Question

Find the ratio of students who attended less than (H)/(2) hours of lectures ?

Answer 1

`Ratio=1/8`

Explanation:

.

`0 <= t_1 <= t_2 <= H`

`0 <= t_1/2 <=t_2/2 <= H/2`

`int_(t_1)^(t_2)20t^2dt=20/3t^3)_(t_1)^(t_2)=20/3(t_2^3-t_1^3)`

`int_(t_1/2)^(t_2/2)20t^2dt=20/3t^3)_(t_1/2)^(t_2/2)=20/3(t_2^3/8-t_1^3/8)=20/3*1/8(t_2^3-t_1^3)`

`Ratio=(20/3*1/8(t_2^3-t_1^3))/(20/3(t_2^3-t_1^3))`

`Ratio=(cancelcolor(red)(20/3)*1/8cancelcolor(red)((t_2^3-t_1^3)))/(cancelcolor(red)(20/3)cancelcolor(red)((t_2^3-t_1^3)))`

`Ratio=(1/8)/1=1/8`