Water flows into a reservoir at a rate of 500 + 7t2 gallons/hour. There is a hole in the reservoir and water leaks out at a rate of 4t + t² gallons/hour. What is the net change in the amount of water in the reservoir over the time interval [1,5]?

Q: Water flows simultaneously into the top of a tank at a rate of (1+ 4t) liters/minute and out of the…

A:

Q: Water is flowing out of a water tower so that after t minutes ther are 10,000-10t-t^3 gallons…

A: Given that the volume of water flowing out  V(t)=10000−10t−t3

Q: The length of a rectangular box is increasing at 3 in/sec, while its width is decreasing at 4…

A: Differentiate volume of rectangular box wrt t

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.