The profile of a specialized parabolic drainage channel is modeled by the curve with equation

2x^2 + \frac{256}{\sqrt{x}} - 100, \quad x > 0

where $h$ is the depth in millimeters and $x$ is the horizontal distance from the left edge of the sensor assembly. The point $P$ is the minimum point on the curve.

Use calculus to show that the $x$ -coordinate of $P$ is 4.

A horizontal laser beam, represented by the line $l$ , passes through point $P$ and is parallel to the $x$ -axis. A shaded region $R$ is bounded by the curve, the laser beam $l$ , and the vertical line $x = 1$ .

Use algebraic integration to find the exact cross-sectional area of the region $R$ .

The profile of a specialized parabolic drainage channel is modeled by the curve with equation

2x^2 + \frac{256}{\sqrt{x}} - 100, \quad x > 0

where $h$ is the depth in millimeters and $x$ is the horizontal distance from the left edge of the sensor assembly. The point $P$ is the minimum point on the curve.

Use calculus to show that the $x$ -coordinate of $P$ is 4.

Use algebraic integration to find the exact cross-sectional area of the region $R$ .

1 Pure Mathematics

Question 435

Markscheme

1 Pure Mathematics

Question 435

Markscheme

1 Pure Mathematics

Question 435

1 Pure Mathematics Questions

1 Pure Mathematics

Question 435

1 Pure Mathematics Questions