Comments
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Here is my Matrix: M=[ [0,4,1,2,3], [4,0,2,1,4], [3,4,0,4,4], [1,3,2,0,2], [3,4,3,1,0] ] And here is my team ranking: Team 3: rating = 0.5621626778711195 Team 5: rating = 0.45596356825094614 Team 2: rating = 0.4451535544402384 Team 1: rating = 0.40012824676275205 Team 4: rating = 0.34322885535517655
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The temperature at the lower right end of the bar looks to be roughly 0.9467 in the steady state.
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The temperature at the midpoint of the insulated side of the triangle when we reached one second is around 0.1725.
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A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by $$g(x)=4x^2−1x.$$ At time $t=0$, its left end is set to temperature 2 and its right end to 0. Here is my (tentative) sketch the temperature distribution at times $t=0$, $t=0.01$, $t=0.1$, and $t=10$.
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Heat flow with a constant internal heat source is governed by u_t = 1u_{xx}+7, u(0,t)=-2, u(1,t)=4. This is how I found the steady state temperature distribution. For the steady state temperature distribution, $u(x,t)$ does not change with respect to time so $u_t=0$, Then for my equation $$0=u_{xx}+7,$$ $$u_{xx}=-7.$$ Then…
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The displacement from equilibrium of the midpoint of the string at time $t=1.2$ seconds into the vibration is $-0.28$.