A hypothetical square grows at a rate of 16 m²/min. How fast are the sides of the square increasing when the sides are 15 m each?

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A hypothetical square grows at a rate of 16 m²/min. How fast are the sides of the square increasing when the sides are 15 m each?

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Answer 1 · 2016-08-30T15:22:20

The sides are increasing at a speed of $8/15$ meters/minute.

Explanation:

The formula for area of a square is $A = s^2$ , where $s$ is the side length.

Differentiating $A$ with respect to time:

$(dA)/dt = 2s((ds)/dt)$

Solve for $(ds)/dt$ , since this represents the change in the sides with respect to time.

$((dA)/dt)/(2s) = (ds)/dt$

$1/(2s) xx (dA)/dt = (ds)/dt$

Here's what we know and what would be our unknown:

-We know the speed at which the area is changing (16 $m^2$ /min)
-We want to know the speed at which the lengths of our sides are changing at the moment when the sides are $15$ meters each.

$1/(2 xx 15) xx 16 =(ds)/dt$

$1/30 xx 16 =( ds)/dt$

$8/15 = (ds)/dt$

Hence, the length of the sides are increasing at a speed of $8/15 "m"/"min"$ when the sides are at length $15$ meters.

Hopefully this helps!

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A hypothetical square grows at a rate of 16 m²/min. How fast are the sides of the square increasing when the sides are 15 m each?

1 Answer

Explanation:

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