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Two model cars race in a straight line. The distance in feet of car A from the starting line is modeled by the function f(t) = 0.25t^2 + 22t - 1, where t is the time in seconds since the start of the race. The distance in feet of car B from the starting line is modeled by the function g(t) = -0.1t^2 + 25t.
Write a model for the difference in feet between car A and car B.
What is the difference in feet between car A and car B after 10 seconds? How can you tell which car is in the lead?

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a. A model for the difference in feet between car A and car B is d(t) = = 0.35t² - 3t - 1.

b. The difference in feet between car A and car B after 10 seconds is 4 feet

c. To tell which car is in the lead,

  • If d(t) > 0, car A is in the lead but
  • if d(t) < 0 car B is in the lead.

a. Write a model for the difference in feet between car A and car B.

Since the distance in feet of car A from the starting line is modeled by the function f(t) = 0.25t² + 22t - 1, where t is the time in seconds since the start of the race.

Also, the distance in feet of car B from the starting line is modeled by the function g(t) = -0.1t² + 25t.

The difference in distance between car A and car B d(t) is the difference between their distance from the starting line.

So, d(t) = f(t) - g(t)

= 0.25t² + 22t - 1 - ( -0.1t² + 25t)

= 0.25t² + 22t - 1 + 0.1t² - 25t

= 0.35t² - 3t - 1

So, a model for the difference in feet between car A and car B is d(t) = = 0.35t² - 3t - 1.

b. What is the difference in feet between car A and car B after 10 seconds?

Since the difference in distance in feet between car A and car B  is d(t) = 0.35t² - 3t - 1.

To find the difference in distance after 10 seconds, we substitute t = 10 into d(t).

So, d(t) = 0.35t² - 3t - 1.

d(10) = 0.35(10)² - 3(10) - 1

= 0.35(100) - 30 - 1

= 35 - 31

= 4 feet

So, the difference in feet between car A and car B after 10 seconds is 4 feet

c. How can you tell which car is in the lead?

Since the difference in distance in feet between car A and car B  is d(t) = 0.35t² - 3t - 1

= f(t) - g(t)

Since

  • f(t) = distance of car A and
  • g(t) = distance of car B.

So, to tell which car is in the lead,

  • If d(t) > 0, car A is in the lead but
  • if d(t) < 0 car B is in the lead.

Learn more about difference in distance in feet here:

https://brainly.com/question/18955317

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