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3 years ago

Pouvez-vous trouvez quatre nombre entier consécutif dont la somme vaut 1254 Et merci à vous

Mathematics

1 answer:

seropon [69]3 years ago

8 0

Answer:

312.5, 313.5, 314.5, 315.5

Step-by-step explanation:

n + (n + 1) + (n +2) + (n+3) = 1254.

Solving gives, 4n + 6 = 1254.

1254/4 = 313.5 as our n.

Substituting for our n's: 313.5 + 313.5 + 1 + 313.5 + 2 313.5 + 3 =

312.5 + 313.5 + 314.5 + 315.5.

<u>Check:</u>

312.5 + 313.5 + 314.5 + 315.5 = 1254.

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For a field trip 20 students rode in cars and the rest filled eight buses. How many students were in each bus if 340 students we

Varvara68 [4.7K]

Answer:

40 students were in each bus on the trip.

Step-by-step explanation:

Since 20 students rode in cars, subtract 20 from 340. This results in 320.

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This results us in 40 students in each bus.

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3 years ago

Read 2 more answers

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

$\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}$

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1 year ago

runners in a marathon are randomly assigned to one of ten corrals to start, and each given a green, blue, or red shirt to wear.

OleMash [197]

Answer:

There isn't a question

Step-by-step explanation:

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2 years ago

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Answer:

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Step-by-step explanation:

Given the ratio

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3 years ago

Drupady [299]

Answer:

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Step-by-step explanation:

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3 years ago