Answer: Choice D)
The angle between the two vectors is approximately 71.6 degrees
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Work Shown:
Each time I write the word "dot" I mean "dot product".
|u| = length of vector u
|u| = sqrt(u dot u)
|u| = sqrt(<8,4> dot <8,4>)
|u| = sqrt(8*8 + 4*4)
|u| = sqrt(64 + 16)
|u| = sqrt(80)
|u| = sqrt(16*5)
|u| = sqrt(16)*sqrt(5)
|u| = 4*sqrt(5)
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|v| = length of vector v
|v| = sqrt(v dot v)
|v| = sqrt(<9,-9> dot <9,-9>)
|v| = sqrt(9*9 + (-9)*(-9))
|v| = sqrt(81+81)
|v| = sqrt(2*81)
|v| = sqrt(2)*sqrt(81)
|v| = sqrt(2)*9
|v| = 9*sqrt(2)
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u dot v = <8,4> dot <9,-9>
u dot v = 8*9 + 4*(-9)
u dot v = 72-36
u dot v = 36
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cos(theta) = (u dot v)/(|u|*|v|)
cos(theta) = (36)/(4*sqrt(5)*9*sqrt(2))
cos(theta) = (36)/(36*sqrt(10))
cos(theta) = 1/(sqrt(10))
cos(theta) = sqrt(10)/10
theta = arccos(sqrt(10)/10)
theta = 71.56505
which rounds to 71.6 when rounding to one decimal place (nearest tenth)
That's why the approximate answer is roughly 71.6 degrees
The least common multiple between those following numbers is C. 90.
For this case we have that the generic equation of the line is given by:
Where,
m: slope of the line
b: intersection with the y axis.
Since the line is parallel to PQ, then the slopes are equal.
We have then:
On the other hand we have:
Substituting values we have:
Answer:
The equation of the line that is parallel to line PQ and that has the and intercept b = -3 is:
Answer:
The slope is 1/3
Step-by-step explanation:
The equation is written in slope-intercept form. This is shown as y=mx+b where m is the slope and b is the y-intercept.
m is 1/3 because of this
Hope this made sense!
Answer:
bvghb vbub b
Step-by-step explanation:
