Comments
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My team matrix: [ [0,3,3,2,2], [4,0,1,3,1], [1,4,0,4,2], [2,1,3,0,2], [3,1,4,2,0] } Team 3: rating = 0.4848807961654844 Team 5: rating = 0.47317429197368976 Team 1: rating = 0.4632070845269747 Team 2: rating = 0.4163867448282543 Team 4: rating = 0.39122624975897735 Team 3 had the highest rating at 0.48488.
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With my unique conditions I formed a polygon where $\kappa=0$ and $f=0$, meaning there was no external heat source present and no signs of growth/decay. After reaching steady state the temperature in the lower right hand corner of the polygon was $u=0.87677$.
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The temperature at the midpoint of the insulated side of the triangle at 1s was 0.096.
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(Redo) A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by: $$g(x)=4x^2-2x$$ At time t=0, its left end is set to t=-3 and the right end t=-1. Sketch of temperature distribution at times t=0, t=.01, t=.1, and t=10 is below:
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My heat flow problem where I found the steady state temperature distribution: $$u_t=3u_{xx}+1$$ My boundary conditions were: $$u(0,t)=-3$$ and $$u(1,t)=4$$ Since $u_t=0$ when the bar is in steady state I used this to solve for $u_{xx}$, which I got was $u_{xx}=\frac{-1}{3}$. Then integrating twice:…
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The displacement of the midpoint from the equilibrium at the time 1.1s is -0.121. (redo)