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1 year ago

The following data gives the number of cars

Mathematics

1 answer:

faltersainse [42]1 year ago

5 0

Answer:

Step-by-step explanation:

2 : (2 + 9 + 16 + 12 + 8 + 6 + 4 + 2 + 1) = 1/30 ≈ 3.33% ≈ 3%

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Answer:

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2 years ago

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

2 years ago

How do I solve this?

Tanya [424]

Y=-3x+5 hope this helps

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2 years ago

On the first Saturday of every month, a local amusement park allows children under the age of 12 to ride for free. Which of thes

DochEvi [55]

Su is the only child under 12 years of age, therefore, she is only child entering for free.

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2 years ago

What is the slope of a line perpendicular to the line whose equation is

jonny [76]

Answer:

$- \frac{1}{2}$

Step-by-step explanation:

How do we find the line that's perpendicular to another?

We find the negative reciprocal. So for example if our slope is 2, the negative reciprocal would be $- \frac{1}{2}$ .

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2 years ago