Answer:
90°
Step-by-step explanation:
The angle between the vectors can be found any of several ways. Here, we observe that the segments from the origin to the two points are at right angles to each other. (Their slopes are opposite reciprocals.) Hence the angle between the vectors is 90°.
__
The slope to point 'a' is y/x = 2/1 = 2.
The slope to point 'b' is y/x = (-1/2)/1 = -1/2.
The product of these slopes is (2)(-1/2) = -1, indicating the vectors are perpendicular. The angle between them is 90°.
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We can also use the trig formula for the tangent of the difference of angles.
tan(α-β) = (tan(α) -tan(β))/(1 +tan(α)tan(β))
The tangents are the slopes, calculated above, so we have ...
tan(α -β) = (2 -(-1/2))/(1 +(2)(-1/2)) = (5/2)/0 = <em>undefined</em>
The tangent is <em>undefined</em> for angles that are odd multiples of 90°. The angle between the vectors is 90°.
Answer:
15 outfits
Step-by-step explanation:
We have 3 possibilities for pants and 5 possibilities for tops.
The tailor has 3 possible pants to choose from and 5 possible tops to choose from. Using the Fundamental Counting Principle, we can simply multiply these two together to get the total number of possible outfits:
3 * 5 = 15 outfits
Or, we could make a tree diagram. See attachment. It will give the same answer.
Answer: The square root of 8 is expressed as √8 in the radical form and as (8)½ or (8)0.5 in the exponent form. The square root of 8 rounded up to 8 decimal places is 2.82842712. It is the positive solution of the equation x2 = 8.
Step-by-step explanation:
[ Answer ]
[ Explanation ]
4 + 3 + 7 ___ 7 + 0 + 7
Solve Each Side:
4 + 3 + 7 = 14
7 + 0 + 7 = 14
14 __ 14
14 is equal to 14, therefore the __ (Or ?) is replaced with an = sign.
![\boxed{[ \ Eclipsed \ ]}](https://tex.z-dn.net/?f=%5Cboxed%7B%5B%20%5C%20Eclipsed%20%5C%20%5D%7D)
Answer:
d
Step-by-step explanation:
100x² - 1 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b), thus
100x² - 1
= (10x)² - 1²
= (10x - 1)(10x + 1) → d
