CalculatorUser

LOLOLOLOL sorry about my silly mistake

Ughhh so hard! I tried using law of cosines, but it didn't work! I got a massive equation that I didn't know how to simplify!

AoPS doesn't have much good math problems currently, as everyone is crying over their AMC 10 score lol. So I came back here

Distance car 1 traveled = x

Distance car 2 traveled = y

Use formula d=rt

Total distance traveled for both cars = 700

x + y = 700

speed = s

7s = x

7(s + 10) = y

Substitute

7s + 7s + 70 = 700

14s = 630

s = 45

Car 1's speed is 45 mph

Car 2's speed is 55 mph

done

Side of square = x

Base of triangle = x

Height of triangle = \(\frac{3x}{4}\)

Area of triangle = \(\frac{3x^2}{8}\)

Area of square = \(x^2\)

Ratio - \(\frac{3x^2}{8x^2}=\frac{3}{8}\)

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or you can just substitute integer numbers

i lov you

whoops! I forgot that you have to multiply everything by 3

Total number of ways people can be seated:

18 choose 3

\(\frac{18!}{3!15!}=816\)

Since no two people can be adjacent we have two cases

Three people adjacent

18 ways (18 choose 1)

Two people adjacent (18 * 14)

So 816 - 18 - (18*4)

546

Is this right?