Question

math?? Caculus 1! screenshot attached

Answer 1

the first step is write down the equation for the area of a circle.
can you do that ?

Answer 2

(x-h)^2+(y-k)^2=r^2

(x-h)+(y+8)=r^2

Answer 3

?

Answer 4

area of a circle
is pi*r^2

Answer 5

\[A(t)=\pi*(r(t))^2 \]

Answer 6

you wrote down the equation of a circle with center (h,k) and radius r
we want the area of a circle.

Answer 7

We wanted that equation because it talked about finding the rate of the area changing when the rate of the radius (of the circle ) is changing.
This means we need to somehow find a relationship between area of a circle and radius of a circle.
The equation that relates them two is the equation for the area of a circle.

Answer 8

okay so @freckles has it right? correct?

Answer 9

no wonder it didn't make sense!

Answer 10

Yes freckles has the area of a circle correct.
Are you asking freckles or phi though. lol.
What? What doesn't make sense?

Answer 11

so it will be like this A(t)=pie *(7(8))^2 @freckles @phi

Answer 12

r(t) wasn't it r times t

Answer 13

i get 9852.03

Answer 14

r(t) was just meant that radius is a function of time

Answer 15

we leave the variables in (until later)

and pi is pi not pie

so
\[ A = \pi r^2 \]

Answer 16

to find rates you need to differentiate

Answer 17

r(t) wasn't r times t*

Answer 18

the next step is to "take the derivative with respect to time"

\[ \frac{d}{dt} A = \pi\frac{d}{dt} r^2 \]

Do you know how to do that ?

Answer 19

r is rate? or radius?

Answer 20

r is radius

Answer 21

no i don't

Answer 22

so i did have it right?

Answer 23

morally speaking, no. The idea is to use calculus to find the change in A with time
and relate that to the change in the radius with time.

Answer 24

okay i am completely lost, it's just setting up the equation to be able to then derive both sides?

Answer 25

this question usually arises later in calculus, when you know how to take derivatives.
Here, both the area A and the radius "r" are changing with time (so dA/dt and dr/dt exist)

\[ \frac{d}{dt} A = \pi\frac{d}{dt} r^2 \\
\frac{dA}{dt} =\pi\frac{d}{dt} r^2
\]

Answer 26

to find the derivative of r^2 you use the power rule
\[ d x^n = n x^{n-1} dx \]

Answer 27

okay thank you, i barely learned how to take derivatives, but of simple problems, not qute this far yet

Answer 28

It takes more than a few hours to learn calculus, but if you have time, you can watch Khan
https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/calculus-derivatives-1-new-hd-version

It may refresh your memory.
btw, your problem in this post is "related rates", which he tackles here
https://www.khanacademy.org/math/differential-calculus/derivative_applications/rates_of_change/v/rates-of-change-between-radius-and-area-of-circle