Answer:
x = 14.4
Step-by-step explanation:
x is sin(angle 24/30)×24
how do we get the angle at 24/30 ?
by using the extended Pythagoras for baselines opposite other than 90 degrees.
c² = a² + b² - 2ab×cos(angle opposite of c)
in our example the angle 24/30 is opposite of the side 18.
so,
18² = 24² + 30² - 2×24×30×cos(angle 24/30)
324 = 576 + 900 - 1440×cos(angle 24/30)
324 = 1476 - 1440×cos(angle 24/30)
1440×cos(angle 24/30) = 1152
cos(angle 24/30) = 1152/1440 = 576/720 = 288/360 = 144/180 = 72/90 = 36/45 = 12/15 = 4/5
angle 24/30 = 36.9 degrees
x = sin(36.9) × 24 = 14.4
Find the common multiples:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48
Multiples of 9: 9, 18, 27, 36, 45
The common multiples are 18 and 36
The first person in line to get both free would be the 18th person and then the 36th person.
So she is correct that the 36th person would get both free, but they wouldn't be the first person to do it.
Answer: 2184
because when you multiply 14 times 12 times 13 you get 2184
