If `(t, t^(2))` falls inside the angle made by the lines `y = x//2, x gt 0` and `y = 3x, x gt 0,` where `t in (a, b)` then find the value of `2a + b`.

Answer

4

Explanation

If lines are `y = (x)/(2)` & `y = 3x`

Then intersection of `y = 3x` &` y = (x)/(2)` is `(0, 0)`
For point `(t, t^(2))` , lope `= (t^(2))/(t) = t`
`(1)/(2)lttlt3`
`t in ((1)/(2), 3)`
`a = (1)/(2), b = 3 , 2a + b = 4`