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

Eight people were asked what the balance of their savings account at the beginning of the month was and how much it increased or decreased by the end of the month. create a scatter plot that represents the data that is shown in the table. the x-axis represents the beginning balance in thousands of dollars and the y-axis represents the change in the savings account in hundreds of dollars. name beginning balance (in thousands of dollars) change in savings account (in hundreds of dollars) jimmy 5 3 kendra 4 7 carlos 5 4 yolanda 3 1 shawn 2 5 laura 3 2 andy 5 6 georgia 4 3

Which is the graph of the piecewise function f(x)? f(x)=[tex]f(x) = \left \{ {{-x+1, x\leq 0 } \atop {x+1, x\ \textgreater \ 0}} \right.[/tex]

In the triangles, bc =de and ac fe.if the mzc is greater than the mze, then ab isdfelth