A landscape architect is designing a feature for a park. The cross-sectional elevation of the terrain is modelled by a curve $C$ with equation

x^{\frac{1}{2}}(15 - x), \quad x \ge 0

where $y$ is the height in decametres and $x$ is the horizontal distance in decametres. The curve $C$ has a stationary point at $P$ .

Using calculus, determine the $x$ -coordinate of $P$ .

The region $R_1$ , representing a hill section, is bounded by the curve $C$ and the $x$ -axis.

The region $R_2$ , representing a valley section, is bounded by the curve $C$ , the $x$ -axis, and the vertical line $x = k$ , where $k > 15$ is a constant.

Given that the area of the hill $R_1$ is equal to the area of the valley $R_2$ , find, using calculus, the exact value of $k$ .

A landscape architect is designing a feature for a park. The cross-sectional elevation of the terrain is modelled by a curve $C$ with equation

x^{\frac{1}{2}}(15 - x), \quad x \ge 0

where $y$ is the height in decametres and $x$ is the horizontal distance in decametres. The curve $C$ has a stationary point at $P$ .

Using calculus, determine the $x$ -coordinate of $P$ .

The region $R_1$ , representing a hill section, is bounded by the curve $C$ and the $x$ -axis.

The region $R_2$ , representing a valley section, is bounded by the curve $C$ , the $x$ -axis, and the vertical line $x = k$ , where $k > 15$ is a constant.

Given that the area of the hill $R_1$ is equal to the area of the valley $R_2$ , find, using calculus, the exact value of $k$ .

1 Pure Mathematics

Question 270

Markscheme

1 Pure Mathematics

Question 270

Markscheme

1 Pure Mathematics

Question 270

1 Pure Mathematics Questions

1 Pure Mathematics

Question 270

1 Pure Mathematics Questions