An autonomous underwater vehicle (AUV) is descending into a lake. Its depth $D\,$ meters relative to its starting point at time $t\,$ seconds is modelled by the function $D (t)$ for $t > 0$ .

The rate of change of the AUV's depth is given by

3\sqrt{t} + 4 - \frac{16}{t^2}

At $t = 4$ , the AUV is at a depth of 15 meters, represented by the point $P (4, 15)$ on the curve $y = D (t)$ .

Determine the equation of the normal to the curve $y = D (t)$ at the point $P$ . Give your answer in the form $a t + b y + c = 0$ , where $b,\,$ and $c\,$ are integers.

Find the expression for $D (t)$ .

An autonomous underwater vehicle (AUV) is descending into a lake. Its depth $D\,$ meters relative to its starting point at time $t\,$ seconds is modelled by the function $D (t)$ for $t > 0$ .

The rate of change of the AUV's depth is given by

3\sqrt{t} + 4 - \frac{16}{t^2}

At $t = 4$ , the AUV is at a depth of 15 meters, represented by the point $P (4, 15)$ on the curve $y = D (t)$ .

Determine the equation of the normal to the curve $y = D (t)$ at the point $P$ . Give your answer in the form $a t + b y + c = 0$ , where $b,\,$ and $c\,$ are integers.

Find the expression for $D (t)$ .

1 Unit 1: Pure Mathematics A

Question 388

Markscheme

1 Unit 1: Pure Mathematics A

Question 388

Markscheme

1 Unit 1: Pure Mathematics A

Question 388

1 Unit 1: Pure Mathematics A Questions

1 Unit 1: Pure Mathematics A

Question 388

1 Unit 1: Pure Mathematics A Questions