Newton's law of cooling Indicates that the temperature of a warm object, such as a cake coming out of the oven, will decrease exponentially with time and will approach the temperature of the surrounding air. The temperature T t is modeled by T t = T a + T 0 − T a e − k t . In this model. T a represents the temperature of the surrounding air, T 0 represents the initial temperature of the object, and t is the dine after the object rearm cooling. The value of k is a constant of proportion relating the temperature of the object to its rate of temperature change. Use this model for Exercises 59-60. Water in a water heater is originally 122°F . The water heater is shut off and the water cools to the temperature of the surrounding air, which is 60°F . The water cools slowly because of the insulation inside the heater, and the value of k is measured as 0.00351. a. Write a function that models the temperature T t in o F of the water t hours after the water heater is Shut off. b. what is the temperature of the water 12 hr after the heater is shut off? Round to the nearest degree. c. Dominic does not like to shower with water less than 115°F . If Dominic mho 24 hr, will the water still be warm enough for a shower?
Newton's law of cooling Indicates that the temperature of a warm object, such as a cake coming out of the oven, will decrease exponentially with time and will approach the temperature of the surrounding air. The temperature T t is modeled by T t = T a + T 0 − T a e − k t . In this model. T a represents the temperature of the surrounding air, T 0 represents the initial temperature of the object, and t is the dine after the object rearm cooling. The value of k is a constant of proportion relating the temperature of the object to its rate of temperature change. Use this model for Exercises 59-60. Water in a water heater is originally 122°F . The water heater is shut off and the water cools to the temperature of the surrounding air, which is 60°F . The water cools slowly because of the insulation inside the heater, and the value of k is measured as 0.00351. a. Write a function that models the temperature T t in o F of the water t hours after the water heater is Shut off. b. what is the temperature of the water 12 hr after the heater is shut off? Round to the nearest degree. c. Dominic does not like to shower with water less than 115°F . If Dominic mho 24 hr, will the water still be warm enough for a shower?
Solution Summary: The author explains Newton's law of cooling, wherein the temperature function is T(t)=60+62e-0.00351t
Newton's law of cooling Indicates that the temperature of a warm object, such as a cake coming out of the oven, will decrease exponentially with time and will approach the temperature of the surrounding air. The temperature
T
t
is modeled by
T
t
=
T
a
+
T
0
−
T
a
e
−
k
t
.
In this model.
T
a
represents the temperature of the surrounding air,
T
0
represents the initial temperature of the object, and t is the dine after the object rearm cooling. The value of k is a constant of proportion relating the temperature of the object to its rate of temperature change. Use this model for Exercises 59-60.
Water in a water heater is originally
122°F
. The water heater is shut off and the water cools to the temperature of the surrounding air, which is
60°F
. The water cools slowly because of the insulation inside the heater, and the value of k is measured as 0.00351.
a. Write a function that models the temperature
T
t
in
o
F
of the water t hours after the water heater is Shut off.
b. what is the temperature of the water 12 hr after the heater is shut off? Round to the nearest degree.
c. Dominic does not like to shower with water less than
115°F
. If Dominic mho 24 hr, will the water still be warm enough for a shower?
T
1
7. Fill in the blanks to write the calculus problem that would result in the following integral (do
not evaluate the interval). Draw a graph representing the problem.
So
π/2
2 2πxcosx dx
Find the volume of the solid obtained when the region under the curve
on the interval
is rotated about the
axis.
38,189
5. Draw a detailed graph to and set up, but do not evaluate, an integral for the volume of the
solid obtained by rotating the region bounded by the curve: y = cos²x_for_ |x|
≤
and the curve y
y =
about the line
x =
=플
2
80
F3
a
FEB
9
2
7
0
MacBook Air
3
2
stv
DG
Find f(x) and g(x) such that h(x) = (fog)(x) and g(x) = 3 - 5x.
h(x) = (3 –5x)3 – 7(3 −5x)2 + 3(3 −5x) – 1
-
-
-
f(x) = ☐
College Algebra with Modeling & Visualization (5th Edition)
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