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3 years ago

8

In a translation, the line segments that connect each point on the preimage to the corresponding point on the image are not only

congruent but also __________.

1 answer:

makvit [3.9K]3 years ago

5 0

Parallel because congruency and parallelism is somehow similar and that word fits in perfectly

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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

Is 100 MG less than 10g

pantera1 [17]

There are 1000 grams in a gram and 1000 times 10 is 10000 so yes 100 mg is less than a 10g

3 0

2 years ago

Read 2 more answers

Negative 33 divided 11 as a fraction

Elodia [21]

-33 / 11 = ?

-33/11

Simplify

-3/1 would be the answer

6 0

3 years ago

Read 2 more answers

Your hair is growing at 1 inch per month. You got your hair cut to 4 inches in length. Write and equation that gives the length

Korvikt [17]

Answer:

Your hair grows 2 to 4 inches in 4 months, 4 to 6 inches in 9 months, and 6 to 8 inches in a year. Though this is how the usual growth cycle works, it also depends on seasonal changes, hair and scalp health, medications, hormonal changes, and diet among other factors.

Step-by-step explanation:

7 0

2 years ago

This trapezoid-based right pyramid has a volume of 48m^3

aliya0001 [1]

Answer:

18

Step-by-step explanation:

Khan Academy

3 0

2 years ago