While performing a piece of music, Shivani strikes the cymbals every 8 beats and the triangle is every 4 beats. If she just struck both at the same time, how many beats will pass before she again strikes them at the same time?

actually it's 8

Step-by-step explanation:

You need to find the smallest number that is a multiple of both 8 and 4. This is the least common multiple.

List the multiples of each number. Find the smallest number that appears in both lists.

Multiples of 8:  8, 16, 24, 32, 40

Multiples of 4:  4, 8, 12, 16, 20

The least common multiple of 8 and 4 is 8. That means that Aisha will strike the cymbals and the triangle together in 8 beats, because 1 repetition of the 8-beat cymbal cycle is a total of 8 beats long and 2 repetitions of the 4-beat triangle cycle is a total of 8 beats long.

8 beats will pass before Aisha again strikes the cymbals and triangle at the same time.

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50