Alan

See https://web2.0calc.com/questions/math_83467#r2

Number of CDs = 2*3*5 + 1

This should help you answer:

Look at the following pattern

I'll leave you to express the resut in the form requested in the question.

Like so

As follows:

As follows:

Replace x by \(x=r\cos \theta\)  and y by \(y=r\sin \theta\)

The general equation of a circle can be written as: \((x-x_c)^2+(y-y_c)^2=r^2\)  where the centre has coordinates \((x_c,y_c)\) and the circle has radius \(r\). We can find \(r\) from \(2\pi r = circumference\)

This should be enough for you to answer the question.

The question 2a asks how many complete loops were made.  This has to be a whole number.  So, if 15/T is not a whole number (which it isn't) we need to take the nearest whole number less than this.  That is what the floor function does.

For 2b, we see that 15/T is 22.5, which means the passenger does 22 complete loops, plus half of a loop.  Since the passenger starts at the bottom, 22 complete loops will leave him/her at the bottom, and another half loop will take them to the top.