How to Solve for Jacobians and Pedal Form Equations in Scientific Notation

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Discussion Overview

The discussion revolves around solving for Jacobians and pedal form equations, specifically focusing on the calculation of the Jacobian determinant for given functions and converting a specific equation into pedal form. The scope includes mathematical reasoning and problem-solving related to these concepts.

Discussion Character

  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant requests a solution for the Jacobian determinant ∂(x,y,z)/∂(u,v,w) given the functions u = 2yz/x, v = 3zx/y, and w = 4xy/z, asserting that it should equal 1/96.
  • Another participant questions the original poster's understanding of the Jacobian and suggests that the difficulty may stem from the requirement to find ∂(x,y,z)/∂(u,v,w) instead of the reverse.
  • The original poster confirms familiarity with finding partial derivatives and acknowledges the functions provided in the problem.
  • A subsequent reply claims that the problem is solved without providing further details or verification.
  • Another participant seeks assistance with converting the equation y^2 = 4ax into pedal form, indicating they have struggled with the problem.

Areas of Agreement / Disagreement

There appears to be no consensus on the solution to the Jacobian problem, as the original poster's request remains unaddressed in terms of verification. Additionally, the pedal form equation remains unresolved, indicating multiple competing views or approaches without agreement.

Contextual Notes

The discussion does not clarify any assumptions or specific methods for calculating the Jacobian or converting to pedal form, leaving potential gaps in understanding the necessary steps or definitions involved.

ADITYABR
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I need the solution for this If u = 2yz/x, v= 3zx/y, w= 4xy/z Show that ∂(x,y.z)/∂(u,v,w) = 1/96. Please
 
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What, exactly, is your difficulty? Do you know what the "Jacobian" is? Do you know how to find the partial derivatives.

Perhaps the difficulty is that you are given u, v, and w as functions of x, y, and z but are asked for [itex]\partial(x, y, z)/\partial(u, v, w)[/itex] rather than [itex]\partial(u, v, w)/\partial(x, y, z)[/itex]? Not to worry!
[tex]\dfrac{\partial(x, y, y)}{\partial(u, v, w)}= \dfrac{1}{\dfrac{\partial(u, v, w)}{\partial(x, y, z)}}[/tex]
 
Yes I do know how to find. Yes I have given function w.r.t x, y, z as it was given in the problem to find the same as above. Thanks for the reply
 
Excellent! Problem solved.
 
I Need the solution to this equation y^2 = 4ax in pedal form? I tried but could not solve it . If anybody found it kindly send the answer and it would be great.
 

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