Answer: sin u = -5/13 and cos v = -15/17
Step-by-step explanation:
The nice thing about trig, a little information goes a long way. That’s because there is a lot of geometry and structure in the subject. If I have sin u = opp/hyp, then I know opp is the opposite side from u, and the hypotenuse is hyp, and the adjacent side must fit the Pythagorean equation opp^2 + adj^2 = hyp^2.
So for u: (-5)^2 + adj^2 = 13^2, so with what you gave us (Quad 3),
==> adj of u = -12 therefore cos u = -12/13
Same argument for v: adj = -15,
opp^2 + (-15)^2 = 17^2 ==> opp = -8 therefore sin v = -8/17
The cosine rule for cos (u + v) = (cos u)(cos v) - (sin u)(sin v) and now we substitute: cos (u + v) = (-12/13)(-15/17) - (-5/13)(-8/17)
I am too lazy to do the remaining arithmetic, but I think we have created a way to approach all of the similar problems.
Answer:
4 oil changes
Step-by-step explanation:
Given that:
Distance after first oil change = 5000 miles
Subsequent oil changes = 3300 miles
If distance in miles moved per week = 250 m
Number of weeks per year = 52
Total miles moved per year = (250 * 52) = 13000 miles
Let Number of oil change per year = n
Difference between successive oil change = d = 3300 miles
Using the relation :
Total miles = Ist change + (n - 1)d
13000 = 5000 + (n - 1)3300
13000 = 5000 + 3300n - 3300
13000 = 1700 + 3300n
13000 - 1700 = 3300n
11300 = 3300n
n = 3.424
Hence, number of oil. Changes in first year = 4
Answer:
7,999,800
Step-by-step explanation:
8,000,000 minus 200 = answer
