MATH SOLVE

5 months ago

Q:
# 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 9 hours of burning, a candle has a height of 17.5 centimeters. After 24 hours of burning, its height is 22 centimeters. What is the height of the candle after 22 hours?

Accepted Solution

A:

Answer: The candle has a height of 21.4 cm after burning for 22 hours.Step-by-step explanation: let x=hours, m=rate of change, and y= candle height First you have to find the slope or, rate of change using the slope formula. y2-y1 divided by x2-x1 . Here is our points (9, 17.5) and (24, 22) x1 y1 x2 y2Now we put these into the equation and solve[tex]\frac{22-17.5}{24-9}[/tex] =[tex]\frac{3}{10}[/tex]Now that we have the slope of 3/10 we can use this to find the y-intercept using the point-slope equation.[tex]y-y_{1} =m(x-x_{1} )[/tex] y-17.5= .3(x-9) Solvey-17.5=.3x-2.7 y -14.8= .3x +2.7 +2.7 +14.8 +14.8y=.3x+14.8 the y-intercept is 14.8Now we use this equation to plug in the 22 hours.y=.3(22) +14.8y=6.6+14.8y= 21.4 The candle has a height of 21.4 cm after burning for 22 hours.