A farmer $F_1$ has a land in the shape of a triangle with vertices at $P\left(0,0\right),Q\left(1,1\right)\text{and}R\left(2,0\right).$ From this land, a neighboring farmer $F_2$ takes away the region which lies between the side PQ and curve of the from $y=x^n\left(n>1\right).$ If the area of the region taken away by the farmer $F_2$ is exactly $30\%$ of the area of $\Delta PQR$, then the value of n is ___.

Views: 817 students