Answer: Choice D)
The angle between the two vectors is approximately 71.6 degrees
----------------------------------------------
----------------------------------------------
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)
-----------------------
|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)
-----------------------
u dot v = <8,4> dot <9,-9>
u dot v = 8*9 + 4*(-9)
u dot v = 72-36
u dot v = 36
-----------------------
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 general equation of a line is y = mx+b. The line is horizontal and the slope (m) of a horizontal line is 0. So y = 0x + b = b. Since the y intercept (where it crosses the y axis) is -1 (or b = -1) then you have the equation y = -1.
Answer: y = -1.
No they don't lie on the same line because all coordinate points would be at different distances from the origin. The only way a point could be at the same line as the others would be they would have to have the same x- or y- axis points. (For example: 6,5; 3,5; and 2,5 would all be on the same line, horizontally, because the 5 in all three coordinates refers to the y- axis aka the horizontal axis
Answer:
answers in this order
5
4
3
2
1
6
Step-by-step explanation:
i kno that the way these numbers are are kinda sus but this is correct
hope this helps <3
