Answer:

Step-by-step explanation:
Area = pi*r^2
Area = pi*9^2
Area = 
Make a change of coordinates:


The Jacobian for this transformation is

and has a determinant of

Note that we need to use the Jacobian in the other direction; that is, we've computed

but we need the Jacobian determinant for the reverse transformation (from

to

. To do this, notice that

we need to take the reciprocal of the Jacobian above.
The integral then changes to

Answer:
It will take 8 minutes for the temperature to reach 76°
Step-by-step explanation:
The expression for the total temperature in degrees at time t can be written as;
T=I+EM
where;
T=total temperature
I=initial temperature
E=temperature increase per minute
M=number of minutes
This can also be written as;
total temperature=initial temperature+temperature increase per minute×number of minutes
In our case;
T=76°
I=40°
E=4.5°
M=m
replacing;
76=40+(4.5×m)
4.5 m=76-40=36
(4.5 m)/4.5=36/4.5
m=8
It will take 8 minutes for the temperature to reach 76°