Prove that the two circles shown below are similar. Circle A is shown with a center at 3, 4 and a radius of 5. Circle C is shown
1 answer:
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- 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:
for
for
for
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
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,
- 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,
Learn more about functions:
Learn more about distance:
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