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1 year ago

A group of three friends cycle from Llanfyllin to Vyrnwy at 12 km/h.

Mathematics

1 answer:

garik1379 [7]1 year ago

6 0

The average speed for the journey from Llanfyllin to Bala is 14 km/h

Average speed is the ratio of total distance travelled to total time taken. Also, average speed can be given as the average of the different speeds.

Let d₁ represent the distance from Llanfyllin to Vyrnwy and t represent the time taken, since the speed is 12 km/h, hence:

12 = d₁/t

d₁ = 12t

Let d₂ represent the distance from Vyrnwy to bala and t represent the time taken. Since they spent the same time, since the speed is 16 km/h, hence:

16 = d₂/t

d₂ = 16t

Average speed = total distance/total time

Average speed = (d₁ + d₂) / (t + t)

Average speed = (12t + 16t) / 2t

Average speed = 28t / 2t

Average speed = 14 km/h

Hence their average speed for the journey from Llanfyllin to Bala is 14 km/h.

Find out more at: brainly.com/question/23774048

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So the particular solution to the recurrence is

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(b) Let $G(x)=\displaystyle\sum_{n\ge0}h_nx^n$ be the generating function for $h_n$ . Multiply both sides of the recurrence by $x^n$ and sum over all $n\ge4$ .

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From here you would write each term as a power series (easy enough, since they're all geometric or derived from a geometric series), combine the series into one, and the solution to the recurrence will be the coefficient of $x^n$ , ideally matching the solution found in part (a).

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