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°.
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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:
_ <u>3a^8-8r^3</u>
4r^3
Step-by-step explanation:
7 tulips and 5 daffodils. An easy way to work this out is to list the multiples of both 5 and 4 until you get up to 55. Then you can find one number from each list which would add up to 55( which in this case would be 35 and 20) 35 being 7th in the 5 times table and 20 being 5th in the 4 times table.