Mathematics 23 Online
OpenStudy (anonymous):

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. ?

OpenStudy (amistre64):

do we know of a relation that relates these?

OpenStudy (amistre64):

OpenStudy (amistre64):

you said you needed help right?

OpenStudy (anonymous):

no i dnt kno the relation

OpenStudy (amistre64):

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

OpenStudy (anonymous):

yes and the derivative of that is pi*2r

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

A' = 2pi * 2 * 80 then

OpenStudy (amistre64):

that 2 meant 24

OpenStudy (amistre64):

my keyboard hates me

OpenStudy (anonymous):

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

OpenStudy (amistre64):

right, cm per sec

OpenStudy (anonymous):

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

OpenStudy (amistre64):

youre welcome, good luck with all of it :)

OpenStudy (anonymous):

thnx

OpenStudy (anonymous):

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 ?