Suppose that x=x(t) and y=y(t) are both functions of t. If
y^2+xy−3x=−5,
and dy/dt=−5 when x=3 and y=−4, what is dx/dt?

Question

Suppose that x=x(t) and y=y(t) are both functions of t. If
y^2+xy−3x=−5,
and dy/dt=−5 when x=3 and y=−4, what is dx/dt?

anonymous · Answer

@jim_thompson5910 could you help guide me through this

jim_thompson5910 · Answer

y^2+xy−3x=−5

d/dt[  y^2+xy−3x ] = d/dt[ −5 ]

2y*dy/dt + y*dx/dt + x*dy/dt - 3x*dx/dt = 0

does that help?

anonymous · Answer

ok il see what i can do

anonymous · Answer

so i just need to derive everything, and then plug in the numbers given?

jim_thompson5910 · Answer

exactly

jim_thompson5910 · Answer

the derivation is already done, you just need to plug in everything and solve for dx/dt

anonymous · Answer

ok but for my other problems, also how do you know if it should be a dy/dt or a dx/dt?

jim_thompson5910 · Answer

well in this case, they give you the value of dy/dt and they want you to solve for dx/dt

jim_thompson5910 · Answer

so it's based on the instructions

anonymous · Answer

ok so the answer is 25/7

anonymous · Answer

this next one im going to try to figure out on my own

jim_thompson5910 · Answer

no it's not 25/7

anonymous · Answer

i just plugged it in and it worked

jim_thompson5910 · Answer

it's saying 25/7 is the correct answer?

jim_thompson5910 · Answer

hmm i must be missing a sign somewhere

anonymous · Answer

ya

anonymous · Answer

Suppose that x=x(t) and y=y(t) are both functions of t. If
y2+x=27,
and dydt=−4 when x=2 and y=5, what is dxdt?

anonymous · Answer

so we have 2y(dy/dt)+(dx/dy)=0 correct?

jim_thompson5910 · Answer

yes so far so good

anonymous · Answer

dx/dt=40

anonymous · Answer

Let A be the area of a circle with radius r. If drdt=4, find dAdt when r=1
so A=pi(r)^2

jim_thompson5910 · Answer

A = pi*r^2

dA/dt = pi*2*r*dr/dt

anonymous · Answer

dA/dt=pi(2rdr/dt)

anonymous · Answer

dA/dt=pi*2*1*4

anonymous · Answer

Find the rate of increase (with respect to r) in the surface area (S=4πr2) of a spherical balloon when:
(A) r=2 inches → Rate of increase = 

(B) r=4 inches → Rate of increase = 

(C) r=6 inches → Rate of increase =

anonymous · Answer

@jim_thompson5910 sorry to keep bothering you, but no idea how to do this one

jim_thompson5910 · Answer

S = 4pi*r^2

dS/dt = 4pi*2*r*dr/dt

jim_thompson5910 · Answer

you would plug in the radius (for each part), but unfortunately dr/dt is missing...hmm

jim_thompson5910 · Answer

that info is probably buried somewhere (else)? idk

anonymous · Answer

ok thank you

jim_thompson5910 · Answer

np