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3 years ago

14

Look at this prism and its net. Rectangular prism with length labeled 5 meters, width labeled 7 meters, and height labeled 12 me

ters. Net of the same rectangular prism with the same dimensionsn labeled. What is the surface area of this rectangular prism? cm²

1 answer:

lord [1]3 years ago

4 0

The surface area is <span>358.</span>

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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

1 year ago

A supervisor wants to know the average number of hours worked by employees in a factory. There are 18 managers, 240 laborers, an

Vinil7 [7]

Answer:

9

Step-by-step explanation:

just too the quiz on edge

3 0

2 years ago

Math question picture attached

babunello [35]

To find the slope, you use the slope formula (m):

$m=\frac{y_2-y_1}{x_2-x_1}$ and plug in the two points

(-3, 4) = (x₁, y₁)

(2, -1) = (x₂, y₂)

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-1-4}{2-(-3)}$ [two negatives cancel each other out and become positive]

$m=\frac{-1-4}{2+3}$

$m=\frac{-5}{5}$

m = -1 The slope is -1

4 0

3 years ago

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gulaghasi [49]

Answer and Step-by-step explanation:

7. 70 - 180 = 110

8. 39 - 180 = 141

9. 81 - 180 = 99

10. 81 - 180 = 99

11. 115 - 180 = 65

12. 41+36 = 77 - 180 = 103

x = answer

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2 years ago

How do I answer the red question?

KengaRu [80]

Answer: who made this question I think you need to round 250 to the nearest whole number I’m not sure.

Step-by-step explanation:

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2 years ago

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