- At 2 hours, the traveler is 725 miles from home.
- At 3 hours, the distance is constant, at 880 miles. --> TRUE.
- The total distance from home after 6 hours is 1,062.5 miles --> TRUE.
Step-by-step explanation:
The function D(t) is defined as follows:
[tex]D(t) = 300t+125[/tex] for [tex]t< 2.5[/tex]
[tex]D(t) = 880[/tex] for [tex]2.5 \leq 3.5[/tex]
[tex]D(t) = 75t+612.5[/tex] for [tex]t\leq 6[/tex]
Where
t is the time in hours
D(t) is the distance covered, in miles, after t hours
Now let's analyze the different statements:
- The starting distance, at 0 hours, is 300 miles. --> FALSE. In fact, if we substitute t = 0 into the 1st equation, we get
[tex]D(0) = (300)(0)+125 = 125[/tex]
So, the distance at t = 0 is 125 miles.
- At 2 hours, the traveler is 725 miles from home. --> TRUE. In fact, if we substitute t = 2 into the 1st equation,
[tex]D(2) = (300)(2)+125 = 725[/tex]
- At 2.5 hours, the traveler is 875 miles from home. --> FALSE. In fact, for t=2.5 we have to use the 2nd equation, which states that the distance is:
D(t) = 880
So, not 875 miles.
- At 3 hours, the distance is constant, at 880 miles. --> TRUE. This is clearly visible from the 2nd equation: for t between 2.5 and 3.5 (so, in this case), the distance is
D(t) = 880
- The total distance from home after 6 hours is 1,062.5 miles --> TRUE. In fact, if we replace t = 6 into the last equation,
[tex]D(6)) = 75(6)+612.5=1062.5[/tex]
Learn more about functions:
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Learn more about distance:
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