Question

The radius of a circular puddle of water is increasing at a rate of 2.5 cm/s. Find the exact rate at which the area is increasing at the instant the radius is 12 cm.

Answer 1

a = pi r^2
find da/dt
you know that dr/dt = 2.5cm/s
find da/dt for r = 12cm

Answer 2

got it jennhy?

Answer 3

let me know if you have doubts

Answer 4

can you please check my solution?

Answer 5

can you rewrite it, you seem to have used x and r for the same things, use r for radius and a for area.

Answer 6

wouldnt that give me the same answer?

Answer 7

\[\frac{da}{dt}=\frac{da}{dr} \times \frac{dr}{dt} = \frac{d \pi r^2}{dr} \times 2.5\]

Answer 8

\[= 2 \pi r \times 2.5\]

Answer 9

at r = 12,
da/dt = 60 pi

Answer 10

Sorry but im unsure of how you got dπr2dr×2.5

Answer 11

using chain rule, or is it product rule? can't remember which is which, but I used that

Answer 12

its the chain rule, what i da/dr?

Answer 13

a = pi r^2
so da/ dr = d(pi r^2)/dr = 2 pi r

Answer 14

OHHHHHH I GET IT NOW! THANK YOU :D

Answer 15

you are welcome

Answer 16

Feel free to solve my other questions if you dont mind hehe

Answer 17

i wont solve them for you, but I can show you the method to follow. post them

Answer 18

YES THEATS FINE :)

Answer 19

*THATS

Answer 20

A bushwalker can walk at 5 km/h through clear land and 3 km/h through bushland. If she has to get from point A to point B following a route indicated at right, find the value of x so that the route is covered in a minimum time.
(Note: time = distance ) speed