Comments
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My matrix was: matrix = [ [0,2,1,2,4], [4,0,4,4,2], [4,2,0,1,2], [3,2,4,0,4], [4,1,4,4,0] ] The ranking for my league is: Team 2: rating = 0.5165517842331686 Team 4: rating = 0.48670829470439997 Team 5: rating = 0.47767125643216296 Team 1: rating = 0.3784150823149017 Team 3: rating = 0.3534423380504801 Team 2 is the best.
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The temperature near the midpoint of the insulated edge of the triangle at $t=1s$ is about $0.17972$
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The temperature in the lower right hand corner of the bar at steady state is roughly 0.91361.
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The temperature near the midpoint of the insulated edge of the triangle at $t=1s$ is $0.57029$
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A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by $$g(x) = 4x^2 - 2x.$$ At time $t=0$ its left end is set to temperature -1 and its right end to -3. Sketch the temperature distribution at times $t=0, \: t=0.01, \: t=0.1, \text{ and } t=10.$
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Heat flow with a constant internal heat source is governed by $$u_t = 2u_{xx} + 3, u(0,t)=-4, u(1,t)=3.$$ Find the steady state temperature distribution. Steady state occurs when $u_t=0$. Solving the above equation for $u_{xx}$ given $u_t=0$, yields $u_{xx}=-3/2$. Integrating this twice gives $u(x)=\frac{-3}{4}x^2+cx+d.$…
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The displacement of the midpoint from equilibrium at time $t=1.5$ seconds is approximately $-0.376$