# Calculus

I am re-posting this question because i wrote the incorrect function last time.

An oil tank is being drained for cleaning. After t minutes there are v litres of oil left in the tank, where v(t)=35(25-t)^2, 0<=t<=25

a) determine the average rate of change of volume during the first 15 minutes

I got -1225 as my answer, is that correct?

b) determine the rate of change of volume at the time t=15 minutes

I'm not sure how to answer this.

1. 👍 0
2. 👎 0
3. 👁 1,373
1. v(0) = 35(25)^2 = 21875
v(15) = 35(10)^2 = 3500

avg rate of change for those 15 minutes
= (2500 - 21875)/(15-0)
= -18375/15 L/min
= -1225 L/min

You are correct

at t=15, you are looking for the instantaneous rate of change, that is,
the derivative of v(t)

v ' (t) = 70(25-t) (-1)
v ' (15) = -70(25-15) = -700 L/min

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Math

A fuel oil tank is an upright cylinder, buried so that its circular top 12 feet beneath ground level. The tank has a radius of 6 feet and is 18 feet high, although the current oil level is only 13 feet deep. Calculate the work

2. ### Statistics

A sign on the gas pump of a certain chain of gasoline stations encourages customers to have their oil checked, claiming that one out of every four cars should have its oil topped up. What is the probability that exactly 3 of the

3. ### math

A large mixing tank currently contains 100 gallons of water into which 6 pounds of sugar have been mixed. A tap will open pouring 20 gallons per minute of water into the tank at the same time sugar is poured into the tank at a

4. ### english

Who is the intended audience for the novel The Scarlet Letter? That is a good question. He wrote of historical times, of sin, guilt, and repentance. He wrote of social mores, social pressure, and the pain of reconciling this with

1. ### Physics

an oil layer floats on 87 cm of water in a tank. the pressure at the bottom of the tank is 120.0 kPa. How thick is the oil?

2. ### mathematics

A circular oil spill continues to increase in size. The radius of the oil spill, in miles, is given by the function r(t) = 0.5 + 2t, where t is the time in hours. The area of the circular region is given by the function A(r) =

3. ### CHEM

Many home barbeques are fueled with propane gas C3H8. What mass of carbon dioxide (in kg) is produced upon the complete combustion of 18.9L of propane (approximate contents of one 5-gallon tank)? Assume that the density of the

4. ### Calculus

An oil storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of r(t) = 105e^−0.02t liters per minute. How much oil leaks out during the first hour? (Round your answer to the nearest liter.) I got 4974.35 and

1. ### calculus

A tank with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 4 meters and its volume is 36 cubic meters. Building the tank costs \$10 per square meter for the base and

2. ### CALCULUS

A cylindrical oil storage tank 12 feet in diameter and 17feet long is lying on its side. Suppose the tank is half full of oil weighing 85 lb per cubic foot. What's the total force on one endof the tank?

3. ### Physics

an open tank contains a layer of oil floating on top of a layer of water (of density 1000 kg/m3) that is 3.0 m thick, as shown. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be

4. ### SS

A scientist was studying the effects of oil contamination on ocean seaweed. He thought that oil runoff from storm drains would keep seaweed from growing normally so he decided to do an experiment. He filled two tanks of equal size