Answer:
So it would takes approximately 6.9 hours to reach 32 F.
Step-by-step explanation:
For this case we have the following differential equationÑ
We can reorder the expression like this:
We can use the substitution 
and 
so then we have:
IF we integrate both sides we got:
If we apply exponential in both sides we got:
And if we replace w = u-T we got:
We can also express the solution in the following terms:
For this case we know that 
since w ehave a cooloing, 
, we have this model:
And if we want that the temperature would be 32F we can solve for t like this:
If we apply natural logs on both sides we got:
So it would takes approximately 6.9 hours to reach 32 F.
The measure of the angle ∠PQR is 90 degrees
<h3>How to prove that ∠PQR is 90 degrees?</h3>
The equation of the line PQ is given as:
3x - y - 2 = 0
The coordinates of the QR are given as:
(0, -2) and (6, -4)
Make y the subject in 3x - y - 2 = 0
y = 3x - 2
The slope of the above line is
m1 = 3
Next, we calculate the slope (m2) of points Q and R.
So, we have:
m2 = (y2- y1)/(x2 - x1)
This gives
m2 = (-4 + 2)/(6 - 0)
Evaluate
m2 = -1/3
The slopes of perpendicular lines are opposite reciprocals.
m1 = 3 and m2 = -1/3 are opposite reciprocals.
This means the lines PQ and QR are perpendicular lines.
The angle at the point of perpendicularity is 90 degrees
Hence, the measure of the angle ∠PQR is 90 degrees
Read more about linear equations at:
brainly.com/question/15602982
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