Find all natural numbers n such that 1+3+5+7+...+(2n-1) sum is divisible by 4
2 answers:
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Answer:
cos q = 3/5
Step-by-step explanation:
Standard position means the vertex (point or corner of the angle) is at (0,0) and one side of the angle is glued to the positive x-axis (facts, but not technical math terms) See image. Special triangles have all three sides nice and clean with whole number lengths, we call these Pythagorean triples. 3-4-5 is your most basic Pythagorean triple. So we don't even have to calculate the hypotenuse, see image. Now the triangle shown is easy to work with, using entry-level trig...cos = ADJ/HYP. So we get 3/5=.6 BUUuuuut, the angle q in the original problem is actually the giant angle, marked in yellow (see image) and we're in the fourth quadrant which means there's negative numbers all over the place. So just to be sure the answer is .6 and not -.6 Check your signs. One trick to remember is the ASTC markings in the quadrants. I use All Students Take Calculus, but what it means is in the first quadrant All the trig functions are positive. Only Sine (and fam) are positive in the 2nd quadrant. Tan (and fam) in the 3rd and Cos and fam in the 4th quadrant. It's a good quick check.
cos q = 3/5 OR cos q = .6
As in each table can seat 8 people and the probability you need to find is about the first person you can ignore this data.
Probability that the first person to enter the room will be randomly seated at a maple table:
#maple tables: 9
# total tables: 9 +10 +5 +7=31