Archimedes Principle Experiment – Part 3
We are going to drop bolts into the cylinder one at a :me. Conduct the experiment by crea:ng a simple table. Take an ini:al measurement. Then drop in nuts and marbles and take a new measurement. Record your data in the table. Repeat un:l you have used up all your nuts and marbles. 1. Create a scaDerplot of your data on graph paper. Make sure to label the x and y axis with the correct quan:ty and units. Make sure to use an appropriate scale. Create a :tle for your scaDerplot 2. Create a 3 Column Process Chart. Input your data into the Domain and Range Columns and use the example 3CPC to complete the middle Process Column. 3. What is the equa:on (func:on rule) governing this rela:onship? 4. Add 6 units to you largest domain value and determine the corresponding range value. Jus:fy your answer verbally, by table, by graph, or algebraically. 5. Add 3.7 to you largest range value and determine the corresponding domain value. Jus:fy your answer verbally, by table, by graph, or algebraically. 6. Does your data depict a con:nuous rela:onship or a discrete rela:onship? Jus:fy your answer. a situa:on that can # texts Discrete: Can you send 0.5 or 0.365 miles Con:nuous: be expressed as a decimal or of text message? No only whole hour frac:on. It is possible to travel texts. A graph of isolated points. month at a speed of 64.24564 mph. 7. Does your data represent an func:onal rela:onship? Jus:fy your answer. 8. Describe the correla:on depicted by your data. Explain your answer. 9. Determine the Domain and Range of your data. Express the informa:on in the correct nota:on.
Using a 3 Column Process Chart: 1. Input your Domain and Range Values 2. Calculate the change in x values and and the change in y values 3. Determine Rate of Change by placing change in y/change in x 4. Input Slope and Domain values into Process Column 5. Find the y-‐intercept Change in x 3-‐0 = 3 6-‐3 = 3 12-‐6 = 6 15-‐12 = 3
Independent Variable (Units) X0= 0 X1= 3 X2= 6 X3= 12 X4= 15
Finding b: 1. 1.2 (0) + b = 3.7 3 2. 0 + b = 3.7 3. b = 3.7
Process f(x)=mx+b
1.2 (0) + 3.7 3 1.2 = (3) + 3.7 3 1.2 = (6) + 3.7 3 1.2 = (12) + 3.7 3 1.2 = (15) + 3.7 3 =
Dependent Variable (Units) y0= 3.7 y1= 4.9 y2= 6.1 y3= 8.5 y4= 9.7
change _ in _ y Change in y change _ in _ x 1.2 4.9-‐3.7 = 1.2 3 1.2 6.1-‐4.9 = 1.2 3 2.4 1.2 = 8.5-‐6.1 = 2.4 6 3 1.2 9.7-‐8.5 = 1.2 3
= slope = m Set up equa:on to solve for b with (x0,y0) Mul:ply and simplify Solu:on; value of the y-‐intercept *A similar process can be used for any ordered pair (xn,yn)
Func:onal Rela:onships x
y
-‐1 5 3
3
-‐1 0
Not a func*on because -‐1 has a y value of 5 and 0
x
-‐1 5 3
3
4
-‐2
Correla:ons Posi:ve Correla:on: as x increases, y increases Nega:ve Correla:on: as x increases, y decreases or as x decreases, y increases No Correla:on: neither above, no trend
Domain and Range Nota:on x
y
-‐3
12
-‐1
10
0
9
2
7
5
3
Domain: [-‐3,-‐1,0,2,5] Range: [12,10,9,7,3]
y
These are func*ons since each x value has only one y value, even if the points repeat.
x
y
-‐1 5 -‐1 5 4
-‐2