Ask question

Ask question

All categories

3 years ago

12

2. The long-jump pit was recently rebuilt to make it level with the runway. Volunteers provided pieces of

1 answer:

lakkis [162]3 years ago

8 0

Answer:2. It’s 24.58

How many boards did the volunteers supply round your calculations to the nearest hundred- 13.44

How many whole boards-14

Step-by-step explanation:

You might be interested in

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

HELP ME PLS I WILL GIVE YOU THE BRAINEST

Fiesta28 [93]

Answer:

The first term should be positive

She did not distribute the -4 properly

She added $\frac{2}{7}$ to negative -4 instead of multiplying

Step-by-step explanation:

In order to tell where she is wrong we should solve the question our selves. we are going to get the following......

$-4(-3x + \frac{2}{7})= -4(-3x) + (-4)(\frac{2}{7} )= 12x - \frac{8}{7}$

So now we see that the three things she did wrong are.

The first term should be positive

She did not distribute the -4 properly

She added $\frac{2}{7}$ to negative -4 instead of multiplying

Hope this helps :)

7 0

3 years ago

Read 2 more answers

HELP PLEASE FOR BRAINLIST!!!!!!!!!!!!

Sindrei [870]

Answer:

a(x) and d(x)

hope that helps, have a good day!

dont forget my brainliest.

Step-by-step explanation:

6 0

2 years ago

you have $20 to spend at the snack bar all the snacks at the snack bar cost $1.25 how much money will you have left if you buy 1

Dominik [7]

You will have $5 left because if you spend 1.25 on 12 snacks you will spend $15

6 0

3 years ago

Read 2 more answers

A model of a famous statue is 2 1/2 inches tall. The actual statue is 3 1/3 feet tall. What is the ratio of the height of the mo

Gekata [30.6K]

1. A model of a famous statue is $2\dfrac{1}{2}$ inches tall that is

$\dfrac{2\cdot 2+1}{2}=\dfrac{5}{2}$ in.

2. The actual statue is $3\dfrac{1}{3}$ feet tall that is

$\dfrac{3\cdot 3+1}{3}=\dfrac{10}{3}\ ft=\dfrac{10}{3}\cdot 12=40\ in.$

3. The ratio of the height of the model to the height of the actual statue in simplest form is

$\dfrac{\dfrac{5}{2}}{40}=\dfrac{5}{2}\cdot \dfrac{1}{40}=\dfrac{1}{16}.$

Answer: $\dfrac{1}{16}.$

4 0

3 years ago