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3 years ago

3x2 - 4x + 2

Mathematics

1 answer:

Oksana_A [137]3 years ago

6 0

Answer:

Step-by-step explanation:

A quadratic trinomial has the form of ax² + bx + c

e.g. 3x² + 4x + 2

A quadratic binomial has the form of ax² + bx

e.g. 3x² + 4x

A cubic binomial has the form : ax³ + bx

3x³ + 4x

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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

#SPJ4

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)

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2 years ago

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lisov135 [29]

Answer:

Then the desired equation is y = -2x - 6.

Step-by-step explanation:

As we move from point (-3, 0) to point (0, -6), x increases by 3 and y decreases by 6. Thus, the slope of the line segment connecting these two points is m = rise / run = -6/3 = -2.

Now use the slope-intercept equation of a straight line to determine the y-intercept of this line:

y = mx + b becomes 0 = -2(-3) + b, so that b = -6.

Then the desired equation is y = -2x - 6.

Check: Does (0, -6) satisfy y = -2x - 6? Is -6 = -2(0) - 6 true? YES

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If an integer is both a square and a cube, it can be of the form:
(a3)^2
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49k^2
, which is in the form of 7 times something
49k^2=7×(7k^2)
Now put
a^3=7k+−1 Square it
and you'll get a number in the form of (7times something +1)

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ANSWER: no

EXPLAIN: because a proportional relationship graph would have a straight line running through the origin

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Liono4ka [1.6K]

Answer:

Step-by-step explanation:

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