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
Rise over run is -2/4 or simplified as -1/2
The second one is
Answer:
The answer to your question is: Yes a parabola can be drawn if we know the focus and the directrix.
Step-by-step explanation:
We can say that it is a vertical parabola that opens downwards.
We conclude that if we graph both the focus and the directrix. Also if we continue the process we can find the vertex (-4, -7) and p = 3.
We have
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A B C D E
-----------------------------------------------
1 yard
--------------
1/5 yard ------------------
7/10 yard
<span>The distance poles B and D= (1-1/5)=4/5 yard
</span>The distance poles B and E= BD+DE=4/5+7/10=(8+7)/10=15/10=3/2 yard
the answer is 3/2 yard (distance poles B and E)
