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3 years ago

How far did marcus racer travel after using five mushrooms?

Mathematics

1 answer:

Lelechka [254]3 years ago

4 0

50 miles or 20 yards but it doesn't matter

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If a x b express 12x(10x5)in simplest form

Mrac [35]

That's easy but I'll give the answer is 600

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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

The NASA Space Shuttle transports material to the International Space Station at a cost of $22,000 per kilogram. What is the num

elena-s [515]

Answer:

$ 5,500

Step-by-step explanation:

Simple, 1 kg = 1000 grams, so, 250 grams is a quarter, just divide the $22,000 by 4 = $ 5,500

6 0

3 years ago

Read 2 more answers

Look at the picture

ValentinkaMS [17]

Answer: 54

Step-by-step explanation:

3 times the square of -3 plus -5 times -3 plus 12

3 times 9 + 15 + 12

27+15+12=

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3 years ago

HURRRY QUICK!!!!!!<br><br> HELP ME ON THIS!!!!!!!!!!!!!!!!!!!!

Vitek1552 [10]

It is exponential growth because it says 18.36% "more than" and it can be linear because it does not stay at a constant rate of change. Answer: Exponential growth
Hope this helps!

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3 years ago

How far did marcus racer travel after using five mushrooms?​

How far did marcus racer travel after using five mushrooms?