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Stolb23 [73]
2 years ago
12

The area of a circular oil slick on the surface of the sea is increasing at a rate of [150m^2/s] how fast is the radius changing

when:
a) the radius is 25 m

b) the area is [1000 m^2]
Mathematics
1 answer:
Akimi4 [234]2 years ago
4 0

Answer with Step-by-step explanation:

We are given that

\frac{dA}{dt}=150m^2/s

a.Radius =25 m

We have to find rate of change of radius.

We know that

Area of circle,A=\pi r^2

Differentiate w.r.t time

\frac{dA}{dt}=2\pi r\frac{dr}{dt}

Substitute the values then we get

150=2\pi (25)\frac{dr}{dt}

\frac{dr}{dt}=\frac{150}{50\pi}=\frac{3}{\pi} m/s

\frac{dr}{dt}=\frac{3}{\pi} m/s

b.A=1000m^2

Substitute the values then we get

1000=\pi r^2

\pi=3.14

r^2=\frac{1000}{3.14}

r=\sqrt{\frac{1000}{3.14}}=17.8m

\frac{dA}{dr}=2\pi r\frac{dr}{dt}

Substitute the values then we get

150=2\pi(17.8)\frac{dr}{dt}

\frac{dr}{dt}=\frac{150}{2\pi(17.8)}=\frac{150}{35.6\pi}m/s

\frac{dr}{dt}=\frac{75}{17.8\pi}m/s

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