Question

@ganeshie8 do you get this one?

it's attached inside:)

Answer 1

The potential is changing at a rate of _________ units per second.

Answer 2

take the derivative with.respect.to.time

Answer 3

use chain rule

Answer 4

how would i set that up? :/ you mean taking derivative of that original equation?

Answer 5

\(\large \Phi = 2\pi\left(\sqrt{x^2+4} - x\right)\)


\(\large \dfrac{d\Phi}{dt} = \dfrac{d}{dt}2\pi\left(\sqrt{x^2+4} - x\right)\)

\(\large ~~~~~ = 2\pi\left(\dfrac{1}{2\sqrt{x^2+4}}\times 2x\times \dfrac{dx}{dt} - \dfrac{dx}{dt}\right)\)

Answer 6

plugin \(x=3\), \(\dfrac{dx}{dt} = -0.6\)

Answer 7

and evaluate

Answer 8

okay :)

and you end up getting this? :/

\[2\pi(\frac{ x }{ \sqrt{x^2+4} }-1)\]

Answer 9

and then plug in those values?

Answer 10

nope, dont simplify anything.
directly plugin the values

Answer 11

\(\large ~~~~~ = 2\pi\left(\dfrac{1}{2\sqrt{x^2+4}}\times 2x\times \dfrac{dx}{dt} - \dfrac{dx}{dt}\right)\)


plugin the given values

\(\large ~~~~~ = 2\pi\left(\dfrac{1}{2\sqrt{3^2+4}}\times 2(3)\times (-0.6) - (-0.6)\right)\)

Answer 12

ohh okay so we get this?

-37.00791305

:/

Answer 13

simplify

Answer 14

doesnt look right, try again

Answer 15

simply feed it to wolfram :
http://www.wolframalpha.com/input/?i=2*pi*%28+1%2F%282sqrt%283%5E2%2B4%29%29*%282*3%28-0.6%29%29+-+%28-0.6%29+++%29

Answer 16

ohh so it's 0.633155 ?

Answer 17

is that the rate?

0.633 units per second? :O

Answer 18

Yep !

Answer 19

awesome! thanks!! :D

Answer 20

np :)