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he function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours. Which times and distances are represented by the function? Select three options. The starting distance, at 0 hours, is 300 miles. At 2 hours, the traveler is 725 miles from home. At 2.5 hours, the traveler is still moving farther from home. At 3 hours, the distance is constant, at 875 miles. The total distance from home after 6 hours is 1,062.5 miles.

Respuesta :

MrRoyal

The true statements are (b), (d) and (e)

  • At 2 hours, the traveler is 725 miles from home.
  • At 3 hours, the distance is constant, at 875 miles.
  • The total distance from home after 6 hours is 1,062.5 miles.

How to determine the times and distances are represented by the function?

From the function, we have the following piecewise function and the domains

D(t) = 300t + 125, 0 ≤ t < 2.5

D(t) = 875, 2.5 ≤ t ≤ 3.5

D(t) = 75t + 612.5, 3.5 < t ≤ 6

When t = 2, we use the domain 0 ≤ t < 2.5

So, we have

D(2) = 300 * 2 + 125

Evaluate the product

D(2) = 600 + 125

Evaluate the sum

D(2) = 725 --- this is true

When t = 3, we use the domain 2.5 ≤ t ≤ 3.5

So, we have

D(t) = 875

This gives

D(3) = 875 -- this is true

When t = 6, we use the domain 3.5 < t ≤ 6

So, we have

D(t) = 75t + 612.5

This gives

D(6) = 75* 6 + 612.5

Evaluate the product

D(6) = 450 + 612.5

Evaluate the sum

D(6) = 1062.5 --- this is true

Hence, the true statements are (b), (d) and (e)

Read more about piecewise functions at:

https://brainly.com/question/19030976

#SPJ1

Complete question

Select three options. The starting distance, at 0 hours, is 300 miles. At 2 hours, the traveler is 725 miles from home. At 2.5 hours, the traveler is still moving farther from home. At 3 hours, the distance is constant, at 875 miles. The total distance from home after 6 hours is 1,062.5 miles.

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