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The function s(x)= [tex]\frac{3600}{60+x}=3600(60+x)^{-1}[/tex]

gives a​ person's average speed in miles per hour if he or she travels one mile in 60+x seconds. Use a linear approximation to s at 0 to find a​ person's approximate average speed if he or she travels one mile in 51 seconds. What is his or her exact​ speed?

The​ person's approximate average speed is___mi/hr

Respuesta :

allstarpitcher923
Well, you travel one mile in a minute if you’re traveling 60 mph... 51 seconds would result in 60/51 miles in a minute. To find the miles per hour, divide 60 by 51/60 to get about 70.59 mile per hour.
fichoh

Using the principle of linear approximation, the approximate average speed of the person in miles per hour is 70.59

Using linear approximation :

  • Average speed = (Distance covered ÷ time taken)

  • Distance covered = 1 mile

  • Time taken = 51 seconds

Average speed = (1 ÷ 51) = 0.0196078 mi/sec

Expressing the average speed in miles per hour :

  • 1 hour = 3600 seconds

0.0196078 mi/sec = (0.0196078 × 3600) mi/hr = 70.588 mi/hr

Therefore, the approximate average speed is 70.59 mi/hr

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