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

The answer to “What is 201.3 divides by 3” is 67.1.
The correlation that is most likely a causation is <span>the positive correlation between the number of sodas sold on a campus and the number of cans in the campus recycling bins.
While the other scenarios may have variables with some relation to each other, in this scenario, we can see that if a campus sells more sodas, they would end up with more cans in the recycling bins; the cans would be caused by the soda sales.</span>
803=800
56=60
So the cost for the refrigerators is
800×60=48000