Question

A hypothetical square grows at a rate of 25 m^2/min. How fast are the sides of the square increasing when the sides are 9 m. each?

Answer 1

It's a related rates problem

Answer 2

Start with listing what you given...

Answer 3

k so
dA/dt= 25

Answer 4

A=s^2

Answer 5

right, square with sides 's', now take the derivative of the area equation with respect to time t

Answer 6

A=2s

Answer 7

remember the chain rule, you are differentiating both sides with respect to time t.

\[\large A=s^2\]

Answer 8

\[\large \frac{ dA }{ dt }=\frac{ d }{ ds }[s^2]*\frac{ ds }{ dt }\]

Answer 9

\[\large \frac{ dA }{ dt }=2s*\frac{ ds }{ dt }\]

Answer 10

good with that?

Answer 11

would it be 7?

Answer 12

oops nvm

Answer 13

\[\frac{ ds }{ dt }=\frac{ 25 }{ 18 }\]

Answer 14

yeah, you can use the differential equation to solve like that, they say the area stays at a rate of 25 m^2/min

\[\large 25=2s* \frac{ ds }{ dt }\]

at any time you have side length s, and a side rate of change of ds/dt

Answer 15

any other probs?

Answer 16

not with this one. Thanks for walking me through it!

Answer 17

welcome