Question

@ganeshie8 do you get this problem? :)

attached inside! :/

Answer 1

The area is changing at a rate of _____ cm^2 per minute.

Answer 2

differentiate \(A\) with.respect.to \(t\)

Answer 3

\(\large A = 3\theta + 4\sin \theta + \dfrac{1}{2}\sin(2\theta)\)


\(\large \dfrac{d}{dt}(A) = ?\)

Answer 4

how would i set that up? :/

so dA/dt ? :/

Answer 5

yes, and keep in mind \(\theta\) itself is a function of \(t\), so u need to use chain rule

Answer 6

ermm

3+4sin+1/2sin ? :/

Answer 7

not quite sure how to differentiate this one :(

Answer 8

\(\large A = 3\theta + 4\sin \theta + \dfrac{1}{2}\sin(2\theta)\)


\(\large \dfrac{d}{dt}(A) = 3 \dfrac{d\theta}{dt} + 4\cos\theta \dfrac{d\theta}{dt} + \cos(2\theta) \dfrac{d\theta}{dt}\)

Answer 9

Notice that the \(\dfrac{d\theta}{dt}\) sticks in everytime u differentiate \(\theta\) with.respect.to \(t\)

Answer 10

Next plugin the given values and evaluate rate of change of Area : \(\dfrac{d}{dt}(A)\)

Answer 11

okay, and in this case, would dø/dt be 0.7 ?

Answer 12

yup !

Answer 13

and \(\theta = \dfrac{\pi}{2}\)

Answer 14

simply plug them in and evaluate

Answer 15

okay so we get this?

5.895055529? :/

Answer 16

doesnt look right. try again