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3 years ago

Answers: a/b= 8/2 B: 3.2/2= a/b C: b/6.4 = 8/5 D: 2/ 3.2= b/a

Mathematics

1 answer:

scoundrel [369]3 years ago

6 0

Answer:

b/6.4 = 8/5

Step-by-step explanation:

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3 years ago

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Answer:

D. Fundamental Principle of Counting
D. 32
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Step-by-step explanation:

Q1

The Fundamental Principle of Counting states that we can find the total number of ways that two or more separate tasks can happen by multiplying the number of ways each task can happen separately.

Q2

No. of ways = 2⁵ = 32

Q3

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Q4

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2 years ago

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

Answers: a/b= 8/2 B: 3.2/2= a/b C: b/6.4 = 8/5 D: 2/ 3.2= b/a​

Answers: a/b= 8/2 B: 3.2/2= a/b C: b/6.4 = 8/5 D: 2/ 3.2= b/a