Will_the_Turtle

The distance of the midpoint from the equilibrium at time t=1.3 is approximately .265

$u_t=u_x{}_x+8 ,u(0,t)=-4 ,u(1,t)=4$ since we are looking for a steady state we are looking for when $$u_t=0$$ because our equation should not change with respect to time. By looking at our first equation we integrate up $$u_x{}_x$$ and net $$u=-4x^2+Ax+B$$ with A and B being some constants. We then solve for A and B using our initial conditions and get B=-4 and A=12 so our steady state looks like $$u(x,t)=-4x^2+12x-4$$

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 3 and its right end to -3. Sketch the temperature distribution at times

t=0,t=0.01,t=0.1, and t=10.

My dude just looks like he is super embarrassed to be on fire.

The temperature of the midpoint at the insulated edge at t=1s is 1.91ish as shown in the image below.

With no external heat source this is what my bar looks like in a steady state. at the vertex denoted by (30,0) the heat is about .947 in the steady state

My team matrix

[0,2,0,1,2,1,0,2],

  [1,0,1,2,1,0,2,2],

  [2,2,0,2,2,2,2,2],

  [2,1,0,0,1,2,2,2],

  [0,2,0,2,0,1,1,0],

  [2,2,1,1,2,0,2,2],

  [2,1,1,0,2,1,0,2],

  [0,1,0,0,2,0,0,0]

Team 3: rating = 0.5330684574735053
Team 6: rating = 0.44328808110881446
Team 4: rating = 0.3658903880213609
Team 2: rating = 0.3361884024157472
Team 7: rating = 0.3288985633701758
Team 1: rating = 0.2800826887310974
Team 5: rating = 0.27160622973048154
Team 8: rating = 0.10974860949549743

Team 3 is the best