A small pool is being drained. There are 1500 gallons of water remaining in the pool after 5 minutes and 1000 gallons after 10 minutes. How much water was in the pool BEFORE it started draining.

Answer 1

Let's call the initial amount of water in the pool "x".

We know that after 5 minutes, there are 1500 gallons of water remaining. This means that in the first 5 minutes, (x - 1500) gallons of water were drained.

Similarly, after 10 minutes, there are 1000 gallons of water remaining. This means that in the next 5 minutes (from 5 to 10 minutes), another (1500 - 1000) = 500 gallons were drained.

So in total, (x - 1500) + 500 = (x - 1000) gallons of water were drained in 10 minutes.

Simplifying this equation, we get:

x - 1000 = (x - 1500) + 500

x - 1000 = x - 1000

Solving for x, we get:

x = 2000

So there were originally 2000 gallons of water in the pool before it started draining.

Answer 2

The first five terms of an arithmetic sequence are 29, 25.5, 22, 18.5, and 15. Which function, f(n), could be used to describe the nth term of the sequence?

Answer 3

Let's first find the common difference, d, between consecutive terms in this arithmetic sequence:

d = 25.5 - 29 = -3.5
d = 22 - 25.5 = -3.5
d = 18.5 - 22 = -3.5
d = 15 - 18.5 = -3.5

We see that the common difference is -3.5 for this arithmetic sequence. Now we can use this to find the general formula for the nth term using the formula:

a_n = a_1 + (n - 1)d

where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference.

Using the given first term, a_1 = 29, and the common difference, d = -3.5, we get:

a_n = 29 + (n - 1)(-3.5)

Simplifying and rearranging, we get:

a_n = 32.5 - 3.5n

Therefore, the function f(n) that could be used to describe the nth term of the sequence is:

f(n) = 32.5 - 3.5n