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3 years ago

Pls help me with A, B, C, D

Mathematics

1 answer:

AlekseyPX3 years ago

8 0

Use PEMDAS with the first 3.

a. 3×(6÷5)

3×(1.2) [Parenthesis first]

3.6. [then multiply]

b. 3÷(5×6)

3÷(30) [Parenthesis first]

.1 [then divide]

c. (3×6)÷5

(18)÷5 [Parenthesis first]

3.6 [then divide]

d. 3×6÷5

18÷5 [Left to right]

3.6 [then divide]

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

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

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

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3. Filling the tank:

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x/y=r/h

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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.

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