Abouncy ball is released from a certain height. on the first bounce, it travels 32cm. with each subsequent bounce, it travels 9/10 the distance of the previous bounce. what is the total distance that the ball has traveled when it completes its 25th bounce?

594?

Step-by-step explanation:

The wording leaves a little to be desired. What does that 32 actually mean?

I don't think it is asking us to add on the distance it has to travel to get a bounce of 32. We are starting with a bounce that is 32 high.

The second bounce is 9/10 of that height which turns out to be 28.8.

The third bounce is 9/10 of 28.8 which is 25.92, I think, and then it continues on.

So here are the Givens

Given

a = 32

r = 9/10

n = 25

Formula

Sum = a(1 - r^n) / (1 - r)

Solution

Sum = 32*(1 - (9/10)^25) / (1 - 9/10)

Sum = 32*(1 - 0.07179) / ( 1 - 9/10)

Sum = 32*(0.9282) / 0.1

Sum = 29.7 / 0.1

Sum = 297

But that number represents only the distance going up. You must also take the distance going down. You have to double this answer.

2*sum = 2 * 297

Sum' = 594

The wording is a real snake. We don't really know if we need to include some height that was a start. If we do, the answer is 594 + k where k is a constant yet to be determined. Usually k is part of the problem.

Or do we take a = 32 as the first drop? We can't tell from the wording.

2/5

step-by-step explanation:

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer