Question

A ditch contains 10 centimeters of water. Rainwater accumulates in the ditch as follows: 10 centimeters of water by the end of the 1st second, 15 centimeters by the end of the 2nd second, 20 centimeters by the end of the 3rd second, and so on. Assuming that the ditch has sufficient capacity for storage, how many centimeters of water will it have after 10 seconds? a. 55 c. 75 b. 65 d. 110

Answer 1

After 10 seconds, the ditch will have 55 centimeters of water.

Step-by-step explanation:

To find the number of centimeters of water in the ditch after 10 seconds, we need to determine the pattern of accumulation. From the information given, we can see that the amount of water increases by 5 centimeters every second (10 cm in the 1st second, 15 cm in the 2nd second, and so on). This means that the amount of water accumulated after each second is an arithmetic sequence. The general formula for an arithmetic sequence is: a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference.

In this case, the first term a_1 is 10 cm and the common difference d is 5 cm. Plugging these values into the formula, we can find the 10th term (a_10): a_10 = 10 + (10-1)5 = 55.

Therefore, after 10 seconds, the ditch will have 55 centimeters of water, which corresponds to option a. 55.

Answer 2

Firstly, let's create a function of f(t) where t represents the time that has past, and f(t) represents the amount of rainwater. We know that when t=1, then f(t)=10, and t=2 then f(t)=15. So, let's take that and analyze it:

(1,10)
(2,15)
m = (15-10)/(2-1) = 5
y-intercept = 5
∴ f(t) = 5t+5

Now we just evaluate t for 10:

f(10) = (5*10)+5
f(10) = 55