Question

The function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours.

D(t) = StartLayout enlarged left-brace 1st Row 1st column 300 t + 125 , 2nd column 0 less-than-or-equal-to t less-than 2.5 2nd Row 1st column 880, 2nd column 2.5 less-than-or-equal-to t less-than-or-equal-to 3.5 3rd Row 1st column 75 t + 612.5, 2nd column 3.5 less-than t less-than-or-equal-to 6 EndLayout

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 875 miles from home.
At 3 hours, the distance is constant, at 880 miles.
The total distance from home after 6 hours is 1,062.5 miles.

Answer 1

The answers are......

At 2 hours, the traveler is 725 miles from home.

At 3 hours, the distance is constant, at 880 miles.

The total distance from home after 6 hours is 1,062.5 miles.

Step-by-step explanation:

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Answer 2

The information about the distance as a function of time of given by the piecewise function include :

• At 2 hours, the traveler is 725 miles from home
• At 3 hours, the distance is constant, at 880 miles.
• The total distance from home after 6 hours is 1,062.5 miles.

At 0 ≤ t < 2.5 ; D(t) = 300t + 125 ;

The starting distance at 0 hours is ;

• D(0) = 300(0) + 125 = 125 miles

At t = 2 hours

• D(2) = 300(2) + 125 = 600 + 125 = 725 miles

At t = 2.5 hours ; At 2.5 ≤ t ≤ 3.5

• D = 880 miles (Fixed)

At t = 3 hours ; 2.5 ≤ t ≤ 2.5

• D = 880 miles

At t = 6 hours ; 3.5 < t ≤ 6

• D = 75(6) + 612.5 = 450 + 612.5 = 1062.5 miles

Therefore, only statements, B, D and E are correct.

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