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2 years ago

Which of the following equations describes the line shown below? Check all that apply.

Mathematics

1 answer:

kondaur [170]2 years ago

7 0

Answer:

B and C

Step-by-step explanation:

Slope: 4-(-1)/-3-(-1)

Slope: 5/-2

Slope:-5/2

Point Slope form: y+1=-5/2(x+1)

Point Slope form: y-4=-5/2(x+3)

Correct answers are B and C

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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

9 months ago

At BYU-Idaho there has been a lot of interest in the performance of students in online classes. Generally, administrators are in

blondinia [14]

Answer:

d. Yes, all of the expected counts are greater than or equal to 5

Step-by-step explanation:

Yes, the requirements satisfied to conduct a hypothesis test and all of the expected counts are greater than or equal to 5.

6 0

2 years ago

52,908 round to the nearest hundred.

IrinaVladis [17]

The hundredth is the 3rd number after the decimal place (so the 9). Look at the number before it and if it is 5 or above then round it to the next hundredth. In this case it is only a zero so we don't change the 9 just substitute it 0's. Therefore the answer is 52,900.

If you need further help let me know, hope this helped you.

6 0

2 years ago

What is the vertex form of y=x^2+4x minus 7

Inessa [10]

Answer: Hello Luv........

Complete the square to find the vertex:

(−2,−11)

Step-by-step explanation:

y=x2+4x−7

=x2+4x+4−11

=(x+2)2−11

Mark me brainest please.

Hope this helps!

Anna ♥

6 0

2 years ago

Help me please this is my last question

almond37 [142]

Already answered the other question which was the same
8= 2 liters of punch
16= 4 liters of punch
20= 5 liters of punch
28= 7 liters of punch

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2 years ago