(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A two-dimensional temperature field is given by the expression [tex]T=4x^2y^2+3y^3[/tex]

(a) What is the magnitude and direction of the temperature gradient at the point (2,3)?

(b) What is the change in temperature [tex]dT/dS[/tex] at the point (2,3) in a direction along the curve [tex]3x-4y^2=-30[/tex] passing through the point (2,3)?

2. Relevant equations

[tex]T=4x^2y^2+3y^3[/tex]

[tex]3x-4y^2=-30[/tex]

3. The attempt at a solution

So part (a) is pretty easy. I just found the gradient and evaluated it at the given point. However, I'm stuck on part (b). I think I have to take the dot product of the gradient of T with some unit vector of that curve. However, I don't know how to formulate this dot product. I figure that I first evaluate the gradient of T at (2,3), and then get a unit vector for that curve, evaluate that result at (2,3), then take the dot product to get dT/dS. Is this correct? If so, how do I handle the RHS of the curve? Would I move it over to the LHS and then find the unit vector? Would the 30 have to be squared when finding the magnitude of the curve too? I guess I'm a little confused with how to handle the nonzero RHS.

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# Homework Help: Change in Temperature of a 2-D Temperature Field

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