(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Sheep are collected in a circular pen in such a way that the number per unit area at radius r is given by

[tex] n(r) = \frac{N_{0}}{\pi} (R - r)[/tex]

Where R = 10, and N0 = 0.3m^-3

Find the Total number of sheep in the pen (round your answer to the nearest integer)

2. Relevant equations

calculus

3. The attempt at a solution

Drawing it out, if you take the segments of the circular pen to be small rings,

then you get a strip, that is

[tex] 2/pi r * dr [/tex] in length

multiplying that by my equation I get the equation

[tex] \int dn(r) = \int \frac{No}{\pi} (R-r) 2\pi r dr [/tex]

moving the constant outside the equation

[tex] \int dn(r) = \frac{No}{\pi} \int (R-r) 2\pi r dr [/tex]

expanding the right side of the equation I get

[tex] R * (2\pi r dr) + -r * (2\pi r dr) [/tex]

integrating I get

[tex] n = \frac{No}{\pi} (\frac{R 2\pi r^2}{2} - \frac{2\pi r^3}{3}) [/tex]

simplifying it giving me the final equation

[tex] n = \frac{No}{\pi} ({R\pi r^2} - \frac{2}{3}\pi r^3 ) [/tex]

I need to figure out how to calculate a number!

pls help

i probably got it wrong, can I just substitute in 10, for the values R and also r?

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# Homework Help: Solve this number equation

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