Mathematics, 12.03.2020 21:32 jamarlittles9132

PLS TRY TO ANSWER ASAP.
A water tank at a filtration plant is built in the shape of an inverted cone with height 5.2 m and diameter 5 m at the top. Water is being pumped into the tank at a rate of 1.2 m³/min. Find the rate at which the water level is rising when there is 8π m³ of water

Answers: 1

Show answers

Answers

Answer from: que81hhh

The rate at which the water level is rising when there is 8π m³ of water in the tank is; dh/dt = 0.075 m /min

Implicit Differentiation

The formula for Volume of a cone is:

V = ¹/₃πr²h

We are given:

diameter; d = 5 m Thus; radius; r = d/2 = 5/2 = 2.5 m height; h = 5.2 m

Thus;

r/h = 2.5/5.2

Thus; r = (25/52)h

Now, when V = 8π m³/min., the height will be gotten from;

V = (¹/₃)π((25/52)h)²h

V = (¹/₃)π(625/2704)h³

V = π(625/8112)h³

Plugging in 8π for V gives us;

8π = π(625/8112)h³

Simplifying this gives;

h³ = 103.8336

h = ∛103.8336

h ≈ 4.7

Now using implicit differentiation, let us differentiate both sides of V = (¹/₃)π(625/2704)h³ to get;

dV/dt = π(625/2704)h²(dh/dt)

We are given;

dV/dt = 1.2 m³/min

To get dh/dt which is the rate of water level rising, we will plug in 1.2 for dV/dt and 4.7 for h to get;

1.2 = π(625/2704)(4.7)²(dh/dt)

Thus;

dh/dt ≈ 0.075 m /min

Read more about implicit differentiation at; link

Answer from: 1536468

0.075 m/min

Explanation:

You need to use derivatives which is an advanced concept used in calculus.

1. Write the equation for the volume of the cone:

$V=\dfrac{1}{3}\pi r^2h$

2. Find the relation between the radius and the height:

r = diameter/2 = 5m/2 = 2.5mh = 5.2mh/r =5.2 / 2.5 = 2.08

3. Filling the tank:

Call y the height of water and x the horizontal distance from the axis of symmetry of the cone to the wall for the surface of water, when the cone is being filled.

The ratio x/y is the same r/h

x/y=r/hy = x . h / r

The volume of water inside the cone is:

$V=\dfrac{1}{3}\pi x^2y$

$V=\dfrac{1}{3}\pi x^2(2.08)\cdot x\\\\\\V=\dfrac{2.08}{3}\pi x^3$

4. Find the derivative of the volume of water with respect to time:

$\dfrac{dV}{dt}=2.08\pi x^2\dfrac{dx}{dt}$

5. Find x² when the volume of water is 8π m³:

$V=\dfrac{2.08}{3}\pi x^3\\\\\\8\pi=\dfrac{2.08}{3}\pi x^3\\\\\\ 11.53846=x^3\\ \\ \\ x=2.25969\\ \\ \\ x^2=5.1062$ m²

6. Solve for dx/dt:

$1.2m^3/min=2.08\pi(5.1062m^2)\dfrac{dx}{dt}$

$\dfrac{dx}{dt}=0.03596m/min$

7. Find dh/dt:

From y/x = h/r = 2.08:

$y=2.08x\\\\\\\dfrac{dy}{dx}=2.08\dfrac{dx}{dt}\\\\\\\dfrac{dy}{dt}=2.08(0.035964m/min)=0.0748m/min\approx0.075m/min$

That is the rate at which the water level is rising when there is 8π m³ of water.

Answer from: Quest

hkhkhkhkhkhkhk

step-by-step explanation:

Answer from: Quest

First subtract 10 from both side
y^2+6y-16=0
(y+8)(y-2)=0
-8 and 2

Another question on Mathematics

Mathematics, 21.06.2019 13:10

An alien has just landed from the planet, iksnimak. he would like to leam how to add two fractions when thedenominators are the same. write a paragraph that explains to our alien friend, in your own words, the detailsabout how to add the fractions, how to change the result to a mixed number, and how to reduce the fractionpart. use this problem as your example: the two fractions are 5/8 & 7/8

Answers: 1

Answer

Mathematics, 21.06.2019 14:40

Astudent simplified a rational expression as shown.

Answers: 3

Answer

Mathematics, 21.06.2019 15:30

Gretchen is setting up for a banquet. she has 300 chairs and needs to distribute them evenly among t tables. how many chairs should she put at each table? write your answer as an expression.

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

Evaluate the expression for the given value of the variable. | ? 4 b ? 8 | + ? ? ? 1 ? b 2 ? ? + 2 b 3 -4b-8+-1-b2+2b3 ; b = ? 2 b=-2

Answers: 2

Answer

You know the right answer?

PLS TRY TO ANSWER ASAP.
A water tank at a filtration plant is built in the shape of an inverted...

Questions

Mathematics, 10.08.2021 19:50

This pyramid has the same base as the prism, and its height is three times the height of the prism. What is the ratio of the volume of the pyramid to...

Mathematics, 10.08.2021 19:50