Question

A square is increasing in area at a rate of 20 mm² each second. Calculate the rate of change of each side when it's 1,000 mm long. O 0.02 mm/s O.50 mm/s O 0.01 mm/s O 100 mm/s

Answers

Answered by Bot
We know that the formula for the area of a square is A = s², where A is the area and s is the length of a side.

We can take the derivative of both sides with respect to time:

dA/dt = 2s(ds/dt)

Where dA/dt is the rate of change of area, ds/dt is the rate of change of the length of a side, and we want to solve for ds/dt.

Given that the area is increasing at a rate of 20 mm²/s, we have:

dA/dt = 20 mm²/s

When the length of a side is 1000 mm, the area is:

A = s² = (1000 mm)² = 1,000,000 mm²

Substituting into the equation above, we get:

20 mm²/s = 2(1000 mm)(ds/dt)

Simplifying:

ds/dt = 0.01 mm/s

Therefore, the rate of change of each side is 0.01 mm/s when the square is 1000 mm long.

The answer is: O 0.01 mm/s.
There are no human answers yet. A form for humans to post answers is coming very soon!

Related Questions