Mathematics: Acircular oil slick is expanding at a rate of 2m^2/h. find the rate at which it s diameter is expanding when it s radius is 1.5m

Acircular oil slick is expanding at a rate of - id22134100, jrjordans13ox06qs

Ответ:

kahliey

10.03.2022

Mathematics

$\frac{4\pi}{3} \text{ meter per hour}$

Step-by-step explanation:

The circular oil slick is expanding at a rate of 2 m^2/h

Let A be the area of the circular oil slick,

So, the changes in A with respect to time (t),

$\frac{dA}{dt} = 2$

$\frac{d(\pi r^2)}{dt} = 2$

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

$\frac{dr}{dt} = \frac{1}{\pi r}$

Also, the change in diameter with respect to time(t),

$\frac{d}{dt} (2 r) = 2 \frac{dr}{dt}$

$\frac{d}{dt} (2 r) = 2 \times \frac{1}{\pi r}$

$\frac{d}{dt} (2 r) = \frac{2}{\pi r}$

For r = 1.5 m,

$\frac{d}{dt} ( 2 r)]_{r=1.5} = \frac{2}{\pi \times 1.5}=\frac{20}{\pi \times 15}=\frac{4\pi }{3}\text{ meter per hour}$

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Ответ:

Maria3737

25.02.2021

Mathematics

AM = 900

CI = 500

I have to be honest, this is the most ridiculously worded question of this type that I have ever seen... ask you teacher, why it was so important to force you to solve it using only one variable?

Step-by-step explanation:

(AM) + (1400-AM) = 1400

2(AM) + 3(1400 - AM) = 3300

2AM + 4200 -3AM = 3300

-AM = -900

AM = 900

CI = 500

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Acircular oil slick is expanding at a rate of 2m^2/h. find the rate at which it's diameter is expanding when it's radius is 1.5m

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