Both functions are the solution to the given Laplace solution.
Given Laplace's equation:
- 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)
Differentiate with respect to x as follows:
Differentiate with respect to y as follows:
Supplement the values in the given Laplace equation.
The given function in this case is the solution to the given Laplace equation.
(2)
Differentiate with respect to x as follows:
Differentiate with respect to y as follows:
Substitute the values to obtain:
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.
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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)
Answer:
-15
Step-by-step explanation:
-3+8-5. 5x3=15 and because it is -p it would be -15.
You have the area of the squares
100 in^2
area of a square = l*w
so length and width of the square both equal 10in
there are 4 squares going across the semi circle so...
diameter of semicircle is 10+10+10+10 =40in and radius is 20in
to find area of semicircle the formula is 1/2 pi r^2
so plug in the numbers 1/2(3.14) (20)^2 = 628 in ^2
now add that to area of big square part of window
40 inches length * 40 inches width = 1600in^2 (or you can just add them all up )
add up the areas now 1600+628= 2228 in^2
i think that is right
Answer:
Option B - 9 hours
Step-by-step explanation:
Given : Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions.
To find : In how many fewer hours of simultaneous operation could the production order be filled?
Solution :
Let the numbers of hours taken including additional machine i.e. 4 machines be 'x' hours.
So, 3 machines take 36 hours
and 4 machines take x hours.
Then,
i.e. 4 machines spend 27 hours to do work.
Number of fewer hours of simultaneous operation could the production order be filled is given by,
hours
Therefore, the work could be done in 9 hours less.
So, the correct answer is B.
Answer:
2/12
Step-by-step explanation:
4 + 2 = 6 + 6 = 12
there is 2 blue pens
so 2 out of 12
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