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4 years ago

11

How would i factor 10x^2 89x-9

1 answer:

Cerrena [4.2K]4 years ago

3 0

I hope this helps you

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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

2 years ago

1. Indicate the number of significant figures in each of the following quantities:

shutvik [7]

Answer:

(a) 3

(b) 4

(c) 3

Step-by-step explanation:

To find the number of significant figure, ignore all zeros on the left and count the remaing digits.

(a) ignore 0.0, so 590 is 3 s. f.

(b) no zeros to the left, so 4 s. f.

(c) ignore 0.00, so 122 is 3 s. f.

6 0

3 years ago

Mallory is 2 years older than three times her brother Jake’s age. Let j represent Jake’s age. During the Strategize step of the

DedPeter [7]

Let j = Jake's age.
Because Mallory is 2 years older than three times Jake, Mallory's age is
3j + 2.

Answer: Mallory's age is 3j + 2

6 0

4 years ago

Can anyone please help me with this

alekssr [168]

Answer:

no

Step-by-step explanation:

The correct explanation is A

$\frac{x^{m} }{a^{n} }$ = $a^{(m-n)}$

Thus

$\frac{9.2}{4}$ × $\frac{10^{8} }{10^{-3} }$

= 2.3 × $10^{(8-(-3))}$

= 2.3 × $10^{11}$

6 0

3 years ago

Helppppp me pls asp plssss

Mariulka [41]

8 pt = 4 qt
1 qt = 4 c? I think it’s asking for cups
8qt = 2 gal
4 qt = 8 pt
5 pts = 10 c
2 pts = 4 c

4 0

3 years ago