Mean: average of the numbers median: middle of the numbers mode: which number appears the most
486/900 = .54 = 54%. .......
Let s = northbound train
Then
2s = southbound train
:
Distance = time * speed
4s + 4(2s) = 600
:
4s + 8s = 600
:
12s = 600
:
s = 600/12
:
s = 50 mph is the northbound train
Then
2(50) = 100 mph is the southbound train
:
:
Check:
4(50) + 4(100) = 600
Answer:
Step-by-step explanation:
The formula for the dot product of vectors is
u·v = |u||v|cosθ
where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.
which is 
which is 
I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.
We also need the angle, which of course has its own formula.
where uv has ITS own formula:
uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.
uv = 96.
To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:
which returns an angle measure of 30.7. Plugging that all into the dot product formula:
gives you a dot product of 96
The integral of e raised to x squared dx to the limit from 1 to 3 translating in equation we get
∫1-3 e^(X^2) dx.
Solving using scientific calculator, we have 1443.082471 or simply 1443.
<em>ANSWER: 1443</em>