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
14,000 because 494 would round down since it is not above 500.
Answer:
YASSSSSSSS
Step-by-step explanation:
Answer:
The answer is 7/36.
Step-by-step explanation:
First, you find out how many possible outcomes there are from rolling a pair of dice. On one cube, you can roll a 1,2,3,4,5, or 6; so there are 6 outcomes. Since there are two cubes, you multiply 6 by itself to get a total of 36 possible outcomes. Next, you find the probability of the sum of the numbers rolled being an even number; the possibilities are 2,4,6,8,10, or 12, which is 6/36. The probability of rolling a multiple of 5; the one possibility is just 5, since we already accounted for rolling a 10 as an even number. So that is 1/36. The word <u>or</u> says that we add the two probabilities, so the final answer is 6/36+1/36=7/36.
D is the answer
(4+8)+1 = 13
4+(8+1) = 13
Therefore equation D is true
