slader How many partitions of the set {1, 2, 3, . . . , 100} are there such that there are exactly three parts and elements 1, 2
1 answer:
Answer:
partitions.
Step-by-step explanation:
As we know if we have x number of elements we can arrange them in x! ways.
here we have 100 elements so we can arrange them in 100! ways.
Now if we have exactly three parts and 1,2 and 3 are in different parts then let consider 1 goes to part 1, 2 goes to part 2, and 3 goes to part 3. For the remaining 97 elements, we have three options for each element, thus we can arrange the remaining 97 elements in ways/partitions.
each of these partition will contain only three elements.
You might be interested in
(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).)