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3 years ago

10

Jason worked 3 hours more than Keith. Jason worked 12 hours. Which equation represents this situation, if k is the numbers of ho

urs Keith worked?

1 answer:

ycow [4]3 years ago

8 0

Answer:

j=k+3 (j=jason k+kieth)

Step-by-step explanation:

he did thrhee more so it will be adding 3 to k

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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

1 year ago

What values of x is x2+2x=24 true

agasfer [191]

The answer is x= 4 and x= -6

4 0

3 years ago

Read 2 more answers

mr Goodwill [35]

3/4, x, and y that is the answer

6 0

3 years ago

Read 2 more answers

Evan randomly selects 30 marbles from a bag. His data is given in the table.

Igoryamba

The probability of selecting a yellow marble is #of yellow marbles/total # of marbles= 6/30 or .2 or 20%

If there are 300 marbles in the bag, a good estimate for the total number of red marbles in the bag is 90.

9/30=.3 = the percentage of red marbles
.3(300) = 90

3 0

1 year ago

This year, for the spring musical, the Drama Club sold 150% of the number of tickets they sold last year. Last year, the club so

babunello [35]

Answer:

C. 342

Step-by-step explanation:

This year, 150% of last year's tickets were sold.

Last year, 228 tickets were sold.

150% as a fraction is 150/100

To find the amount of tickets sold this year, we take the 150/100 and multiply it by 228:

150/100*228= 342 tickets

7 0

3 years ago