Question

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 11 hours of burning, a candle has a height of 27.8 centimeters. After 26 hours of burning, its height is 24.8 centimeters. What is the height of the candle after 23 hours?

Answer 1

Hey! The answer is 25,4 centimeters.

Explanation:

In a linear function you can use y=mx+n

So if x = hours and y= height.

You know that

`\left \{ {{27,8=11m +n} \atop {24,8=26m +n}} \right.`

So:

If you multiply (24,8=26m +n) x-1

It is: -24,8 = -26m -n

Adding up the other equation

-24,8 = -26m -n

27,8 = 11m + n

3 = -15m

m= -0,2

So

27,8 = 11 x 0,2 + n

27,8 = -2,2 + n

30 = n

This results that te linear function for this equation is:

y = -0,2x + 30

The answer is

y=23(-0,2) + 30

y=-4,6+30

y=25,4