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charle [14.2K]
2 years ago
10

How many trips can a truck with a 1 by 2 meter cylindrical tank take to fill a 890,000 liters tank?

Mathematics
1 answer:
Reil [10]2 years ago
4 0
Tank diameter = 1m
radius = 0.5m
height = 2m
Volume of tank of truck = πr²h = 3.142 * 0.5² * 2 = 1.571m³ = 1571 litre

Volume of tank to be filled = 890,000 litre

no. of trips = 890000/1571 = 566.52 ≈ 567 trips
 

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Answer:

7 times

Step-by-step explanation:

30 miles per 1 gallon

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Let X ~ N(0, 1) and Y = eX. Y is called a log-normal random variable.
Cloud [144]

If F_Y(y) is the cumulative distribution function for Y, then

F_Y(y)=P(Y\le y)=P(e^X\le y)=P(X\le\ln y)=F_X(\ln y)

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The nth moment of Y is

E[Y^n]=\displaystyle\int_{-\infty}^\infty y^nf_Y(y)\,\mathrm dy=\frac1{\sqrt{2\pi}}\int_0^\infty y^{n-1}e^{-\frac12(\ln y)^2}\,\mathrm dy

Let u=\ln y, so that \mathrm du=\frac{\mathrm dy}y and y^n=e^{nu}:

E[Y^n]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{nu}e^{-\frac12u^2}\,\mathrm du=\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{nu-\frac12u^2}\,\mathrm du

Complete the square in the exponent:

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E[Y^n]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{\frac12(n^2-(u-n)^2)}\,\mathrm du=\frac{e^{\frac12n^2}}{\sqrt{2\pi}}\int_{-\infty}^\infty e^{-\frac12(u-n)^2}\,\mathrm du

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so we end up with

E[Y^n]=e^{\frac12n^2}

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We can see that, when the input is 5, the output is 24.

<h3>How to evaluate an equation?</h3>

Here we have the equation:

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We want to evaluate it with the input as 5, so we need to replace the variable x by the number 5, we will get:

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If you want to learn more about evaluating functions:

brainly.com/question/1719822

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