anonymous
  • anonymous
find xy+(z^3)x-2yz=0 in terms of z
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
whts in terms of z mean?
anonymous
  • anonymous
the answer should be z= f(x,y). so i am asking what f(x,y) is
amistre64
  • amistre64
x.z^3 -2yz = -xy

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amistre64
  • amistre64
z(-2y +x.z^2) = -xy -2y +x.z^2 - -xy/z
anonymous
  • anonymous
It's complicated to solve for z.
anonymous
  • anonymous
yeah its a cubic eqn in z
anonymous
  • anonymous
Could you write the original question, if it is not this?
amistre64
  • amistre64
-2y +x.z^2 = -xy/z x.z^2 = (-xy+2yz)/z z^3 = (-xy+2yz)/x
anonymous
  • anonymous
i am supposed to find dz/dx at the point (1,1,1) of that equation
anonymous
  • anonymous
then say that
anonymous
  • anonymous
spo i assumed i needed z as a function of x and y
amistre64
  • amistre64
you dont need to solve for z then...
anonymous
  • anonymous
u dont need to..i think not
amistre64
  • amistre64
dz/dx = g(F).d(xbar)/dx
anonymous
  • anonymous
ok, sorry about tha
anonymous
  • anonymous
You don't have to solve for z.
anonymous
  • anonymous
bt then how to do it???
amistre64
  • amistre64
get the gradient vector but partialling the equation of the plane there
amistre64
  • amistre64
get the gradient vector but partialling the equation of the plane there
amistre64
  • amistre64
F= a = dz/dx...but not that dz/dx...the funny looking one lol
anonymous
  • anonymous
then do df/dx / df/dz?
amistre64
  • amistre64
amistre64
  • amistre64
plug in the values from your point know to get the gradianet vector
amistre64
  • amistre64
<2,-1,1> is your normal vector/gradient..
anonymous
  • anonymous
oh ok, i got the gradient vector, then plug in the point (1,1,1) to df/dx to get the answer?
amistre64
  • amistre64
dot product that with the vecotr that is the point...<1,1,1>
anonymous
  • anonymous
i got <2, -1, 1> yes
amistre64
  • amistre64
2(x-1)-1(y-1)+1(z-1) = dz/dx i think :)
anonymous
  • anonymous
is it right??
anonymous
  • anonymous
is that the plane equation?
anonymous
  • anonymous
i dont have the answer
amistre64
  • amistre64
that is the plane equation
anonymous
  • anonymous
doesnt the gradient vector give ... in that case we can simply do df/dx / df/dz???
anonymous
  • anonymous
the answer isnt an equation...its a value
amistre64
  • amistre64
him; dunno havent read that far yet :)
anonymous
  • anonymous
thats wht m sayin
anonymous
  • anonymous
is the answer 2???
amistre64
  • amistre64
the answer would be 2 then right?
amistre64
  • amistre64
gradient . point
anonymous
  • anonymous
i think so! thanks!
anonymous
  • anonymous
is it 2??
anonymous
  • anonymous
i dont know the value, but it seems right
anonymous
  • anonymous
u understood how it ws done?
amistre64
  • amistre64
i dont think I evenknow how it was done lol
anonymous
  • anonymous
I got -2.
anonymous
  • anonymous
yes, get the gradient, and plug in the x,y and z valuse of the point into the gradient and divide df/dx by df/dz to get dz/dx right?
anonymous
  • anonymous
Not entirely sure though.
anonymous
  • anonymous
i thnk it shld be right..there might b calculation errors bt b surev f d method
amistre64
  • amistre64
<2,-1,1> <1, 1,1> --------- 2 -1 +1 = 2
anonymous
  • anonymous
so i said
anonymous
  • anonymous
david wht grade u in?
anonymous
  • anonymous
im a sophomore in college. im studying for my calc 3 final

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