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2 years ago

Please help me with 1,2,3,4,5 and show me the steps and the answers do not send me link please

Mathematics

1 answer:

lina2011 [118]2 years ago

4 0

Answer:

I did the first one on paper

Step-by-step explanation:

i also sent one page of my personal notes on right triangle Pythagoerean thereom I hope this helps

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3y''-6y'+6y=e*x sexcx

Simora [160]

From the homogeneous part of the ODE, we can get two fundamental solutions. The characteristic equation is

$3r^2-6r+6=0\iff r^2-2r+2=0$

which has roots at $r=1\pm i$ . This admits the two fundamental solutions

$y_1=e^x\cos x$
$y_2=e^x\sin x$

The particular solution is easiest to obtain via variation of parameters. We're looking for a solution of the form

$y_p=u_1y_1+u_2y_2$

where

$u_1=-\displaystyle\frac13\int\frac{y_2e^x\sec x}{W(y_1,y_2)}\,\mathrm dx$
$u_2=\displaystyle\frac13\int\frac{y_1e^x\sec x}{W(y_1,y_2)}\,\mathrm dx$

and $W(y_1,y_2)$ is the Wronskian of the fundamental solutions. We have

$W(e^x\cos x,e^x\sin x)=\begin{vmatrix}e^x\cos x&e^x\sin x\\e^x(\cos x-\sin x)&e^x(\cos x+\sin x)\end{vmatrix}=e^{2x}$

and so

$u_1=-\displaystyle\frac13\int\frac{e^{2x}\sin x\sec x}{e^{2x}}\,\mathrm dx=-\int\tan x\,\mathrm dx$
$u_1=\dfrac13\ln|\cos x|$

$u_2=\displaystyle\frac13\int\frac{e^{2x}\cos x\sec x}{e^{2x}}\,\mathrm dx=\int\mathrm dx$
$u_2=\dfrac13x$

Therefore the particular solution is

$y_p=\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x$

so that the general solution to the ODE is

$y=C_1e^x\cos x+C_2e^x\sin x+\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x$

7 0

3 years ago

BRAINLIEST if correct 4

Viefleur [7K]

Answer:

Yes it is biased

Step-by-step explanation:

It shows favoritism

4 0

3 years ago

Read 2 more answers

Amanda has 4 liters of juice and some glasses. She will pour 1/4 liter of juice into each glass. What is the total number of gla

scZoUnD [109]

Answer:

16 glasses

Step-by-step explanation:

If 1 glass = 1/4 liter of juice

then 16 glasses = 4 liters of juice

because 4 divided by 1/4 = 16

8 0

3 years ago

It takes a person 50 minutes to get to campus. He spends t minutes walking to the bus stop and the rest of the time riding the b

amid [387]

Answer:

16.2

Step-by-step explanation:

cause. ur a noob at math

8 0

3 years ago

Maggie says that if the expression was 12÷3to the second power, you would divide before simplifying 3 to the second power. Is sh

mezya [45]

Answer:

Maggie is incorrect.

Step-by-step explanation:

PEMDAS tells us the order of operations and the steps of solving a mathematical statement. It states that exponents must be performed before multiplication or division.

P - Parentheses

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

Therefore, to solve 12÷3² correctly, 3² needs to be simplified to 9 before dividing.

I hope this helps!

4 0

3 years ago