Day 8
Intro to Engineering
Allen Sam
6-20-18
Activity 4.1c
1. Consider the data that you have graphed and answer the following.
a. Would you expect that this data is linear; that is, if you were to measure the mass of other pieces with more than six cubes or fewer than four cubes, would the points fall on a straight line on the graph? Explain your answer.
I expected the data to be linear because the cubes are similar enough to be the same mass. On a graph, they should fall in the same line because the weight and number of cubes should be proportional.
b. If you were to sketch a line-of-best fit, what would be a reasonable y-intercept. That is, where would the line-of-best fit cross the vertical axis? Explain your answer.
It should cross the vertical axis at (0,0) because having no cubes should result on 0 mass.
c. Based on your data, what would you predict for the mass of a single wooden cube? Explain your answer or show your work.
the data shows a cube has an average of 4.1 grams.
(4+4+4+4+4+5)/6 = 4.166
2. Using your predicted y-intercept, sketch a line-of-best-fit for your data on the grid above.
(in the graph)
3. Using your line-of-best-fit, complete the following.
a. Estimate the slope of your line-of-best-fit (include the appropriate units). Explain the interpretation of the slope in words.
The best fit line estimates the slope at 5. It means that every cube has around five grams of mass.
b. Write an equation for your line of best fit.
y=5x where y is the total mass and x is the number of cubes in a piece
c. Rewrite your equation for the line-of-best-fit in function notation where M(n) = mass of the puzzle piece and n = the number of wooden cubes.
M(n)=5n
d. Estimate the mass of a puzzle piece that includes two wooden cubes. Show your work.
M(2)=5(2) = around 10g
e. If a puzzle piece has a mass of 31.5 grams, how many wooden cubes would you predict were used to create the puzzle piece? Show your work.
31.5=5n
n=31.5/5
n=6.3 around six cubes
4. Use the equation of the trend line to answer the following.
a. Rewrite the equation of the trend line using function notation where M(n) represents mass and nrepresents the number of cubes.
M(n)=5n
b. What is the domain of the function? That is, what values of n make sense?
The domain would be [0, 6] (in interval notation).
c. What is the range of the function?
The range of [0, ∞)
d. What is the slope of your trend line? Explain the interpretation of the slope in words.
the slope of the trend line is around 4-5. It means that every cube weighs around 4-5 grams
e. How does the slope of your line-of-best-fit compare to the slope of the trend line? Why is there a difference?
The slope of the best fit line and the trend line are generally the same because the function is a line. There should be no difference between them in this case because the data does not vary too much.
f. Predict the mass of a puzzle piece that is comprised of 9 wooden cubes. Show your work.
each cube is around 4.1 grams
9 x 4.1= 36.9 grams
g. If a puzzle piece had a mass of 49 grams, how many wooden cubes would it contain? Show your work.
each cube is around 4.1 grams
49/4.1= 11.95 rounds to around 12 cubes
h. Is the trend line a good representation of the relationship between the number of wooden cubes and the weight of the puzzle? Justify your answer.
The line is generally a good way to estimate a block's weight because these blocks are usually the same size, made of the same material, and are the same shape.
Conclusion:
1. What is the advantage of using Excel for data analysis?
Using excel allows you to accurately analyze the data created between the variables. It also allows you to see all the data gathered on one document for comparison.
2. What precautions should you take to make accurate predictions?
We could use the same amount of glue for each time we glue and weigh each cube to make sure they are the exact same weight.
3. What is a function? Explain why the mathematical models that you found in this activity are functions.
A function is a relationship involving one or more variables. Lines are considered to be simple functions. In this case our variables were mass and the number of blocks in each piece
