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2 years ago

The oblique rectangular prism below has a length of 6 cm, a width of 8 cm, and a height

Mathematics

1 answer:

Rufina [12.5K]2 years ago

6 0

Answer:

48 , 336

Step-by-step explanation:

B= 6 x 8 = 48

V=BH

V=48 x 7

V= 336

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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

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

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1 year ago

90 out of 120 students in your grade are girls at your school. What percentage are boys?

sesenic [268]

30% Bc there are 30 boys and 90 girls or it’s 10% boys

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3 years ago

Elsa's magic wand can cast 53 spells. Her wand can cast 17fewer spells than her sister Anna's wand, which is a little bigger and

Mademuasel [1]

Answer:

Anna's wand can cast 70 spells

Step-by-step explanation:

Elsa's wand can cast 53 spells

her wand casts 17 fewer cells than her sister Anna's

Amount of spells cast by Anna's wand = ?

We write the question down in the form of an equation

$x - 17 = 53$

where $x$ is the amount of spells Anna's wand can cast.

we then proceed to solve by collecting like terms to different sides of the equation. We'll have

$x = 53 + 17$

which leaves us with

$x = 70$

This means that Anna's wand can cast 70 spells.

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Ilya [14]

169 because you have to add the angles from the inside and the firat angke is 90

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FinnZ [79.3K]

Answer:

x² + x - 30

Step-by-step explanation:

Given

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Each term in the second factor is multiplied by each term in the first factor, that is

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= x² + x - 30

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3 years ago