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Elis [28]
3 years ago
12

A square has a side length x cm and area A cm2.

Mathematics
1 answer:
Karolina [17]3 years ago
5 0

Answer:

The rate of increase of x when A = 25 is 0.0006 cm/s.

Step-by-step explanation:

Area of a square A = x^{2} sq. cm

So, x = \sqrt{A} cm

\frac{dx}{dt} =\frac{1}{2\sqrt{A} } (\frac{dA}{dt} ) --- (1)

It is given that the area is increasing at the rate of 0.03 cm^{2}/s.

Therefore,

\frac{dA}{dt} =0.03 cm^{2} /s

We need to find the rate of increase of x when A = 25.

Now, substituting the values of A and \frac{dA}{dt}, (1) becomes

\frac{dx}{dt} =\frac{1}{2\sqrt{25} } (0.03)

= 0.0006

Hence, the rate of increase of x when A = 25 is 0.0006 cm/s.

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