Determine whether each of the following functions is a solution of laplace's equation uxx + uyy = 0. (select all that apply.) u = e^(−x) cos(y) − e^(−y) cos(x) u = sin(x) cosh(y) + cos(x) sinh(y)

Answer with Step-by-step explanation:

We are given that Laplace's equation

We have to determine given function is  solution of given laplace's equation.

If a  function is solution of given Laplace's  equation then  it satisfy the solution.

1.

Differentiate w.r.t x

Then, we get

Again differentiate w.r.t x

Now differentiate u w.r.t y

Again differentiate w.r.t y

Substitute the values in given Laplace's equation

Hence, given function is a solution of given Laplace's equation.

2.

Differentiate w.r.t x

Again differentiate w.r.t x

Now, differentiate u w.r.t y

Again differentiate w.r.t y

Substitute the values then we get

Hence, given function is a solution of given Laplace's equation.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

7/2

(decimal: 3.5)

welcome ; )

step-by-step explanation: