(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:
Y=x+6
Step-by-step explanation:
F ( x ) = k * x²
f ( 4 ) = 96
96 = k * 4²
96 = 16 k
k = 96 : 16
k = 6
f ( 2 ) = 6 * 2² = 6 * 4 = 24
ANSWER D
Answer:
8
Step-by-step explanation:
Let the initial values of the height and the diameter be h and 2r.
Then the volume of the non-enlarged cylinder is \pi r^2 h
The volume of the enlarged cylinder becomes \pi(2r)^2 2h = \pi 4r^2*2h =8*\pi r^2 h.
So the 2nd volume is obtained by multiplying the 1st volume by 8.
Therefore the cylinder is enlarged by factor 8.
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