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2 years ago

Find the mode of the following data:

Mathematics

1 answer:

frutty [35]2 years ago

5 0

Answer:

Step-by-step explanation:

The data which has higher frequency in the given data set is the mode.

Mode = 33

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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:

brainly.com/question/14040033

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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

How do u solve 4p - 40 = 7(-2p + 2) ?

mr Goodwill [35]

Answer:

Simplifying

4p + -40 = 7(2p + 2)

Reorder the terms:

-40 + 4p = 7(2p + 2)

Reorder the terms:

-40 + 4p = 7(2 + 2p)

-40 + 4p = (2 * 7 + 2p * 7)

-40 + 4p = (14 + 14p)

Solving

-40 + 4p = 14 + 14p

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-14p' to each side of the equation.

-40 + 4p + -14p = 14 + 14p + -14p

Combine like terms: 4p + -14p = -10p

-40 + -10p = 14 + 14p + -14p

Combine like terms: 14p + -14p = 0

-40 + -10p = 14 + 0

-40 + -10p = 14

Add '40' to each side of the equation.

-40 + 40 + -10p = 14 + 40

Combine like terms: -40 + 40 = 0

0 + -10p = 14 + 40

-10p = 14 + 40

Combine like terms: 14 + 40 = 54

-10p = 54

Divide each side by '-10'.

p = -5.4

Simplifying

p = -5.4

Step-by-step explanation:

brainliest????

8 0

4 years ago

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What is the quotient? 6)12 A 2 B. 3 C. 4 D. 5

Dahasolnce [82]

Answer:

A.2 po

Step-by-step explanation:

himdi po ako sure sa answer ko

3 0

3 years ago

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Determine the total numbers of zero f(x) = 23 – 3x2 – 2x + 6

AleksandrR [38]

Answer:

f(x) = 29

Step-by-step explanation:

f(x)=23-(3x0)-(2X0)+6

f(x)=23+6

f(x)=29

4 0

3 years ago

Please help me on math and explain how to get the answer.

Lynna [10]

Answer:

x = 128

Step-by-step explanation:

ill name the empty angle y for clarification

y + 38 + 90 = 180

y + 128 = 180

y = 52

180 - y = x

180 - 52 = x

x = 128

4 0

3 years ago

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