Answer:
The arc length of the circle(l) is given by:
....[1]
where,
r is the radius of the circle
is the angle in radian.
As per the statement:
In a circle a radius 25 inches, a central angle of 35 degree
⇒r = 25 inches
Use conversion:
1 degree = 0.0174533 radian
then
35 degree = 0.6108655 radian
⇒ radian
Substitute these values in [1] we have;
inches
Therefore, in a circle a radius 25 inches, a central angle of 35 degree will intersect the circle forming an arc of length of 15.27 inches
Let = amount of salt (in pounds) in the tank at time
(in minutes). Then
.
Salt flows in at a rate
and flows out at a rate
where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.
Then the net rate of salt flow is given by the differential equation
which I'll solve with the integrating factor method.
Integrate both sides. By the fundamental theorem of calculus,
After 1 hour = 60 minutes, the tank will contain
pounds of salt.