Comments
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At $t=1s$, the temperature near the midpoint of the insulated edge of the triangle is approximately $.15480$.
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My heat flow equation was $$u_t=1u_{xx}+2$$ with boundary conditions of $$u(0,t) = 0$$ and $$u(1,t) = 7.$$ When $u_t = 0$ we can solve for $u_{xx}$ giving us $u_{xx}=-2$. Integrating this twice gives us $$u(x,t) = -x^2 + c_1x + c_2.$$ We can then solve for these constants using our boundary conditions mentioned above,…
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The temperature at the lower right corner is approximately 0.806 at a steady state.
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My matrix was: matrix = [ [0,3,3,3,1], [2,0,3,1,3], [3,3,0,3,1], [4,1,1,0,4], [1,1,3,4,0] ] and the eigen ranking was: Team 3: rating = 0.4627375562956863 Team 1: rating = 0.46273755629568625 Team 4: rating = 0.46088857575916814 Team 5: rating = 0.4269598459305646 Team 2: rating = 0.4207551766581456 Team 3 is barely ahead…
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A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by $$g(x)=6x^2-1x$$. At time $t=0$, its left end is set to temperature -2 and its right end to 2. Sketch the temperature distribution at times $$t=0,t=0.01,t=0.1, \text{ and } t=10.$$