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2 years ago

Figure lmno is a parrellelogram The sum of measures of angles l and m is

Mathematics

1 answer:

snow_tiger [21]2 years ago

7 0

Answer:

l+m = 180°{being co-interior angle}

Step-by-step explanation:

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What is the factored form of 8X^2 +12X?

pogonyaev

The highest common factor of both terms is 4x, so take this out by dividing each term by 4x

8x^2 / 4x = 2x
12x / 4x = 3

So the factored form is:
4x(2x+3)

8 0

2 years ago

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

1 year ago

What is the value for f(x)4^2x -100 when x=2 ?<br><br> (the ^2x is a exponent)

PolarNik [594]

Answer:

156

Step-by-step explanation:

f(x)= 4^(2x) -100

Let x =2

f(2)= 4^(2*2) -100

= 4^4 - 100

= 256 -100

= 156

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2 years ago

What's the length of the missing leg?<br><br>

ValentinkaMS [17]

Answer:

Step-by-step explanation:

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2 years ago

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Levart [38]

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Step-by-step explanation:i got it right on the quiz

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1 year ago