I kind of owe someone a favor :P and I have no idea
A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 9 inches.
Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning. For example, the point (0, 9) would represent a height of 9 inches after 0 hours. Explain how you obtained the ordered pairs.
Part B: Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A.
Part C: If the rate at which the candle burned was 0.45 inches per hour instead of 0
thanks
h = 9 - .5 t
or if you insist on x and y
y = 9 - .5 x
(0,9) obviously
(1,8.5)
(2,8)
(3,7.5) etc etc etc
yes, there is one y for every x
y = 9 - .45 x
A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 9 inches.
Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning. For example, the point (0, 9) would represent a height of 9 inches after 0 hours. Explain how you obtained the ordered pairs. (5 points)
The ordered pairs would be (0,9), (2,8), (4,7), (6,6), (8,5), (10, 4), 12, 4). I went with these since every 2 hours the candle burns 1 inch.
Part B: Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A. (2 points)
This is a function. I know this since none of the answers repeat and they follow a pattern. It is also linear. There is only one value for each x if you use the coordinates.
I haven't finished the last part tho.
thsnks!
Part A: To obtain the ordered pairs, we need to determine the height of the candle at different time intervals. Since the candle burns down at a rate of 0.5 inches per hour, we can subtract 0.5 inches from the previous height to find the current height.
Starting with the initial height of 9 inches, after 1 hour, it would have burned down by 0.5 inches, leaving us with a height of 9 - 0.5 = 8.5 inches. Therefore, the first ordered pair would be (1, 8.5).
Continuing in the same manner, we can find the successive heights of the candle at different time intervals:
- After 2 hours: height = 9 - (0.5 * 2) = 9 - 1 = 8 inches. Ordered pair: (2, 8)
- After 3 hours: height = 9 - (0.5 * 3) = 9 - 1.5 = 7.5 inches. Ordered pair: (3, 7.5)
- After 4 hours: height = 9 - (0.5 * 4) = 9 - 2 = 7 inches. Ordered pair: (4, 7)
- After 5 hours: height = 9 - (0.5 * 5) = 9 - 2.5 = 6.5 inches. Ordered pair: (5, 6.5)
- After 6 hours: height = 9 - (0.5 * 6) = 9 - 3 = 6 inches. Ordered pair: (6, 6)
So, the list of ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) is:
(1, 8.5), (2, 8), (3, 7.5), (4, 7), (5, 6.5), (6, 6).
Part B: Yes, this relation is a function. In a function, each input (x-value) has only one corresponding output (y-value). In the ordered pairs we obtained, each time value (x) has a unique height (y), meaning there are no repeated x-values. Therefore, by examining the list of ordered pairs created in Part A, we can conclude that this relation is a function.
Part C: If the rate at which the candle burned was 0.45 inches per hour instead of 0.5 inches per hour, we would need to recalculate the heights at different time intervals using the new rate.
However, as you mentioned "0" after "0.", I assume there was a typo, and you meant the rate to be "0.45 inches per hour instead of 0." In that case, the process to determine the ordered pairs would be the same as in Part A, but using the new rate:
Starting with the initial height of 9 inches, after 1 hour: height = 9 - (0.45 * 1) = 9 - 0.45 = 8.55 inches. Ordered pair: (1, 8.55).
Continuing in the same manner, we can find the successive heights of the candle at different time intervals using the new rate of 0.45 inches per hour.
Note: If you meant the rate to be 0, it would mean the candle is not burning at all, and the height would remain constant at 9 inches regardless of the time.