1) m : n = 1 : 4, n : p = 4 : 5. If p =1000, find m.
2) The circumference of a circle is 1, find the central angle corresponding to the arc which 2/5 long
you have $\displaystyle \frac mn = \frac 14 \implies n = \frac 1{4m}$
you also have $\displaystyle \frac np = \frac 45 \implies n = \frac 4{5p}$
but we found that $\displaystyle n = \frac 1{4m}$
thus, $\displaystyle \frac 1{4m} = \frac 4{5p}$
$\displaystyle \Rightarrow m = \frac {5p}{16}$
now continue
do you work in radians or degrees?2) The circumference of a circle is 1, find the central angle corresponding to the arc which 2/5 long