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NARA [144]
2 years ago
15

Which would be an equivalent way to write y= 2 - 3x ?

Mathematics
1 answer:
Fudgin [204]2 years ago
6 0
The answer is B, because the numbers in the equation are 2, and -3x. The signs have to stay with the numbers they are with. So if you move the 3 to the front you have to keep the negative with it.
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In this problem, you will use undetermined coefficients to solve the nonhomogeneous equation y′′+4y′+4y=12te^(−2t)−(8t+12) with
Zarrin [17]

First check the characteristic solution:

<em>y''</em> + 4<em>y'</em> + 4<em>y</em> = 0

has characteristic equation

<em>r</em> ² + 4<em>r</em> + 4 = (<em>r</em> + 2)² = 0

with a double root at <em>r</em> = -2, so the characteristic solution is

y_c = C_1e^{-2t} + C_2te^{-2t}

For the particular solution corresponding to 12te^{-2t}, we might first try the <em>ansatz</em>

y_p = (At+B)e^{-2t}

but e^{-2t} and te^{-2t} are already accounted for in the characteristic solution. So we instead use

y_p = (At^3+Bt^2)e^{-2t}

which has derivatives

{y_p}' = (-2At^3+(3A-2B)t^2+2Bt)e^{-2t}

{y_p}'' = (4At^3+(-12A+4B)t^2+(6A-8B)t+2B)e^{-2t}

Substituting these into the left side of the ODE gives

(4At^3+(-12A+4B)t^2+(6A-8B)t+2B)e^{-2t} + 4(-2At^3+(3A-2B)t^2+2Bt)e^{-2t} + 4(At^3+Bt^2)e^{-2t} \\\\ = (6At+2B)e^{-2t} = 12te^{-2t}

so that 6<em>A</em> = 12 and 2<em>B</em> = 0, or <em>A</em> = 2 and <em>B</em> = 0.

For the second solution corresponding to -8t-12, we use

y_p = Ct + D

with derivative

{y_p}' = C

{y_p}'' = 0

Substituting these gives

4C + 4(Ct+D) = 4Ct + 4C + 4D = -8t-12

so that 4<em>C</em> = -8 and 4<em>C</em> + 4<em>D</em> = -12, or <em>C</em> = -2 and <em>D</em> = -1.

Then the general solution to the ODE is

y = C_1e^{-2t} + C_2te^{-2t} + 2t^3e^{-2t} - 2t - 1

Given the initial conditions <em>y</em> (0) = -2 and <em>y'</em> (0) = 1, we have

-2 = C_1 - 1 \implies C_1 = -1

1 = -2C_1 + C_2 - 2 \implies C_2 = 1

and so the particular solution satisfying these conditions is

y = -e^{-2t} + te^{-2t} + 2t^3e^{-2t} - 2t - 1

or

\boxed{y = (2t^3+t-1)e^{-2t} - 2t - 1}

7 0
2 years ago
Do you think all rectangles are similar to each other? What about squares?
Dominik [7]

Answer: they are all similar

Step-by-step explanation: they all are the same shape no matter how long or tall they are

5 0
3 years ago
Read 2 more answers
Alejandro loves to go to the movies. He goes both at night and during the day. The cost of a matinee is 7 dollars. The cost of a
saw5 [17]

Answer:

<u>Alejandro went to 8 matinee shows and 4 evening shows.</u>

<u>Our system of equations:</u>

<u>x + y = 12</u>

<u>7x + 12y = 104</u>

Correct statement and question:

Alejandro loves to go to the movies. He goes both at night and during the day. The cost of a matinee is 7 dollars. The cost of an evening show is 12 dollars.

Alejandro went to see a total of 12 movies and spent $ 104. How many of each type of movie did he attend? Write a system of equations.

Source:

Previous question that can be found at brainly

Step-by-step explanation:

Step 1:

Let x to represent the number of matinee shows Alejandro went to.

Let y to represent the number of evening shows Alejandro went to.

Now, let's write our system of equations:

x + y = 12

7x + 12y = 104

*********************

x = 12 - y

*********************

7 (12 - y) + 12y = 104

84 - 7y + 12y = 104

5y = 104 - 84

5y = 20

y = 20/5

<u>y = 4 ⇒ x = 12 - 4 = 8</u>

<u>Alejandro went to 8 matinee shows and 4 evening shows.</u>

4 0
3 years ago
At a high school 7 student volunteer for a committtee how many different 5 person committees can be chosen
ki77a [65]
Total number of volunteer students for a committee = 7
Number of committee = 5

Number of ways of selecting the committee from the 7 volunteers = 7C5 = 7!/(5!*2!) = 21 ways.

There are 21 ways in which the 5-committee member can be selected from the 7 volunteers.
5 0
3 years ago
PLEASE HELP ILY IF YOU DO
agasfer [191]

Answer:

who the holy christmas is ily

Step-by-step explanation:

maybe you call your dog that

wait do you have a dog?

anyways

thanks for the points

3 0
2 years ago
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