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slamgirl [31]
3 years ago
11

Which expression is the factorization of x^2 + 10x + 21?

Mathematics
2 answers:
Llana [10]3 years ago
7 0

Answer:

(x+3)(x+7)

Step-by-step explanation:

umka21 [38]3 years ago
5 0

Answer:

(x + 3)(x + 7).

Step-by-step explanation:

x^2 + 10x + 21.

You need  2 numbers whose product is the last number in the function (+21) and whose sum is the coefficient of x (+10).

These are + 3 and + 7, so the factors are:

(x + 3)(x + 7).

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

#SPJ4

The correct question is given below:
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