What is the answer to <br> 5 + 3 x 3x -2 X=2

Determine whether each of the following functions is a solution of laplace's equation uxx uyy = 0.

ratelena [41]

Both functions are the solution to the given Laplace solution.

Given Laplace's equation: $u_{x x}+u_{y y}=0$

We must determine whether a given function is the solution to a given Laplace equation.
If a function is a solution to a given Laplace's equation, it satisfies the solution.

(1) $u=e^{-x} \cos y-e^{-y} \cos x$

Differentiate with respect to x as follows:

$u_x=-e^{-x} \cos y+e^{-y} \sin x\\u_{x x}=e^{-x} \cos y+e^{-y} \cos x$

Differentiate with respect to y as follows:

$u_{x x}=e^{-x} \cos y+e^{-y} \cos x\\u_{y y}=-e^{-x} \cos y-e^{-y} \cos x$

Supplement the values in the given Laplace equation.

$e^{-x} \cos y+e^{-y} \cos x-e^{-x} \cos y-e^{-y} \cos x=0$

The given function in this case is the solution to the given Laplace equation.

(2) $u=\sin x \cosh y+\cos x \sinh y$

Differentiate with respect to x as follows:

$u_x=\cos x \cosh y-\sin x \sinh y\\u_{x x}=-\sin x \cosh y-\cos x \sinh y$

Differentiate with respect to y as follows:

$u_y=\sin x \sinh y+\cos x \cosh y\\u_{y y}=\sin x \cosh y+\cos x \sinh y$

Substitute the values to obtain:

$-\sin x \cosh y-\cos x \sinh y+\sin x \cosh y+\cos x \sinh y=0$
The given function in this case is the solution to the given Laplace equation.

Therefore, both functions are the solution to the given Laplace solution.

Know more about Laplace's equation here:

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The correct question is given below:
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)

6 0

2 years ago

A jam recipe requires 3 quarts of raspberries. Raspberries are available in 1.5 pint containers at a grocery store. How many con

attashe74 [19]

There are two pints per quart

3 q * 2 p/qt = 6 pints needed

6 pint /1.5 pint/container = 4 containers

4 0

3 years ago

Lina is packing to move to a new house. She has 561 items to transfer to the new house. 36 of the items are large items that wil

Lyrx [107]

Answer: See explanation

Step-by-step explanation:

Your question isn't complete but let me give different scenarios to help you solve.

Firstly, assuming we want to calculate the amount of items left after the large items are carried alone, this will be:

= 561 - 36

= 525

Secondly, if we want to know the percentage of the large items that will be carried alone. This will be:

= 36/561 × 100.

= 6.42%

Thirdly, if you want to know the percentage of the items that will be left after the large ones have been carried alone. This will be:

= 100% - 6.42%

= 93.58%

5 0

3 years ago

Plz help like fr help

MrRissso [65]

The answer is (2,28).

8 0

2 years ago

Read 2 more answers

A parachutist's speed during a free fall reaches 264 feet per second. What is this speed in meters per second? At this speed, ho

Paul [167]

Answer: They will fall 800 meters. And they are falling 80 meters per second.

Step-by-step explanation: You must first take 264 divided by 3.3 which equals 80, then multiply is by 10.

6 0

3 years ago

What is the answer to 5 + 3 x 3x -2 X=2