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Kazeer [188]
4 years ago
15

Find the excluded value of the rational expression 2x + 6/4x - 8

Mathematics
2 answers:
alukav5142 [94]4 years ago
5 0
2x + (6/(4x)) - 8 = 2x + 2(3/(2x)) - 8  => excluded value is 0
<span>(2x + 6)/(4x - 8) = [2(x+3)]/[4(x-2)] = (x+3)/[2(x-2)] => excluded value is 2</span>
frozen [14]4 years ago
3 0

Answer:

for connections

1.a

2.c

3.d

4.c

Step-by-step explanation:

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I’m pretty sure it’s D
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Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x
djverab [1.8K]

I'll assume the ODE is

y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}

Solve the homogeneous ODE,

y'' - 3y' + 2y = 0

The characteristic equation

r^2 - 3r + 2 = (r - 1) (r - 2) = 0

has roots at r=1 and r=2. Then the characteristic solution is

y = C_1 e^x + C_2 e^{2x}

For nonhomogeneous ODE (1),

y'' - 3y' + 2y = e^x

consider the ansatz particular solution

y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x

Substituting this into (1) gives

a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1

For the nonhomogeneous ODE (2),

y'' - 3y' + 2y = e^{2x}

take the ansatz

y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}

Substitute (2) into the ODE to get

b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1

Lastly, for the nonhomogeneous ODE (3)

y'' - 3y' + 2y = e^{-x}

take the ansatz

y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}

and solve for c.

ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16

Then the general solution to the ODE is

\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}

6 0
2 years ago
Solve for x. Enter the solutions from least to greatest. 6x^2 +1 =487 lesser=x greater=x
jok3333 [9.3K]

Answer:

(-9, 9)

Step-by-step explanation:

6x^{2} +1 = 487                                             (Given)

       -1       -1                                     (Getting "x" alone)

6x^{2}  = 486                                        (Cont. Getting "x" alone)

÷6      ÷6                                                           ↓

x^{2} = 81                                                              ↓

\sqrt{x} ^2 = \sqrt{81}                           (9 and -9 squared are both equal to 81)

↓             ↓                                                        ↓

x = 9      x = -9                                            (Answer)

Hope this Helps! :)

<em>Have any questions? Ask below in the comments and I will try my best to answer.</em>

-SGO

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yaroslaw [1]

Answer:

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Step-by-step explanation:

It just is

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Answer:

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