Solve Laplace’s equation inside a rectangle 0 ≤ x ≤ L, 0 ≤ y ≤ H, with the following boundary conditions. [Hint: Separate variables. If there are two homogeneous boundary conditions in y, letu(x, y)=h(x)φ(y), and if there are two homogeneous boundary conditions in x, letu(x, y)=φ(x)h(y).]:

∂u /∂x (0,y) = 0,

∂u /∂x (L, y) = 0,

u(x,0) = 0,

u(x, H)=f(x)

A)a square brown tarp has a square green patch green in the corner the side length of the tarp is (x + 8) and the side length of the patch is x what is the area of the brown part of the tarpb)a square red placemat has a gold square in the corner the side length of the gold square is (x - 2) inches with the width of the red region is 4 in what is the area of the red part of the placemat