Question

2nd question) Need to calculate rate of change of length of square whose area equal to 100m2, where rate of change
dAdt=1m2s

Answer 1

\[\frac{ dA }{ dt }=1 \frac{ m ^{2} }{ s }\]

Answer 2

Need to find rate of change of this square's length

Answer 3

Okay so remember the chain rule: \[
\frac{dA}{dt}=\frac{dA}{dx}\frac{dx}{dt}
\]Where \(x\) is the length of a side in this case.

Answer 4

"rate of change of length of square"
This means they want us to find: \[
\frac{dx}{dt}
\]

Answer 5

So first of all, can you dentify what \(dA/dx\) is?

Answer 6

Consider what \(A(x)\) is first.

Answer 7

A=L^2

Answer 8

Well, \(x\) not \(L\) in this case.

Answer 9

So what is \[
\frac{dA}{dx}
\]?

Answer 10

i dont know, what can be x?

Answer 11

Well, we know \[
A=100m^2
\]And \[
A=x^2
\]

Answer 12

\[\frac{ dA }{ dx }=\frac{ dx ^{2} }{ dx }=2x\]

Answer 13

Right!

Answer 14

so 20m/s is the answer?

Answer 15

\[
1\frac{m^2}{s}=2(10m)\frac{dx}{dt}
\]

Answer 16

It's not \(20mx/\)

Answer 17

1/20?

Answer 18

Yes.

Answer 19

damn it), i made a mistake, thx for a second time :D