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2 years ago

(please anwser quick) y = 2/5x + 2 Which of the following graphs represents the equation above?

Mathematics

1 answer:

Bond [772]2 years ago

5 0

Answer:

B. Y

Step-by-step explanation:

go to an online graph line a type in the question

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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

A train will stop every 3/10 of a mile. Which of the following statements are correct?

Tju [1.3M]

Answer:

Step-by-step explanation:

Its fourth stop

also can i get your snap ?

4 0

3 years ago

Plz help asap... Explain as much as possible to me plz

Solnce55 [7]

Answer:

see explanation

Step-by-step explanation:

Since the 2 figures are similar then the ratios of corresponding sides are equal, that is

$\frac{8}{x}$ = $\frac{18}{6}$ ( cross- multiply )

18x = 48 ( divide both sides by 18 )

x = $\frac{48}{18}$ = $\frac{8}{3}$ = 2 $\frac{2}{3}$

Similarly

$\frac{5}{y}$ = $\frac{18}{6}$ ( cross- multiply )

18y = 30 ( divide both sides by 18 )

y = $\frac{30}{18}$ = $\frac{5}{3}$ = 1 $\frac{2}{3}$

3 0

3 years ago

16. Jerome is a co-owner of a small company and received 1/3 of the company’s profits this year. What were the company’s overall

AlekseyPX

Remark
The trick to this question is realizing what you took 1/3 of. Did you take it of the 150000 or is it 1/3 of some total you have to find. I don't think you could come up with a third choice.

It turns out that the answer is 1/3 of a number you don't know.

Equation
(1/3) x = 150000 Multiply both sides by 3
3*(1/3) x = 150000 * 3
x = 150000 * 3
x = 450000

Conclusion
The amount the company makes is 450000 dollars / year.

6 0

3 years ago

Which symbol is used to name a line with two points A and B

Mars2501 [29]

Answer:

Step-by-step explanation:

I think that's the answer

5 0

3 years ago

Read 2 more answers