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 candle has a height of 24.6 centimeters. after 21 hours of burning, its height is 18.6 centimeters. what is the height of the candle after 9 hours?

The height of the candle after 9 hours can be written as 23.4 cm.

The linear relationship is the relationship between two variables such that it follows a straight line.

As it is given that the height of the candle is linear to the amount of time. Now, let's the time be on the x-axis and the y-axis be the height of the candle. therefore, the slope of the linear relationship can be represented as,

Point1 of the slope, (x₁, y₁) = (6, 24.6)

Point2 of the slope, (x₂, y₂) = (21, 18.6)

Now, since we know the two points of the linear relationship, therefore, the slope can be written as,

Thus, the slope of the linear relationship is -0.4.

Now, the equation of the linear relationship can be written as,

Thus, the Linear relationship of the candle height and the amount of time can be written as .

Now, In order to calculate the height of the candle after 9 hours, we will substitute the value of the x as 9.

Hence, the height of the candle after 9 hours can be written as 23.4 cm.

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Given: After 6 hours of burning, a candle has a height of 24.6 centimeters. After 21 hours of burning, its height is 18.6 centimeters.

Solution: We could write coordinates for number of hours and height of the candle (hours, height) for the above data as

(6,24.6) and (21,18.6).

In order to find the linear function, we need to find the slope between those two coordinates.

Slope would represent the rate at which length of candle is decreasing.

Let is find slope between those two coordinates now.

We know, slope formula

We have (x1,y1)=(6,24.6)  and (x2,y2) = (21,18.6).

Plugging values of x1,y1,x2 and y2 in slope formula, we get

Simplfying fraction -6/15 into simplest form, we get

-2/5.

So, the slope m=-2/5.

In decimal form -2/5 = -0.4.

Applying point-slope form of the linear equation

y-y1 = m(x-x1)

y- 24.6= -0.4(x-6).

Distributing -0.4 over (x-6), we get -0.4*x -0.4*-6 = -0.4x +2.4

y-24.6 = -0.4x +2.4

Adding 24.6 on both sides, we get

y-24.6+24.6 = -0.4x +2.4+24.6

y = -0.4x + 27.

Now, we need to find height of the candle after 9 hours.

x represents number of hours there.

Plugging x=9 in above function we got,

y = -0.4(9) + 27

y= -3.6 +27

y =23.4

Therefore, 23.4 centimeters is the height of the candle after 9 hours.

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.