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(d) The particle moves in the positive direction when its velocity has a positive sign. You know the particle is at rest when and
, and because the velocity function is continuous, you need only check the sign of
for values on the intervals (0, 3) and (3, 6).
We have, for instance and
, which means the particle is moving the positive direction for
, or the interval (3, 6).
(e) The total distance traveled is obtained by integrating the absolute value of the velocity function over the given interval:
which follows from the definition of absolute value. In particular, if is negative, then
.
The total distance traveled is then 4 ft.
(g) Acceleration is the rate of change of velocity, so is the derivative of
:
Compute the acceleration at seconds:
(In case you need to know, for part (i), the particle is speeding up when the acceleration is positive. So this is done the same way as part (d).)
Answer:
See below, please!
Step-by-step explanation:
We can set up a system of equations to model this problem. Let's consider the student's ticket as x, and y for the adult ticket.
So since the student ticket is $1.50, and adult is $4, we can set up the following equation: , since they collected $5050 total.
We can set up another equation modeling the number of people who came to the game. This would be x+y=2200.
Solve this, and we get x= 1500 and y=700. So, they sold 1500 student tickets and 700 adult tickets.
Hope this helped!