When Ms. Sugar turned on her oven, the temperature inside was 70 degrees Fahrenheit. The temperature began to rise at a rate of
2 answers:
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Let the additional weight that can be added be = x
Current weight of the bag = 38 pounds
Total weight can be = 50 pounds
The equation becomes:
Hence, a weight of 12 pounds cab be added to the current wight.
At the start, the tank contains
(0.25 lb/gal) * (100 gal) = 25 lb
of sugar. Let be the amount of sugar in the tank at time
. Then
.
Sugar is added to the tank at a rate of <em>P</em> lb/min, and removed at a rate of
and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,
Separate variables, integrate, and solve for <em>S</em>.
Use the initial value to solve for <em>C</em> :
The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time
has passed. At this time, we want the tank to contain
(0.5 lb/gal) * (5 gal) = 2.5 lb
of sugar, so we pick <em>P</em> such that