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3 years ago

On a 6-sided die, what is the probability of rolling an even number that is not 4? 1/6 1/3 2/3 5/6

Mathematics

1 answer:

myrzilka [38]3 years ago

8 0

The probability of rolling an even number on a six sided die is 1/3.

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Find a particular solution to the nonhomogeneous differential equation y??+4y?+5y=?10x+e^(?x).

Firdavs [7]

Answer:

A) Particular solution:

$2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

B) Homogeneous solution:

$y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))$

C) The most general solution is

$y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

Step-by-step explanation:

Given non homogeneous ODE is

$y''+4y'+5y=10x+e^{-x}---(1)$

To find homogeneous solution:

$D^{2}+4D+5=0\\D^{2}+4D+4-4+5=0\\\\(D+2)^{2}=-1\\D+2=\pm iD=-2 \pm i\\y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))---(2)$

To find particular solution:

$y_{p}=Ax+B+Ce^{-x}\\\\y'_{p}=A-Ce^{-x}\\y''_{p}=Ce^{-x}\\$

Substituting $y_{p},y'_{p},y''_{p}$ in (1)

$y''_{p}+4y'_{p}+5y_{p}=10x+e^{-x}\\Ce^{-x}+4(A-Ce^{-x})+5(Ax+B+Ce^{-x})=10x+e^{-x}\\$

Equating the coefficients

$5Ax+2Ce^{-x}+4A+5B=10x+e^{-x}\\5A=10\\A=2\\4A+5B=0\\B=-\frac{4A}{5}B=-\frac{8}{5}2C=1\\C=\frac{1}{2}\\So,\\y_{p}=2x+\frac{1}{2}e^{-x}-\frac{8}{5}---(3)\\$

The general solution is

$y=y_{h}+y_{p}$

from (2) ad (3)

$y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

6 0

3 years ago

A number decreased by 23 is 44. Find the number.

Irina-Kira [14]

A) can.
because the number (x) has been decreased by 23 and is now 44.

Hope this helps :)

4 0

3 years ago

Read 2 more answers

What is the slope of the line that passes through the following points:<br> (4, -3), (-5, 10)

umka21 [38]

Answer:

-9/13

Step-by-step explanation:

The formula for slope is [ y2-y1/x2-x1 ].

10-(-3)/-5-4

13/-9

-9/13

Best of Luck!

5 0

3 years ago

What is 3h^2+6h-18x as a product of two factors?? Please help,*a lot of points*

Vaselesa [24]

-3 is one of them hope this helps

4 0

3 years ago

A kingfish needs to be cut into 8-ounce pieces. If the fish weights 12.5 pounds, how many pieces can be cut? 1 pound=16 ounces

Mkey [24]

Answer:

25 pieces

Step-by-step explanation:

12.5 * 16= 200 ounces

therefore 200/8=25

7 0

3 years ago