After burning 5 minutes, the candle is t inches tall. The candle will be 6 inches tall after burning 50 minutes. The candle will be 3 inches tall after burning k minutes. h(3) = k h(5) = t h(50) = 6 h(k) = 3 h(6) = 50 h(t) = 5

To find the value of ( k ) in the context of the candle’s height after burning for different durations, we can observe a linear relationship based on the information given.

1. Understanding the height function: You have the heights of the candle at different times:

– ( h(5) = t )

– ( h(50) = 6 )

– ( h(k) = 3 )

2. Finding the rate of height change:

– To find how much the candle burns in that time, we can establish a linear relationship.

– The candle height change from ( h(50) ) to ( h(5) ) can be calculated as:

[

text{Change} = h(50) – h(5) = 6 – t

]

– The time change is ( 50 – 5 = 45 ) minutes.

3. Finding the height at ( k ):

– From the height at ( k ) minutes, it can be inferred that:

[

h(k) = 3

]

4. Using these values:

– We know that as time increases, the height decreases. To find ( k ), we can set up proportions or simply observe:

– The rate of burning (height change per minute) can be calculated using points we have.

Without doing calculations explicitly and to