(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:
-1/6
Step-by-step explanation:
5a+2/3=-1/6
5a=-1/6-2/3
5a=-1/6-4/6
5a=-5/6
a=(-5/6)/5
a=(-5/6)(1/5)
a=-5/30
simplify
a=-1/6
Answer:
Kevin will take 3 hours to make all pieces.
Step-by-step explanation:
Kevin is building a large model of a soccer ball which is made of 20 hexagons and 12 pentagons.
Time taken by Kevin to measure and cut each hexagon = 6 minutes
Therefore, time taken to make 20 hexagons = 6×20 = 120 minutes
Similarly time taken by him to measure and cut a pentagon = 5 minutes
So, time taken to make 12 pentagons = 12×5 = 60 minutes
Total time taken to measure and cut 12 pentagons and 20 hexagons = 60+120 = 180 minutes
Therefore, Kevin will take 180 minutes or 3 hours to make all pieces.
