A subaquatic probe is descending into an ocean trench. Its rate of descent, v m min−1v\text{ m min}^{-1}v m min−1, is monitored over a 50-minute period. The following velocity readings were extracted from the probe's telemetry system at 10-minute intervals:
| t (min)t \text{ (min)}t (min) | 0 | 10 | 20 | 30 | 40 | 50 |
|---|---|---|---|---|---|---|
| v (m min−1)v \text{ (m min}^{-1})v (m min−1) | 15.0 | 42.4 | 58.6 | 55.2 | 39.8 | 12.5 |
An oceanographer, Marcus, claims that in the period 10≤t≤4010 \le t \le 4010≤t≤40, the probe descends approximately 1550 metres.
Determine whether Marcus is correct, showing clearly the calculations you have used based on the trapezium rule with all available data for this interval.
125 exam-style questions on OCR A Level Maths 1.9 Numerical Methods (A-level only), covering 1.9.1 Locating roots by sign change (A-level only), 1.9.2 Failure of sign change methods (A-level only), 1.9.3 Simple iterative methods (A-level only), 1.9.4 Newton-Raphson method (A-level only), 1.9.5 Failure of iterative methods (A-level only), 1.9.6 Numerical integration (A-level only), and 1.9.7 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.