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3 years ago

I need help!!! what is the highest common factor of 30 and 60?

Mathematics

2 answers:

PtichkaEL [24]3 years ago

8 0

The Greates Common Factor (GCF) is: 2 x 3 x 5 = 30

Agata [3.3K]3 years ago

7 0

I thought it was 10 because 10 x 3 and 10 x6 but it is 2

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Answer:

Step-by-step explanation:

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3 years ago

Which measure of center is shown in a box plot? A.mean B.median C.mode

Dima020 [189]

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3 years ago

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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

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

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3 years ago

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Amanda [17]

Answer: You could move Circle 2 10 units to the right and up 5 up.

Doing this would put the centers of the circles at the same location. They would both be at the point (8, 5).

For the dilation, the radius changed from 2 to 6. Solve the following equation.
2x = 6
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slega [8]

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2 years ago