

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Answered: A yam is put into a hot oven,…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Newton’s law of cooling is given by ϴ =ϴ0e-kt, where the excess of temperature at zero time is ϴ0oC and at time t seconds of temperature is ϴo C. Determine the rate of change of temperature after 40 s, given that ϴ0 =16oC and k = -0.03
1. The period T of oscillation (in seconds) of a simple pendulum of length L (in feet) is given by T = 2n 32 a.) What is the rate of change of T with respect to L when L = 8 inches? b.) What is the average rate of change of T from L = 2 inches to L = 8 inches?
A hot bowl of soup is served at a dinner party. It starts to cool according to Newton's law of cooling so that its temperature at time t is given by T=65 +145e-0.05t tis measured in minutes and T is in °F. What is the initial temperature of the soup? where
When you use a spray can and press the valve at the top, you decrease the pressure of the gas in the can. This decrease of pressure causes the volume of the gas in the can to increase. Because the gas needs more room than is provided in the can, it expands in spray form through the small hole near the valve. In general, if the temperature is constant, the pressure, P, of a gas in a container varies inversely as the volume, V, of the container. The pressure of a gas sample in a container whose volume is 8 cubic inches is 12 pounds per square inch. If the sample expands to a volume of 22 cubic inches, what is the new pressure of the gas?
Suppose the oscillatory motion of an object can be modeled using the equation s(t) = 4sin(2.6t) where time is measured in seconds and distance is measured in inches. Find the number of cycles (oscillations) the object makes per second. (Provide 4 decimal places.)
A dead body was found within a closed room of a house where the temperature was a constant 65° F. At the time of discovery the core temperature of the body was determined to be 80° F. One hour later a second measurement showed that the core temperature of the body was 75° F. Assume that the time of death corresponds to t = and that the core temperature at that time was 98.6° F. Determine how many hours elapsed before the body was found. [Hint: Let t₁ > 0 denote the time that the body was discovered.] (Round your answer to one decimal place.) 1.6 Xhr
Newton's law of cooling relates the rate at which a body cools to the difference in temperature between the body and the environment into which it is introduced. The formula is F(t) = To + Cb¹, where F(t) is the temperature of the body at time t, To is the constant temperature of the environment into which the body is introduced, and C and b are constants. Use Newton's law of cooling to solve the problem below. A cup of coffee has cooled from 98° to 50° after 15 minutes in a room at 23°. How long will it take to cool to 30°? It will take approximately minutes. (Round to the nearest integer as needed.) (...)
A bowl of steamed rice is served at a dinner party. It starts to cool according to Newton's Law of Cooling. Its temperature T (measured in degrees Fahrenheit) after t minutes is given by T(t) = 77 + 180e-0.06t
A thermometer reading 96o is placed inside a cold storage room with a constant temperature of 37o If the thermometer reads 88o in 5 minutes, how long before it reaches 53o Assume the cooling follows Newton's Law of Cooling: U = T + (Uo - T)ekt.
Near the surface of the earth, a ball (with p = 0.1) is released from rest and its flight through the air offers resistance that is proportional to its velocity. How long will it take the ball to reach one-half of its terminal velocity? How far will it travel during this time?
2. On a certain day, the depth off a pier at high tide was 6m. After 6h, the depth of the water was 3m. Assume a 12h cycle a. Find the equation of the depth of water, with respect to its average depth, in terms of the time, t hours since high tide. b. Find the depth of water at t=8h

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