ANSWER. Robert takes a roast out of the oven when the temperature of the roast is 165 F. After 15 minutes, the temperature of the roast drops to 135 F. The temperature of the room is 70 F. How long does it take for the temperature of the roast to drop to 110 F? ANSWER IS 34
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Answers
Final answer:
To find out how long it takes for the temperature of the roast to drop to 110 F, we can use the Newton's Law of Cooling equation. By setting up and solving a differential equation, we find that it takes approximately 34 minutes for the temperature of the roast to drop to 110 F.
Explanation:
To find out how long it takes for the temperature of the roast to drop to 110 F, we can use the Newton's Law of Cooling equation. This equation states that the rate of change of temperature of an object is proportional to the difference between its temperature and the temperature of its surroundings.
In this case, we can write the equation as: dT/dt = -k(T - Troom),
where dT/dt represents the rate of change of temperature with respect to time, T is the temperature of the roast, Troom is the temperature of the room, and k is a constant.
We know that when the roast was taken out of the oven, its temperature was 165 F, and after 15 minutes, its temperature dropped to 135 F. Using these values, we can set up the initial value problem:
dT/dt = -k(T - 70), T(0) = 165
Solving this differential equation, we find the value of k to be 1/15. Using this value, we can find the time it takes for the temperature to drop to 110 F:
dT/dt = -1/15(T - 70)
Integration of the equation gives: ln|T - 70| = -t/15 + C
Using the initial condition T(0) = 165, we can find the value of the constant C as: ln|165 - 70| = 0 + C
Therefore, C = ln(95).
Substituting back into the equation, we get:
ln|T - 70| = -t/15 + ln(95)
T - 70 = e^(-t/15 + ln(95))
T = 70 + 25e^(-t/15)
Now, we can substitute T = 110 and solve for t:
110 = 70 + 25e^(-t/15)
25e^(-t/15) = 40
e^(-t/15) = 40/25
-t/15 = ln(40/25)
t = -15ln(40/25)
Simplifying, we find that it takes approximately 34 minutes for the temperature of the roast to drop to 110 F.
Learn more about Newton's Law of Cooling here:
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length = 22 cm; width = 18 cm
length = 24 cm; width = 16 cm
length = 23 cm; width = 14 cm
Answers
Answer:
Length = 25 cm , Width = 15 cm.
Step-by-step explanation:
Given : The length of a rectangle is 5 centimeters less than twice its width. The perimeter of the rectangle is 80 cm.
To find : What are the dimensions of the rectangle.
Solution : We have given
Perimeter = 80 cm .
According to question :
Let width of rectangle = W .
Length is twice its width.
L = 2W .
Length of a rectangle is 5 centimeters less than twice its width.
L = 2W - 5.
Then ,
Perimeter = 2 ( length + width).
Plug the values
80 = 2 ( 2W - 5 + W ) .
80 = 2( 3W -5) .
On dividing both sides by 2
40 = 3W - 5 .
On adding both sides by 5.
45 = 3 W .
On dividing both sides by 3.
W = 15 cm .
L = 2W - 5.
L = 2 ( 15) - 5 .
L = 30 -5 .
L = 25 cm .
Therefore, Length = 25 cm , Width = 15 cm.
Answer A
Let's the width of the rectangle
2a-5 its length
Teh half perimeter is 80/2=40
a+2a-5=40 ==>3a=45==>a=15 and 2a-5=30-5=25
Answers
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