# Calculus

posted by .

Fuel is flowing into a storage tank which can be filled to a depth of 6 metres.
When the fuel started flowing the tank was already filled to a depth of 2.5m. If the rate at which the depth of fuel in the tank is increasing, in metres per hour is given by d'(t) = 4t +5, find:
(i) the rate at which the height is increasing after 20 minutes
(ii) the height of water in the tank after 20 minutes
(iii) the time it takes to fill the tank

• Calculus -

Let the depth of the water be d(t)

if d ' (t) = 4t+5 , where t is in hours
d(t) = 2t^2 + 5t + c, where c is a constant
given: when t=0, d(0) = 2.5
2.5 = 0 + 0 + c , ----> c = 2.5

d(t) = 2t^2 + 5t + 2.5

a) when t = 20 min, t = 1/3 hrs
d ' (1/3) = 4(1/3) + 5 = 19/3 m/hr

b) after 20 min or after 1/3 hr
d(1/3) = 2(1/9) + 5(1/3) + 2.5 = 79/18 or appr 4.39 minutes

c) to fill the tank ...
2t^2 + 5t + 2.5 = 6
2t^2 + 5t - 3.5 = 0
by the formula ...
t = (-5 ± √53)/4
= .57 hrs or a negative time, which we will reject

.57 hrs = 34.2 minutes

## Similar Questions

1. ### AP CALCULUS!!! HELPP

related rates: the base of a pyramid-shaped tank is a square with sides of length 12 meters, and the vertex pyramid is 13 meters above the base. the tank is filled to a depth of 5 meters, and water is flowing into the tank at the rate …
2. ### AP CALCULUS!! HELPPP URGENT

related rates: the base of a pyramid-shaped tank is a square with sides of length 12 meters, and the vertex pyramid is 13 meters above the base. the tank is filled to a depth of 5 meters, and water is flowing into the tank at the rate …
3. ### solid mensuration

A cylindrical tank with flat ends has a diameter of two meters and is 5meters long. It is filled with fuel to a depth of one and one-half meters. Find the volume of the fuel in the tank in liters. plsss help!!
4. ### calculus

Water is flowing freely from the bottom of a conical tank which is 12 feet deep and 6 feet in radius at the top. If the water is flowing at a rate of 2 cubic feet per hour, at what rate is the depth of the water in the tank going down …
5. ### AP calculus

The base of a cone-shaped tank is a circle of radius 5 feet, and the vertex of the cone is 12 feet above the base. The tank is being filled at a rate of 3 cubic feet per minute. Find the rate of change of the depth of water in the …
6. ### Calculus

Fuel is flowing into a storage tank which can be filled to a depth of 6 metres. When the fuel started flowing the tank was already filled to a depth of 2.5m. If the rate at which the depth of fuel in the tank is increasing, in metres …
7. ### math

Ben placed a stone in an empty rectangular tank, 50cm long and 40cm wide. He then filled the tank with water flowing from a tap at a rate of 10 liters per minute. it took 3 min to fill the tank to a depth of 18cm to cover the stone …
8. ### Physics

A water tank is filled to a depth of 10 m, and the bottom of the tank is 20 m above ground. A water-filled hose that is 2.0 cm in diameter extends from the bottom of the tank to the ground, but no water is flowing in this hose. The …
9. ### Math

The base of a pyramid-shaped tank is a square with sides of length 12 feet, and the vertex of the pyramid is 10 feet above the base. The tank is filled to a depth of 4 feet, and water is flowing into the tank at the rate of 2 cubic …
10. ### Calculus

The radius of a conical tank is 2.7 meters and the height of the tank is 4.3 meters. Water is flowing into the tank at a constant rate of 59.5 m3/minute. At the instant the the depth of the water is 0.6 meters, answer the following: …

More Similar Questions