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So, In a question about finding volume in a dome we were

Given that V = pi.k(k^2/r - k^2/3r^3 - r/8)

And K = m/2pi.p.t

Firstly we are asked to obtain an expression for the value of r that maximises the volume of air and rearrange to obtain an equation of the form ar^4 + br^2 + c = 0

V' => r^4/8 + kr^2 - k^2 = 0

So far im confident that is correct, but next it asks you to solve the equation for r^2 and hence find r, approximate squareroot of 96 to be 10.

Therefore pi^2 = 10

and substituting the value of k into this equation i obtained,

r^4/8 + mr^2/2pi.p.t - m^2/4pi^2.p^2.t^2 = 0

That is where i get stuck and i hope someone can help me out, thnx :\

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# Mathematical modelling question

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