A circular ripple in a pond is produced when a rock is dropped into the water. If the outer radius of the ripple is expanding at a rate of 24 cm/sec, at what rate is the area of the circular ripple changing when the radius is 80 cm. ?

Question

amistre64 · Answer

do we know of a relation that relates these?

amistre64 · Answer

radius to area

amistre64 · Answer

you said you needed help right?

anonymous · Answer

no i dnt kno the relation

amistre64 · Answer

Hmm, would you agree that the area of a circle is determined by the equation:  pi r^2 ?

anonymous · Answer

yes and the derivative of that is pi*2r

amistre64 · Answer

correct, except for we need to include an r' for the rate of the change of the radius

amistre64 · Answer

$$A = pi\  r^2$$
$$A' = 2pi\  r\ r'$$

amistre64 · Answer

r' is told to us to be 24, and the radius = 80

amistre64 · Answer

A' = 2pi * 2 * 80 then

amistre64 · Answer

that 2 meant 24

amistre64 · Answer

my keyboard hates me

anonymous · Answer

lol i understood what you mean ... but when i did all that i qot 12063.71579

amistre64 · Answer

right, cm per sec

anonymous · Answer

i  had that answer but it was telling me i was wrong but i had a 5 instead of 6 thnk yu sooooo much yu r qreatly appreciated

amistre64 · Answer

youre welcome, good luck with all of it :)

anonymous · Answer

thnx

anonymous · Answer

A 14 foot ladder is leaning on a wall, slowly sliding down. If the base of the ladder is sliding away from the wall at 1.3 ft/second, how fast is the top sliding vertically along the wall when the bottom of the ladder is 9 feet from the wall?  do i approach it the same way ?