If x² + y² = 5 and dx/dt = -3, then what is dy/dt when x = 1 and y = 2? Please show work

Question

amistre64 · Answer

dx/dt tells us that the value of x is moving at a rate of -3 for every unit of time that passes.  but that is a side not for the moment.

Lets get the derivative of the function implicitly since there is no (t) in the actual equation.  Implicit deriviation is the same as normal except that you leave in your answers because they dont become (1).

(d/dt)(x^2) + (d/dt)(y^2) = (d/dt)(5)

(dx/dt)2x + (dy/dt)2y = (d5/dt)0

get (dy/dt) by itself thru algebra techniques:

(dy/dt) = [(d5/dt)0 - (dx/dt)2x] / 2y

fill in what we know:

(dy/dt) = [0 -(-3)(1)]/2

(dy/dt) = 3/2

And there we go :)

anonymous · Answer

thanks alot i've been trying to solve that for a lil while now. makes sense, thank you. Are you good with word problems, too

amistre64 · Answer

lol....depends on the word problem :)

anonymous · Answer

right. well here you go. Boyle's law states that if the temperature of a gas remains constant, then PV = c, where P = pressure, V = volume and c is a constant. Given a quantity of gas at constant temperature, if V is  decreasing at a rate of 14 in³/sec, at what rate is P increasing

amistre64 · Answer

Owww....that gives me a headache..  sorry, but I havent tried that one yet.  It seems to be in every calc book, but I havent tried it yet.  sorry :)

I can do the one with how much work does it take to pump out liguid from odd shaped containers :)

anonymous · Answer

lol ok no problem