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:
400
Step-by-step explanation:
i think you should revise the q. it looks incorrect...
all but 3 students said they would NOT vote for a tiger...** if that"s the thing then this answer is correct did it by ratio file is attatched:)
Answer:
The greatest number of rows that can be planted, and have nothing left over, would be 3
Step-by-step explanation:
Find the greatest common factor (gcf) of 15 and 9
15: 1 3 5 15
9: 1 3 9
In this case, the gcf of 15 and 9 would be 3.
<span>Animal and plants organs are organized into organ systems,<span>much like you organize your homework in SCHOOL
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Step-by-step explanation:

0.0666666666666