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3 years ago

13

Help please.............

2 answers:

garri49 [273]3 years ago

8 0

81 inches x 1 foot
------------
12 inches

81/12 = 6.75 C

larisa86 [58]3 years ago

4 0

A. you can never go wrong with 69 ( ͡° ͜ʖ ͡°)

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Harrizon [31]

Answer:

<u>0.075 m/min</u>

Explanation:

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

<u>1. Write the equation for the volume of the cone:</u>

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

<u />

<u>2. Find the relation between the radius and the height:</u>

r = diameter/2 = 5m/2 = 2.5m

h = 5.2m

h/r =5.2 / 2.5 = 2.08

<u>3. Filling the tank:</u>

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/h

y = x . h / r

The volume of water inside the cone is:

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

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

<u>4. Find the derivative of the volume of water with respect to time:</u>

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

<u>5. Find x² when the volume of water is 8π m³:</u>

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

<u>6. Solve for dx/dt:</u>

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

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

<u />

<u>7. Find dh/dt:</u>

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.

4 0

3 years ago