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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 6 hours of burning, a candlehas a height of 19.4 centimeters. After 20 hours of burning, its height is 11 centimeters. What is the height of the candle after 8 hours?

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 6 Hours Of Burning A Candlehas class=

Sagot :

Given that the height of a candle (in centimeter) is a linear function of time (in hour) it has been burning.

Let at time t, the height of the candle be h

Since h is a linear function of t, let us assume

[tex]h=at+b[/tex]

After 6 hours of burning, the candle has a height of 19.4 centimeters.

After 20 hours of burning, its height is 11 centimeters.

So, the line representing h passes through the points (6,19.4) and (20,11)

Using two-point formula

[tex]\begin{gathered} \frac{h-11}{19.4-11}=\frac{t-20}{6-20} \\ \frac{h-11}{8.4}=\frac{t-20}{-14} \\ h=-\frac{3}{5}t+23 \end{gathered}[/tex]

So, the height of the candle is

[tex]h=-\frac{3}{5}t+23[/tex]

Now, putting t=8, it gives

[tex]\begin{gathered} h=23-\frac{3}{5}\times8 \\ =23-\frac{24}{5} \\ =\frac{115-24}{5} \\ =\frac{91}{5} \end{gathered}[/tex]

So, after 8 hours, the height of the candle is 18.2 centimeters.

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