Start from 110 feet away, a person on a bicycle rides towards a checkpoint and then passes it. The rider is travelling at a cons
tant rate of 30 feet per second. The distance between the bicycle and the checkpoint is given by the equation d=|110-30t| at what times is the bike 40 feet away from the checkpoint?
a. 2.3 sec and 5 sec
b. 1.6 sec and 5 sec
c. 2.3 sec and 4.6 sec
d. 1.6 sec and 4.6 sec
a. 2.3 sec and 5 sec
b. 1.6 sec and 5 sec
c. 2.3 sec and 4.6 sec
d. 1.6 sec and 4.6 sec
1 answer:
Answer:
a. 2.3 sec and 5 sec
Step-by-step explanation:
The graph is symmetrical about the time (t) that makes d=0. That makes the line of symmetry be ...
110/30 = t ≈ 3.67
This will be the average of the two times, so their sum is ...
t1 +t2 = 2×3.67 = 7.3
Only one answer choice has a sum of 7.3 seconds:
2.3 sec and 5 sec
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Answer:
Part 1) AJ drawn the parabola opening upwards, instead of drawing it opening downwards
Part 2) see the explanation
Step-by-step explanation:
Part 1) What mistake did AJ make in the graph?
we have
This is the equation of a vertical parabola written in vertex form
The parabola open downward (because the leading coefficient is negative)
The vertex represent a maximum
The vertex is the point (-2,-1)
therefore
AJ drawn the parabola opening upwards, instead of drawing it opening downwards
Part 2) Evaluate any two x-values (between -5 and 5) into AJ's function. Show your work. How does your work prove that AJ made a mistake in the graph?
take the values x=-4 and x=4
For x=-4
substitute the value of x in the quadratic equation
For x=4
substitute the value of x in the quadratic equation
According to AJ's graph for the value of x=-4 the function should be positive, however it is negative and for the value of x=4 the function should be positive and the function is negative
therefore
AJ made a mistake in the graph