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Liono4ka [1.6K]
3 years ago
14

2x-3(1-x)+7=-5 Please show steps

Mathematics
1 answer:
ad-work [718]3 years ago
7 0
Hope this helps :333

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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
Is 3 sin(alpha)+4 cos(beta)=8 possible
babunello [35]
No because the maximum amount for sin and cos is 1.if alpha is 90 and beta is 0 the answer is 7 so it's not right.
3 0
3 years ago
Read 2 more answers
Work out the area of this circle.
Troyanec [42]

Answer:

36π mm²

Step-by-step explanation:

Formula: πr²

r=radius

r=6

π6²=36π

6 0
2 years ago
James and Sarah went out to lunch. The price of lunch for both of them was $40. They tipped their server 20% of that amount. How
zmey [24]

Answer:

Each person paid $24.

Step-by-step explanation:

1. Find 20% of 40. Since 20% is equal to 1/5, we can divide 40 by 5 to get 8. Together they tipped $8.

2. We know that the total amount they paid was $48, so we divide that in half to get the answer. 48 divided by 2 is 24.

4 0
2 years ago
Read 2 more answers
Math 7 Grade 7. Can anyone help me answer these questions?
zaharov [31]
1. What is the opposite of -2?  2

2. When we add opposites together they will always equal = ? 0

This is also known as what ?
additive inverse 

Adding with integers with SAME signs.

-8 + -3 = -11

-12 + -15 = -27

-3 + -9 + -25 = -37
6 0
3 years ago
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