It takes Mr. Martin 12 minutes to drive his bus route without stopping to pick up any passengers. For each passenger stop, he es
1 answer:
It is given that Mr Martin takes 12 minutes to drive his bus route without stopping on any of the stops.
On Tuesday, it took him 14 minutes when he stooped to take the passengers. He estimated that it takes 30 sec for each stop.
60 second = 1 minute.
30 second = 0.5 minutes.
Let us assume, there were x stops.
Since it takes him 12 minutes without stopping, 12 minutes here acts as a fixed time.
Total time is given by the equation
.... (1)
where t is the total time and x is the number of passengers.
To find the number of passengers, solve equation (1) for x ,
.... (2)
Plug y= 14 into equation number (2) gives 4 stops.
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Answer:
a)
b)
c)
d)
e)
And we take the absolute value on the middle integral because the distance can't be negative.
f)
g) The particle is speeding up
And would be slowing down from
Step-by-step explanation:
For this case we have the following function given:
Part a: Find the velocity at time t.
For this case we just need to take the derivate of the position function respect to t like this:
Part b: What is the velocity after 3 s?
For this case we just need to replace t=3 s into the velocity equation and we got:
Part c: When is the particle at rest?
The particle would be at rest when the velocity would be 0 so we need to solve the following equation:
We can divide both sides of the equation by 3 and we got:
And if we factorize we need to find two numbers that added gives -6 and multiplied 5, so we got:
And for this case we got
Part d: When is the particle moving in the positive direction? (Enter your answer in interval notation.)
For this case the particle is moving in the positive direction when the velocity is higher than 0:
So then the intervals positive are
Part e: Find the total distance traveled during the first 6 s.
We can calculate the total distance with the following integral:
And if we replace we got:
And we take the absolute value on the middle integral because the distance can't be negative.
Part f: Find the acceleration at time t.
For this case we ust need to take the derivate of the velocity respect to the time like this:
Part g and h
The particle is speeding up
And would be slowing down from
Lets remember the property "alternative-interior angles" when we have parallels lines:
Given two paralles lines, the following is true:
In our question, we have:
We know that the angles J + P + K=180
So, the triangles have all the angles the same, so they are similar by angle-angle-angle, and they have one side congruent, AC=CD, so the triangles are congruents.
