Question 895070
To answer (a) and (b), you simply have r as a factor in only one term, so solving for r is simple.  For (b), you just substitute the values and evaluate ------ r.


{{{P=2pi*r+2x}}}
{{{P-2x=2pi*r}}}
{{{highlight((P-2x)/(2pi)=r)}}}


Question part (c) is not complicated.  P or r is a linear function of r or P.  Same with r and x.  Think about the formula given, and you understand that x is the straight length of the track.  If the track has NO straight section to length then you simply have a circular track, and x=0.  Clear, right?  r is what now?  

Look again:  {{{P=2pi*r+2x}}}, and if x becomes zero, then
{{{P=2pi*r+2*0}}}
{{{P=2pi*r}}}
{{{r=P/(2pi)}}}