We have a bug moving alone the curve y = 4 - x^2/16. The distance is measured in feet. When the bug passes through point (4,3) its y-coordinate is increasing at 20 ft/sec so at what rate is its x-coordinate changing?

Question

anonymous · Answer

:/ sorry not good with this kind of stuff, i could call for help tho @taylorannbs @makayla_finkbeiner_ @Bookworm14 @aprilann143

anonymous · Answer

wow thanks man

anonymous · Answer

no prob

ganeshie8 · Answer

you're given :
$\dfrac{dy}{dt}  = 20$

ganeshie8 · Answer

you need to find $\dfrac{dx}{dt}$

ganeshie8 · Answer

differentiate the given function with.respect.to $t$

anonymous · Answer

wait this is lagging

ganeshie8 · Answer

yeah, just differentiate ur function,
plugin given values, 
solve for dx/dt

anonymous · Answer

so that is t/x + 1/8t^2 with implicit diff right?

ganeshie8 · Answer

$y = 4 - \dfrac{x^2}{16}$

ganeshie8 · Answer

Is that ur given curve ?

anonymous · Answer

ok so i need to find dx/dt of that right?

anonymous · Answer

I believe so, that would give me -t^2(x) right?

ganeshie8 · Answer

what do u mean u believe so ?
you're not given the question/equation in correct format ?

ganeshie8 · Answer

whats wid two `//` in the question ?

`y = 4 - x^2//16`


what kind of operator is a `//` ?

anonymous · Answer

ohhhh that was an accident

ganeshie8 · Answer

lol okay, take a snapshot of the question and attach if psble

anonymous · Answer

i changed it and made it right

ganeshie8 · Answer

okay :)

ganeshie8 · Answer

$y = 4 - \dfrac{x^2}{16}$

differentiate both sides with.respect.to $t$ :

$\dfrac{dy}{dt} = 0 - \dfrac{1}{16}(2x)\dfrac{dx}{dt}  $

ganeshie8 · Answer

^^simplify

anonymous · Answer

one second

anonymous · Answer

lol i'm horrible with this but I got x/2t + 4t/x

anonymous · Answer

wait no
dy/dt = -32x dx/dt

ganeshie8 · Answer

could u show me how u got that ?

ganeshie8 · Answer

careful, 2 is in numerator and 16 is in denominator

ganeshie8 · Answer

$\dfrac{dy}{dt} = 0 - \dfrac{1}{16}(2x)\dfrac{dx}{dt} $

simplifies to

$\dfrac{dy}{dt} =  - \dfrac{x}{8}\dfrac{dx}{dt} $

anonymous · Answer

oh well i got the other one by simplifying 0-1/16(2x)

ganeshie8 · Answer

plugin the given values :
$x = 4$
$\dfrac{dy}{dt} = 20$

and solve $\dfrac{dx}{dt}$

ganeshie8 · Answer

$\dfrac{dy}{dt} =  - \dfrac{x}{8}\dfrac{dx}{dt} $


$20 =  - \dfrac{4}{8}\dfrac{dx}{dt} $

ganeshie8 · Answer

solve $\dfrac{dx}{dt}$

anonymous · Answer

it's not -40 is it?

ganeshie8 · Answer

-40 is right !

anonymous · Answer

no way

anonymous · Answer

that's final?

ganeshie8 · Answer

thats final.

anonymous · Answer

well thanks a lot i mean i got a study guide and i need the help to get ready for this final