Answer:
the angle between u=(8, -2) and v=(9,3) is 32.5°
Step-by-step explanation:
u=(8,-2)=(u1,u2)→u1=8, u2=-2
v=(9,3)=(v1,v2)→v1=9, v2=3
We can find the angle between two vectors using the formula of dot product:
u . v =║u║║v║cos α (1)
And the dot product is:
u . v = u1 v1 + u2 v2
u . v = (8)(9)+(-2)(3)
u . v = 72-6
u . v = 66
║u║=√(u1²+u2²)
║u║=√((8)²+(-2)²)
║u║=√(64+4)
║u║=√(68)
║u║=√((4)(17))
║u║=√(4)√(17)
║u║=2√(17)
║v║=√(v1²+v2²)
║v║=√((9)²+(3)²)
║v║=√(81+9)
║v║=√(90)
║v║=√((9)(10))
║v║=√(9)√(10)
║v║=3√(10)
Replacing the known values in the formula of dot product (1):
u . v =║u║║v║cos α
66 = 2√(17) 3√(10) cos α
Multiplying:
66 = 6√((17)(10)) cos α
66 = 6√(170) cos α
Solving first for cos α: Dividing both sides of the equation by 6√(170):


Simplifying: Dividing the numerator and denominator on the left side of the equation by 6:
(66/6)/(6√170/6)=cosα→11/√170=cosα→cosα=11/√170
cosα=11/13.03840481→cosα=0.84366149

Answer:
-159
Step-by-step explanation:
Find the mean and median of the data set 3,5,6,2,10,9,7,5,11,6,4,2,5,4
Tanya [424]
Answer:
mean: 5.6 ; median: 5
Step-by-step explanation:
first order them:
2, 2, 3, 4, 4, 5, 5, 5, 6, 6, 7, 9, 10, 11
now we can see that the median is 5 since it's in the middle
and the mean is adding all and dividing by how many numbers we have (AKA 14) so 2+2+3+4+4+5+5+5+6+6+7+9+10+11 = 79 and now we divide 79 by 14 which is:
5.64285714
Answer:
For red you have a 1/5% chance for pink you have a 2/4% chance also know as 50% chance
Step-by-step explanation:
Answer:
268
Step-by-step explanation: