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4 years ago

How many times will 11/12 of a gallon of milk fill a vessel holding 1/5 of 4/5 of a gallon?

Mathematics

1 answer:

RideAnS [48]4 years ago

5 0

Every time, Because the 11/12 gallon is larger then both the vessel and the other gallon.

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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

A train travels 68 kilometers in 2 hours, and then 64 kilometers in 3 hours. What is its average speed

skad [1K]

Average speed is the distance traveled by an object in total and divided by the amount of time an object covers the distance. The formula is -
Average speed = total distance traveled / total time taken
= 68km+64km / 2 hrs.+3hrs.
= 132km / 5hrs.
= 26.4km/hr.
Therefore, the train's average speed is 26.4km/hr.

5 0

3 years ago

How do you do 2 divided by 7

laiz [17]

Do long division but the answer is 2/7 or 0.2857

6 0

3 years ago

Find the interest earned and the balance of the account: P=$650 R=4% T=2 Years

Dmitry_Shevchenko [17]

I have no idea.... Try to ask your teacher or your parents

8 0

4 years ago

A line segment has an endpoint at (5,2) and has a negative slope. Which of the following points could be the other endpoint?

slavikrds [6]

<span>C. (4,3)

Draw and plot on a graph and (4,3) could be the other end point, which
x < 5
y > 2</span>

6 0

4 years ago