Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
2 answers:
Answer:
Step-by-step explanation:
Given : P = (5, 8) and Q = (6, 9)
To find: the component form and magnitude of vector PQ.
Solution: It is given that P = (5, 8) and Q = (6, 9).
The component form of the vector PQ is given as:
The magnitude of vector PQ is given as:
Thus, the component form of the vector PQ is and the magnitude form is
.
You might be interested in
Answer:
1, 2, 2, 2, 3, 8, 9
Step-by-step explanation:
The following data represent the times in minutes required for 18 co-workers to commute to work
48 42 31 29 41 22 38 38 21 39 22 48 22 12 34 32 23 28
Rewrite this data in ascending order
12 21 22 22 22 23 28 29 31 32 34 38 38 39 41 42 48 48
Now, the stem-and-leaf plot is
The second row represents the leaves for the given data points in the range 20 to 29 for this stem-and-leaf plot, so the answer is
1, 2, 2, 2, 3, 8, 9
The half-range sine series is the expansion for 
with the assumption that is considered to be an odd function over its full range, 
. So for (a), you're essentially finding the full range expansion of the function
with period 2 so that
for 
and integers 
.
Now, since is odd, there is no cosine series (you find the cosine series coefficients would vanish), leaving you with
where
In this case,
, so
The half-range sine series expansion for is then
which can be further simplified by considering the even/odd cases of, but there's no need for that here.
The half-range cosine series is computed similarly, this time assuming is even/symmetric across its full range. In other words, you are finding the full range series expansion for
Now the sine series expansion vanishes, leaving you with
where
for
. Again, . You should find that
Here, splitting into even/odd cases actually reduces this further. Notice that when is even, the expression above simplifies to
while for odd, you have
So the half-range cosine series expansion would be
Attached are plots of the first few terms of each series overlaid onto plots of. In the half-range sine series (right), I use 
terms, and in the half-range cosine series (left), I use 
or 
terms. (It's a bit more difficult to distinguish from the latter because the cosine series converges so much faster.)
with period 2 so that
Now, since
where
In this case,
The half-range sine series expansion for
which can be further simplified by considering the even/odd cases of
The half-range cosine series is computed similarly, this time assuming
Now the sine series expansion vanishes, leaving you with
where
for
Here, splitting into even/odd cases actually reduces this further. Notice that when
while for odd
So the half-range cosine series expansion would be
Attached are plots of the first few terms of each series overlaid onto plots of