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3 years ago

What is the number of seven hundred thirty-one millon, nine hundred thirty- four thoudand thirty in standered form?

Mathematics

1 answer:

myrzilka [38]3 years ago

6 0

It is written like this: 731,934,030

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Find the solution of the initial value problem<br><br> dy/dx=(-2x+y)^2-7 ,y(0)=0

Leokris [45]

Substitute $v(x)=-2x+y(x)$ , so that $\dfrac{\mathrm dv}{\mathrm dx}=-2+\dfrac{\mathrm dy}{\mathrm dx}$ . Then the ODE is equivalent to

$\dfrac{\mathrm dv}{\mathrm dx}+2=v^2-7$

which is separable as

$\dfrac{\mathrm dv}{v^2-9}=\mathrm dx$

Split the left side into partial fractions,

$\dfrac1{v^2-9}=\dfrac16\left(\dfrac1{v-3}-\dfrac1{v+3}\right)$

so that integrating both sides is trivial and we get

$\dfrac{\ln|v-3|-\ln|v+3|}6=x+C$

$\ln\left|\dfrac{v-3}{v+3}\right|=6x+C$

$\dfrac{v-3}{v+3}=Ce^{6x}$

$\dfrac{v+3-6}{v+3}=1-\dfrac6{v+3}=Ce^{6x}$

$\dfrac6{v+3}=1-Ce^{6x}$

$v=\dfrac6{1-Ce^{6x}}-3$

$-2x+y=\dfrac6{1-Ce^{6x}}-3$

$y=2x+\dfrac6{1-Ce^{6x}}-3$

Given the initial condition $y(0)=0$ , we find

$0=\dfrac6{1-C}-3\implies C=-1$

so that the ODE has the particular solution,

$\boxed{y=2x+\dfrac6{1+e^{6x}}-3}$

5 0

3 years ago

Write the expression in terms of sin x and cos x only. sin(2x)+cos(3x)

BartSMP [9]

Sin2x=2sinxcosx, cos2x=1-2sin^2x
sin(2x)+cos(3x)=2sinxcosx+cos(x+2x)
cos(x+2x)=cosx(1-2sin^2(x))-sinx2sinxcosx
sin(2x)+cos(3x)=2sinxcosx(1-sinx)+cosx(1-2sin^2(x))

5 0

3 years ago

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Need help please thanks

tangare [24]

Answer:

i think it would be b

Step-by-step explanation:

3 0

3 years ago

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8. If BD=BC, BD = 5x -26, BC = 2r + 1, and AC = 43, find AB.

charle [14.2K]

Answer:

Step-by-step explanation:

BD=DC

5x-26=2x+1

5x-2x=1+26

3x=27

x=9

BC=2x+1

=2*9+1

BC =19

so AB=AC-BC

AB=43-19

AB=24

8 0

3 years ago

Tara has a magnet collection from places she visited. She measures the length of the magnets to the nearest half inch and record

gregori [183]

Answer:

there are more magnets that longer than 2 1/2

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.

Please have a look at the attached photo.

My answer:

From the photo, we can see that:

Length of the magnet:

1 inch there is 1 magnet
$1\frac{1}{2}$ inches there are 2 magnets
2 inches there are 3 magnets
3 inches there are 4 magnets
$3\frac{1}{2}$ there is 1 magnet
4 inches there are 2 magnets

=> the total number of magnets that longer than 2 1/2 are: 4+1+2 = 7

=> the total number of magnets that shorter than 2 1/2 are: 1+2+3 = 6

Hence, there are more magnets that longer than 2 1/2

Hope it will find you well.

8 0

3 years ago

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