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4 years ago

What is 965,000,000,000,000 in scientific notation?

1 answer:

4 0

The answer is 9.65x10^14 because in order for the decimal point to be between 9 and 6 you need to move 14 decimal places back

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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:

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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

Please help, (AP is arithemtic progression)

defon

Answer:

p = 8

Step-by-step explanation:

The n th term of an AP is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₉ = 4 + 5p and d = 5, then

a₁ + 8d = 4 + 5p, that is

a₁ + 8(5) = 4 + 5p

a₁ + 40 = 4 + 5p ( subtract 40 from both sides )

a₁ = 5p - 36

a₂ = 5p - 36 + 5 = 5p - 31

a₃ = 5p - 31 + 5 = 5p - 26

a₄ = 5p - 26 + 5 = 5p - 21

Given that the sum of the first 4 terms = 7p - 10, then

5p - 36 + 5p - 31 + 5p - 26 + 5p - 21 = 7p - 10, that is

20p - 114 = 7p - 10 ( subtract 7p from both sides )

13p - 114 = - 10 ( add 114 to both sides )

13p = 104 ( divide both sides by 13 )

p = 8

7 0

3 years ago

What is the answer X=-2(6+4)

Digiron [165]

Answer:

X = -20

Step-by-step explanation:

X = -2(6+4)

^ add 6 and 4 together first because they are in parentheses

-2(10)

^ this parenthesis means you want to multiply -2 and 10

because 2 x 10 = 20

that must mean -2 x 10 = -20

therefore, the value of X is -20

X= -20

3 0

3 years ago

Set both given equations equal to zero, then combine them into standard form equation. Simplify if possible

sergij07 [2.7K]

Answer:

4x-6=4+4y+8=2

Step-by-step explanation:

3 0

3 years ago

Please Help me, what the answer

Rus_ich [418]

It’s either 1. Or 2. I’m really not sure which one tho so sorry! There’s not enough information given but if I had to guesstimate I would say 1.

6 0

3 years ago