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Mars2501 [29]
2 years ago
6

Which statement or inequalities describe the number line graph?

Mathematics
1 answer:
Gennadij [26K]2 years ago
4 0

Answer:

Step-by-step explanation:

( - ∞ , - 3 ) ∪ [ - 1 , ∞ )

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Find all the solutions for the equation:
Contact [7]

2y^2\,\mathrm dx-(x+y)^2\,\mathrm dy=0

Divide both sides by x^2\,\mathrm dx to get

2\left(\dfrac yx\right)^2-\left(1+\dfrac yx\right)^2\dfrac{\mathrm dy}{\mathrm dx}=0

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2\left(\frac yx\right)^2}{\left(1+\frac yx\right)^2}

Substitute v(x)=\dfrac{y(x)}x, so that \dfrac{\mathrm dv(x)}{\mathrm dx}=\dfrac{x\frac{\mathrm dy(x)}{\mathrm dx}-y(x)}{x^2}. Then

x\dfrac{\mathrm dv}{\mathrm dx}+v=\dfrac{2v^2}{(1+v)^2}

x\dfrac{\mathrm dv}{\mathrm dx}=\dfrac{2v^2-v(1+v)^2}{(1+v)^2}

x\dfrac{\mathrm dv}{\mathrm dx}=-\dfrac{v(1+v^2)}{(1+v)^2}

The remaining ODE is separable. Separating the variables gives

\dfrac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=-\dfrac{\mathrm dx}x

Integrate both sides. On the left, split up the integrand into partial fractions.

\dfrac{(1+v)^2}{v(1+v^2)}=\dfrac{v^2+2v+1}{v(v^2+1)}=\dfrac av+\dfrac{bv+c}{v^2+1}

\implies v^2+2v+1=a(v^2+1)+(bv+c)v

\implies v^2+2v+1=(a+b)v^2+cv+a

\implies a=1,b=0,c=2

Then

\displaystyle\int\frac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=\int\left(\frac1v+\frac2{v^2+1}\right)\,\mathrm dv=\ln|v|+2\tan^{-1}v

On the right, we have

\displaystyle-\int\frac{\mathrm dx}x=-\ln|x|+C

Solving for v(x) explicitly is unlikely to succeed, so we leave the solution in implicit form,

\ln|v(x)|+2\tan^{-1}v(x)=-\ln|x|+C

and finally solve in terms of y(x) by replacing v(x)=\dfrac{y(x)}x:

\ln\left|\frac{y(x)}x\right|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C

\ln|y(x)|-\ln|x|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C

\boxed{\ln|y(x)|+2\tan^{-1}\dfrac{y(x)}x=C}

7 0
3 years ago
Simplify.<br><br> (0.4n)(16n)
BigorU [14]
=(0.4n)(16n)
multiply 0.4 & 16 and n & n
=(0.4*16)(n * n)
=6.4n^2

Hope this helps! :)
4 0
3 years ago
[(b+3)÷(a–2)](−4) if a=−5, b=6
MAXImum [283]

Answer:

36/7

Step-by-step explanation:

{(6+3)/(-5-2)}(-4)

36/7

4 0
3 years ago
3.366 rounded to the nearest tenth of a ounce
olga nikolaevna [1]

Answer:

The answer is 3.4

Step-by-step explanation:

5 or more, round up

4 or less, round down

rounding 6

round up

so...

3.4

(-2, -7) and (-4, -9)

6 0
2 years ago
Read 2 more answers
Which place value do you use to<br> compare 437,812 and 432,729?
dusya [7]

Answer: the hundreds place

8 0
3 years ago
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