Find the solution u(x, y) of laplace's equation in the rectangle 0 < x < a, 0 < y < b, that satisfies the boundary conditionsu(0, y) = 0, u(a, y) = 0, 0< y< b, u(x, 0) = 0, u(x, b) = g(x), 0 ≤ x ≤ a.

Step-by-step explanation:

The Laplace's equation in rectangular coordinates is:

For the solution, we assume that u can be write as

Replace

Divide

The only way that this can be true, is that every term is the same constant, so we say that

With a constant.

Now, we solve every part. For

The solution is:

For

Is the differential equation for a harmonic oscillator, so the solution is

Now, we evaluate the boundary conditions:

The other

For :

So,

The other condition:

So,

$32,660

step-by-step explanation:

a net is a diagram that shows a “flattened” view of a solid. in a net, each face and base is shown with all of its dimensions. a net can also serve as a pattern to build a three-dimensional solid.

a pyramid is a three-dimensional object with a base that is a polygon and triangular faces that meet at one vertex.

" the net of a triangular pyramid consists of four triangles. the base here we are given of the pyramid is a equilateral   triangle, and the lateral faces are also triangles "