ACT MATH HARD

Test Preparation ACT Preparation
1

Jill and matt began at the same point but ran around the track in opposite directions. Jill ran at a constant speed that was 2 meters faster than Matt’s constant speed. jill passed Matt for the first time in 40 seconds. Jill ran at a constant rate of how many meters per second? (400 meter long track, they run 10 laps daily)
A4
B5
C6
D7
E10

Correct answer is C

if n!/(n-2)! = 30, then (n-1)!=
A15
B24
C60
D120 (correct)
E720

I got this one right but I was wondering why it couldn’t be another answer as well?
what forms f(gx))= square root of 2X^2+3

f(x) = square root of x, g(x) = 2x^2+2

and this was wrong but why? f(x)= square root of x^2+3, g(x)= 2X

2

bump?

3

@xxupenngal

  1. [quote]

    Jill ran at a constant speed that was 2 meters faster

    [/quote]

    Do you mean “2 meters per second faster?”

If so, then Jill runs at m+2 meters per second, while Matt runs at m meters per second. In 40 seconds, they run a combined total of 400 meters, so we have 40(m + (m+2)) = 400 --> 2m+2 = 10 --> m = 4. Then Jill’s speed is 6 m/s.

  1. n!/(n-2)! cancels to n(n-1). So we have n(n-1) = 30 --> n = 6. Then (n-1)! = 5! = 120.
  2. Make sure you type carefully because you have +3 in one expression and +2 in another.

If f(x) = sqrt(x^2 + 3) and g(x) = 2x, then f(g(x)) = f(2x) = sqrt(4x^2 + 3) which is not the same as the what we wanted.