TEAM PROJECT. Series for Dirichlet and Neumann Problems A) Show that un rncos ne, un = rn sin ne, n = 0, 1, are solutions of Laplace's equation V2u = 0 with V2u given by (5). (What would un be in Cartesian coordinates? Experiment with small n)
B) Dirichlet problem:
Assuming that termwise differentiation is permissible, show that a solution of the Laplace equation in the disk r < R satisfying the boundary condition u(R, 0) = f(e) (R and fgiven) is
u(r) = ao + Σ (an(/rR)n cos ne
where an, b are the Fourier coefficients of f.
C) Dirichlet problem. Solve the Dirichlet problem using (20) if R = 1 and the boundary values are u(e) = -100 volts if -T<< 0, u (8) = 100 volts if 0<

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation: