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
9514 1404 393
Answer:
(b) (1, 1/6)
Step-by-step explanation:
The "unit rate" is always the y-value for x=1 when the relationship is proportional (as it is here).
That point is not specifically shown on the graph. It would be (1, 1/6).
Answer:
The area of the triangular sail is 216 ft²
Step-by-step explanation:
Since the sail is triangular, we solve the area using the area of a triangle
Area of triangle = 1/2 of base × height
base is 18 and height is 24
Area = 1/2 × 18 × 24
= 9×24
= 216 ft²
25,*55**3,552
*is the digit in the hundred thousand place
**is the digit that has 1/1000 the value of the digit.
(*) indicates the number after the *.
I doubled check this work, but I will update comment with a triple check
