roibeyj
05.03.2020 •
Mathematics
A tortoise and a hare are competing in a 1600-meter race. The arrogant hare decides to let the tortoise have a 510-meter head start. When the start gun is fired the hare begins running at a constant speed of 9 meters per second and the tortoise begins crawling at a constant speed of 5 meters per second.
a. Define a function f to represent the tortoise's distance from the finish line (in meters) in terms of the number of seconds t since the start of the race.
b. Solve f(t)=0for t.
c. Define a function g to represent the hare's distance from the finish line (in meters) in terms of the number of seconds t since the start of the race.
d. Solve g(t)=0 for t
e. Who won the race?
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Ответ:
(a)f(t)=1090-5t
(b)f(0)=1090metres
(c)g(t)=1600-9t
(d)g(0)=1600metres
(e)The Hare
Step-by-step explanation:
Total Distance =1600 metres
(a)The tortoise has a 510m headstart and a speed of 5m/s
Distance=Speed X Time
Distance at 5m/s = 5t
Total Distance covered by the tortoise at any time t= 510+5t
Therefore, The tortoise's distance from the finish line (in meters) in terms of the number of seconds t since the start of the race is given as:
f(t)=1600-(510+5t)
f(t)=1090-5t
(b)f(0)=1090-(5X0)
=1090metres
(c)The hare has a speed of 9m/s
Distance=Speed X Time
Distance at 9m/s = 9t
Total Distance covered by the hare at any time t= 9t
Therefore, The hare's distance from the finish line (in meters) in terms of the number of seconds t since the start of the race is given as:
g(t)=1600-9t
(d)
g(0)=1600-(9X0)=1600metres
(e)The race is finished when the distance from the finish line=0
For the Tortoise
f(t)=1090-5t=0
1090=5t
t=218seconds
For the Hare
g(t)=1600-9t=0
9t=1600
t=177.8seconds
The hare takes a shorter time to reach the finish line so he won the race.
Ответ:
3rd one im pretty sure because they are opposites :)
Step-by-step explanation: