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2 years ago

5

Determine the volume of the cylinder

1 answer:

Igoryamba2 years ago

6 0

Answer:

about 904.78

Step-by-step explanation:

πr^2h pi(6)^2 * 8

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6,237.2<br> The 2 in hundreds place is___ the value of the 2 in the tenths place.

Reil [10]

The 2 in the hundreds place is 1000* the 2 in the tenths place

3 0

2 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

What is product of x/3 and 6/x when x=0 ? <br>A.2 <br>B.18 <br>C.2/x^2<br> D.18/x^2

Ahat [919]

Answer:

A) But if anyone thinks this they should go back to preschool

Step-by-step explanation:

On any other value of x you would take the numerators and denominators and multiply them across:

$\frac{x}{3}*\frac{6}{x}=\frac{x*6}{x*3}=\frac{6}{3} =2$

But, this literally does not make since considering the fact that you cannot divide any value by zero. Try it, it won't work. If we plug these into a trusty dusty calculator, we get this:

$\frac{0}{3}=0\\\\\frac{6}{0}=DOMAINERROR$

0*DOMAINERROR= You can't do it.

There are other reasons why you can't divide by zero, I would suggest looking them up on YT and learning about them.

I would answer A, but the person who wrote this question just wasn't focusing when they wrote the question.

4 0

3 years ago

The average height of a family of five is 150 cm. If the height of 4 family members is 153, 150, 151, and 152, find the height o

Lady bird [3.3K]

J can find the height of the fifth member on this way
S=150
S1=153
S2=150
S3=151
S4=152
S5=?
S= (s1+s2+s3+s4+s5)/5:
5*150= <span>153+150+151+152+S5
S5=5*150-606=750-606=144
Answer is 144 cm</span>

5 0

2 years ago

What is the value of x? Enter your answer in the box. units

Arte-miy333 [17]

Check the picture below.

6 0

3 years ago