The wave equation u_tt = u_xx , is given in the range t > 0 , x∈ |0, π| , with Dirichlet boundary conditions, u(0, t) = 0 , u( π ,t) = 0 . a. Find the general solution of the problem.
b. Identify the particular solution obeying the initial conditions:
u(x,0) = sin(x) , u_t( x ,0) = 2sin(x) - 3sin(2x)

step-by-step explanation:

this is not a question

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.