MATHEMATICS HIGH SCHOOL

Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1.5 m/s, how fast is the area of the spill increasing when the radius is 30 m?

Answers

Answer 1

Answer:

Answer:

The area of the oil spill is increasing at a rate 180 π m²/s, when the radius is 30 m.

Step-by-step explanation:

Derivative Rule:

$(d)/(dx)x^n=nx^(n-1)$
$(d)/(dx)(y^n)=ny^(n-1)(dy)/(dx)$

Given that

The radius of the oil spill increases at a rate 1.5 m/s.

i.e $(dr)/(dt)= 1.5\ m/s$

We need to find the rate of area increase i.e $(dA)/(dt)$ .

We know,

The area of the oil spills A = $\pi r^2$ ( since it spreads in circular pattern)

$\therefore A=\pi r^2$

Differentiating with respect to t

$(dA)/(dt)=\pi. 2r(dr)/(dt)$

Plug the value of $(dr)/(dt) =1.5 \ m/s$

$(dA)/(dt)=\pi. 2r(3\ m/s)$

$\Rightarrow (dA)/(dt)=6\pi r \ m/s$

Plug r= 30 m

$\Rightarrow (dA)/(dt)=6\pi (30\ m) \ m/s$

=180 π m²/s

The area of the oil spill is increasing at a rate 180 π m²/s, when the radius is 30 m.

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Answers

Step-by-step explanation:

x+y=3

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Answer:

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b) What is the length of RP Explain your answer.
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Answers

I found the image that is part of this problem.

Circle R has a radius of 6. The radius is from R to Q, edge of the circle. Another radius is formed from R to S.

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Answers

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Answers

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Answers

Answer:

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Step-by-step explanation:

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