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Sagot :
Candle burns down at the rate of 0.5 inches per hour gives the order pair (1, 5.5), (2, 5), (3, 4.5) (4, 4) (5, 3.5) and (6, 3).
- a) 6 ordered pairs to show the height of the candle is (1, 5.5), (2, 5), (3, 4.5) (4, 4) (5, 3.5) and (6, 3)
- b) The relation has a function.
- c) The function is continue but the output value is changed.
What is rate of decrement?
The rate of decrement is the rate by which the amount of a thing or object is reducing.
Given information-
The rate of candle burns down is 0.5 inches per hour.
The original height of the candle is 6 inches.
- 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-
As the rate of candle burns down is 0.5 inches per hour.
This means that the height of the candle reduces 0.5 inches after every hour passing on. Thus reduce 0.5 form each time as the 1 hour pass to make the order.
Thus the 6 ordered pairs to show the height of the candle in inches is (1, 5.5), (2, 5), (3, 4.5) (4, 4) (5, 3.5) and (6, 3)
- b) Relation of function-
The equation for the height of the candle in inches (y) as a function of time in hours (x) can be given as,
[tex]y=6-0.5x[/tex]
To make the list for 6 ordered pair, put the value of (x) as ,1,2,3,4,5 and 6.
The height after 1 hour passed is,
[tex]y=6-0.5\times 1\\y=6-0.5\\y=5.5[/tex]
Thus the first order pair of time and height of candle is (1, 5.5).
The height after 2 hour passed is,
[tex]y=6-0.5\times 2\\y=6-1\\y=5[/tex]
Thus the second order pair of time and height of candle is (2, 5).
The height after 3 hour passed is,
[tex]y=6-0.5\times 3\\y=6-1.5\\y=4.5[/tex]
Thus the third order pair of time and height of candle is (3, 4.5).
The height after 4 hour passed is,
[tex]y=6-0.5\times 4\\y=6-2\\y=4[/tex]
Thus the forth order pair of time and height of candle is (4, 4).
The height after 5 hour passed is,
[tex]y=6-0.5\times 5\\y=6-2.5\\y=3.5[/tex]
Thus the fifth order pair of time and height of candle is (5, 3.5).
The height after 6 hour passed is,
[tex]y=6-0.5\times 6\\y=6-3\\y=3[/tex]
Thus the sixth order pair of time and height of candle is (6, 3).
Hence, the relation has a function.
- c) If the rate at which the candle burnt was 0. 3 inches per hour instead of 0. 5 inches per hour, will the relation continue to be a function
If the candle burnt at the rate of 0.3 inches per hour, then the relation of the relation is changed as,
[tex]y=6-0.3x[/tex]
As the relation is change the values will also be change. Lets check with input and output values by after 1 hour.
[tex]y=6-0.3\times1\\y=5.7[/tex]
Thus the first order is change as (1, 5.7).
For second hour the order is (1, 5.4)
Thus the function is continue but the output value is changed.
Hence,
- a) 6 ordered pairs to show the height of the candle is (1, 5.5), (2, 5), (3, 4.5) (4, 4) (5, 3.5) and (6, 3)
- b) The relation has a function.
- c) The function is continue but the output value is changed.
Learn more about the rate of decrement here;
https://brainly.com/question/25560561
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