3 years ago

What is the quotient of the following rational expression?

Mathematics

1 answer:

astraxan [27]3 years ago

8 0

Answer:

The one that has X+3 and -2x+11

Step-by-step explanation:

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The general solution of 2 y ln(x)y' = (y^2 + 4)/x is

Sav [38]

Replace $y'$ with $\dfrac{\mathrm dy}{\mathrm dx}$ to see that this ODE is separable:

$2y\ln x\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{y^2+4}x\implies\dfrac{2y}{y^2+4}\,\mathrm dy=\dfrac{\mathrm dx}{x\ln x}$

Integrate both sides; on the left, set $u=y^2+4$ so that $\mathrm du=2y\,\mathrm dy$ ; on the right, set $v=\ln x$ so that $\mathrm dv=\dfrac{\mathrm dx}x$ . Then

$\displaystyle\int\frac{2y}{y^2+4}\,\mathrm dy=\int\dfrac{\mathrm dx}{x\ln x}\iff\int\frac{\mathrm du}u=\int\dfrac{\mathrm dv}v$

$\implies\ln|u|=\ln|v|+C$

$\implies\ln(y^2+4)=\ln|\ln x|+C$

$\implies y^2+4=e^{\ln|\ln x|+C}$

$\implies y^2=C|\ln x|-4$

$\implies y=\pm\sqrt{C|\ln x|-4}$

4 0

3 years ago

Factor the expression using GCF <br> 15w + 65

labwork [276]

That would be 5(3w + 13)

The GCF is 5

5 0

4 years ago

Julia has 2 identical rooms in her house. if each room measures 8 feet on one side and 12 feet on another, what is the total are

Jlenok [28]

First we have the work out the area of 1 room. So that is 8ft * 12ft which is 96ft^2. And if there are 2 of these rooms, then we multiply this value by 2. Giving us a total area of 192ft^2.

5 0

4 years ago

A tortoise is walking in the desert. It walks at a speed of 2 meters per minute for 2.56 meters. For how many minutes does it wa

zaharov [31]

distance = rate * time

2.56 meters = 2meter/min * t

divide by 2 on each side

2.56/2 =t

1.28 minutes =t

8 0

3 years ago

11] (8•10^-3)(2•10^10

Oduvanchick [21]

Answer:

16*10^7 or 160000000

Step-by-step explanation:

combine whole numbers: 8*2

and combine exponents: 10^-3*10^10=10^7

8*2*10^7

16*10^7

160000000

5 0

3 years ago