2. First show that for the completely insulated bar ut = c2uxx; 0 < x < L; t > 0: ux(0; t) = 0; t > 0 ux(L; t) = 0; t > 0 u(x; 0) = f(x); 0 < x < L the separation of variables gives the solution u(x; t) = A0 + 1 Ancos n x e ( cn )2t L n=1 L X where 2 Z0 L n x An = f(x)cos dx; n = 1; 2; 3:::; L L then nd the temperature in the bar with L = ; c = 1; and f(x) = x

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The skating rink rented 872 pairs of skates during april and may.why? : if the skating rink rented three times the pair of skates in april during may, they rented 654 skates. 218 x 3 = 654then, if they want to know how many they rented during both april and may, then you just add 654 (may) and 218 (april) to give you 872 pairs of skates for both months.654 + 218 = 872hope this !