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2 years ago

12

Find the value of x.

1 answer:

allsm [11]2 years ago

8 0

Answer:

x=51

Step-by-step explanation:

Formula: 35+16=x

Step 1: Simplify both sides of the equation.

35+16=x

(35+16)=x(Combine Like Terms)

51=x

51=x

Step 2: Flip the equation.

x=51

Hope this helps.

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Find the 22nd term of the following sequence:<br> 5, 8, 11, ...<br> 63 <br> 71<br> 14<br> 68

Wittaler [7]

68 is the 22nd term of the following sequence.

<u>Step-by-step explanation:</u>

The given sequence is with the same common difference between the two consecutive number in the series thus it is said to be the Arithmetic progression ( AP).
For finding the nth term in the AP we have a formula tn = a + (n-1) × d
Here a is the first term , n is the number of the term to be founded and d is the common difference between the two consecutive number in the series.
Thus here tn = 5 + ( 22 - 1 ) × 3.
On subtracting we get tn = 5 + (21 ) × 3
On multiplying we get tn = 5 + 63
After adding we get tn = 68. It is the 22nd term in the given series.

5 0

3 years ago

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

If every minute i geh 4.5 million yen, how much would i get in 24 hours.

hammer [34]

Step-by-step explanation:

hear is your answer in attachment

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2 years ago

Again.. your girl needs help again ..

Maru [420]

<u>Answer:</u> C. $3x^{2}$ + $3$

<u>Explanation:</u> you basically combine f(x) and g(x).

$2x^{2} + 5 + x^{2} -2$ combine your terms

$3x^{2} + 2$ your final answer

hope this helps!❤ from peachimin

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3 years ago

Graph the line with slope −1/2 and y-intercept −5.

Allushta [10]

First, we can write the equation of the line using the information provided:

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Now, we can create a table:

Finally, we can graph the line:

5 0

1 year ago