We appreciate your visit to Suppose that the height in centimeters of a candle is a linear function of the amount of time in hours it has been burning After. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Answer:
The height of the candle after 14 hours is 15.4 centimeters
Step-by-step explanation:
A linear function is a polynomial function of the first degree of the form:
f(x)= m*x + b or y= m*x + b
where m is the slope of the function and b is the ordinate at the the y-intercept.
In this case height=m*time + b
Given two points of the line, point 1 (x1, y1) and point 2 (x2, y2), we can find the equation of the line or linear function.
You must first find the slope of the line using the expression:
[tex]m=\frac{y2 - y1}{x2 - x1}[/tex]
In this case you know the two points are (x1, y1)= (10,17) and (x2, y2)=(21,12.6)
So the slope is:
[tex]m=\frac{12.6-17}{21-10}[/tex]
m= -0.4
Now you find the value of b, replacing m in the equation, the values of x and y by the values of the coordinates of one of the points and solving for b to obtain its value.
Replacing (x1, y1)= (10,17) and m=-0.4 in the expresion y=m*x+b:
17= -0.4*10 + b
and solving you get:
17= -4 + b
17 + 4= b
21= b
So: height= -0.4*time + 21 where the height is expressed in centimeters and the time in hours.
To calculate the height of the candle after 14 hours, you simply replace the time by 14:
height= -0.4*14 + 21
height= 15.4
The height of the candle after 14 hours is 15.4 centimeters
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