Asphere and a cylinder have the same radius and height. The volume of the cylinder is 18 cm3.
1 answer:
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Remember
translates to 
and
so
4096=16^3
divide both sides by 3
translate
3x-2=16
add 2 to both sides
3x=18
divide both sides by 3
x=6
and
so
4096=16^3
divide both sides by 3
translate
3x-2=16
add 2 to both sides
3x=18
divide both sides by 3
x=6
(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).)