Problem: A metal plate whose temperature at the point (x,y) is given T(x,y)=200-5x^2-3xy-y^2.

Carole Juarez

Carole Juarez

Answered question

2022-02-22

Problem: A metal plate whose temperature at the point (x,y) is given T(x,y)=2005x23xyy2. Given a function f(x,y), the vector f=<fx,fy> points in the direction of greatest increase for f.
Problem 1: Compute T(x,y)
Question 1: T(x,y)=<10x3y,3x2y>. Is it right?
Problem 2: Denote the position at time t by r(t)=(x(t),y(t)). We want r(t)=T(r(t)) for all t to ensure the temperature is increasing as much as possible. Interpret this equation as a system of linear ODEs with the form r=Ar
Question 2: not sure how to proceed.

Answer & Explanation

aksemaktjya

aksemaktjya

Beginner2022-02-23Added 6 answers

(i) yes (ii)
[x˙y˙]=[10332][xy]

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