anonymous
  • anonymous
Cartesian and polar coordinates are related through the transformation equations {x = r cos Theta or {r^2= x^2 + y^2 {Y = r sin theta { tan theta = y/x A. Evaluate the partial derivatives Xr, Yr,Xtheta, and Ytheta. B. Evaluate the partial derivatives Rx, Ry, Theta x, Theta y. C. For a function z = f(x,y), find z, and Ztheta, where x and y are expressed in terms of r and theta. D. for a function z = g(r,theta), find Zx, and Zy, where r and theta are expressed in terms of x and y. E. show that (∂z/∂x)^2 + (∂z/∂y)^2 = (∂z/∂r)^2 + 1/r^2 (∂z/∂theta)^2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
polars give me a headache still :)
anonymous
  • anonymous
we haven't learned this and she gives it as a quiz problem smh
amistre64
  • amistre64
a and b are simple enough id think

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amistre64
  • amistre64
z is a circle
anonymous
  • anonymous
lol i am not that smart. still trying to figure out the answer for other one
amistre64
  • amistre64
partials mean that the only thing changing is variable we are diffing with. wrt to r means that every thing that aint r is not changing, when things dont change they are consant. Xr = cos(t) ; Yr = sin(t)
amistre64
  • amistre64
x = r cos(t) ; Xr means that only r changes, everything else remains consant Xr = cos(t) then
amistre64
  • amistre64
Xt would mean that r doesnt change and remains constant .... Xt = -r sin(t)
anonymous
  • anonymous
this is for a and b right
amistre64
  • amistre64
that is the concepts behind a and b yes
anonymous
  • anonymous
yea
amistre64
  • amistre64
z = f(x,y); this ones a bit vague to me since it really doesnt provide us with a structure for f(x,y) other than to assume we use x and y in the rule for the function
amistre64
  • amistre64
z = xy - x^2 +3y would be a function of z in x and y
amistre64
  • amistre64
if we allow z to mimic the results of the vector function: z = we get a circle centered at the origin of radius r
anonymous
  • anonymous
i am so confused
amistre64
  • amistre64
to which: z^2 = r^2 -(x/r)^2 -(y/r)^2
amistre64
  • amistre64
lol, im just a little confused ;)
anonymous
  • anonymous
lol i have no clue whats going on
amistre64
  • amistre64
yeah, after a and b im lost :) srry
anonymous
  • anonymous
i am even lost on a and b

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