5. A tank is being filled with water at a rate ofr(t) = 2t + 3, where r(t) is in ounces per second, and t is the time in seconds. (a) What is the total change in the amount of water in the tank between t = 3 and t = 5 seconds? (b) What is the average rate of change of water in the tank between t = 3 and t = 5 seconds? (c) Find a function that gives the amount of water in the tank at a given time t if there are initially 4 ounces of water in the tank.

Q: 3. The number of sales per day S(t), measured in thousands, of a new toy is found to be 400 t+25…

A: Need to answer the following parts for the given sales function with respect to the number of days.

Q: Find F.

A: f''(t) = 3/t1/2 f'(t) =     Given, f'(4) = 4 So, 6(4)1/2 + C = 4 or, 12+C = 4 or C = -8 Therefore,…

Q: The height of a hill (in feet) is given by h(x, y) = 21(14-4x-4y+3xy+28x-17y) where X is the…

A: To find the rate of change

Q: 12. Air is being released from a balloon at a rate of R(t) = 40(1 +t²)- cubic feet per minute. How…

A: Given air is being released from a balloon at the rate of R(t)=401+t2-1 cubic feet per minute. To…

Q: 42. Average velocity. Suppose that in t hours, a truck trav- els s(t) miles, where s(t) = 1012. a)…

A: To Determine:  a) find s5-s2 b) find the average rate of change of distance with respect to time as…

Q: The deck of a bridge is suspended 285 feet above a river. If a pebble falls off the side of the…

A: Given that the height of the pebble above the water surface after t seconds is y=285-16t2 and t=2.…

Q: 8. The value of a car, t years after it is bought, is modeled by V(t) = 2100 + 8t 1 + 0.5t + 150. a)…

A:

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.