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Assuming is differentiable over the interval (1, 5), by the mean value theorem we know that there is some
such that
We're given that for all
, so
that is, the minimum possible value is 8, and the maximum possible value is 12.
Answer:
- See below
Step-by-step explanation:
a)
i)
<u>Use the law of cosines:</u>
ii)
<u>Use the law of sines:</u>
- sin ∠A / PB = sin ∠P / AB
- sin ∠A / 100 = sin 80 / 107.31
- sin ∠A = 100 sin 80 deg / 107.31
- sin ∠A = 0.92
- ∠A = arcsin 0.92
- ∠A = 67° (rounded)
iii)
<u>Bearing of B from A:</u>
- 90° + (67° - 30°) =
- 127°
b)
<u>PB is longer distance. Time to reach B:</u>
- t = d/s
- t = 100/20 = 5 hours
<u>The speed s of the slower ship:</u>
- s = d/t
- s = 60/5 = 12 km/h