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
Answer:
c. 4x + 20 = 140
Step-by-step explanation:
Perimeter = 140 feet
Width = L + 10
P = 2w + 2L
P = 2(L + 10) + 2L
P = 2L + 20 + 2L
P = 4L + 20
Answer:
y = 0
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
There are two 1/8 in one 1/4. There are eight 1/8 in 1. 8/8 + 1/8 + 1/8 = ten 1/8.
<u>ANSWER</u>
A. (4,12)
<u>EXPLANATION</u>
The equations are:
and
To eliminate a variable we make the coefficients of that variable the same in both equations.
It is easier to eliminate x.
We multiply the first equation by 2 to get:
We add equations (2) and (3).
Divide both sides by 23
Put x=4 into equation (1).
The solution is (4,12)
