Answer:
C. 4.2a + 0.8
Step-by-step explanation:
Given:
The two binomials given for addition are:
and
Now, adding both the binomials, we get:
Distributing the positive sign inside the second binomial, we get:
Now, combining like terms using the commutative property of addition, we get:
Simplifying the above expression, we get:
Therefore, the resulting addition of the given binomials is
Hence, option C is the correct answer.
(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).)