Mathematics: Find the arithmetic mean of 64 and 69

Find the arithmetic mean of 64 and 69 - id646912262690, buchmannhannah0

kira96

28.03.2021

66.5

Step-by-step explanation:

64+69=133

133÷2=66.5

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edith47

12.05.2021

Step-by-step explanation:

Given that ||v|| = 2 and ||w|| = 3, and the angle between v and w is 120 degrees

We know by definition of dot product and properties that

a.b = ||a||||b||cos t where t is the angle between them

Using this we find

(a) v·w = $2(3) cos 120\\=-3$

(b) ∥2v+w∥

(2v+w).(2v+w) = 4 v.v +4 w.v +w.w= 4(2)^2+4(-3)+9 =13

$||2v+w||^2 =13\\||2v+w||=\sqrt{13}$

(2v-3w).(2v-3w) = 4 v.v -12 w.v +9w.w= 4(2)^2-12(-3)+9(9) =133

$||2v-3w||^2 =133\\||2v-3w||=\sqrt{133}$

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