2.2+Keeping+Things+Balanced+0910

SM 30/8/09

Problem 2.2- Keeping Things Balanced BIG Idea: Many real world situations can be modeled and predicted using mathematics. Essential Question: How can I model a non-linear relationship? My group data was collected on this table, what this says about the relationship between the distance and weight is that it is defiantly not linear, and as the weight increases the distance decreases, the graph line would be heading down.
 *  A.)  **** Do the experiment described above, and make a table of the (distance, weight) combinations you find. What does your table suggest about the relationship between distance and weight? **
 * ** Distance ** || ** Weight ** ||
 * 41 || 2 ||
 * 35 || 3 ||
 * 31 || 4 ||
 * 20 || 5 ||
 * 18 || 6 ||

This graph revealed the same thing as part A’s explanation.
 *  B.)  **** Make a graph of your data, and draw a straight line or a curve that models the trend. What does your graph suggest about the relationship between distance and weight? **

The pattern of change in this experiment and that of 2.1 are similar, as the x value increases, the y decreases.
 *  C.)  **** How is the pattern of change in the data similar to and different from the pattern of change in the data of problem 2.1 **

The pattern of change in this experiment and those of 1.1 and 1.2 are different, the most obvious cause is that that graph’s line goes upward, while this one’s goes down.
 *  D.)  ****  How is the pattern of change in the data similar to and different from the pattern of change in the data from problems 1.1 and 1.2 **

** Problem 2.2 Follow Up ** If 2 weights are placed 30 centimeters left of the fulcrum, then the data will be smaller because as one weight is taken, and it is placed closer to the fulcrum, which will decrease its capacity. For the 4 weights 30 centimeters, the results will be roughly the same, the 4 weights will make it heavier but placing them closer to the fulcrum will lessen its strength. The 2 weights and 50 centimeters will increase the data since the weights are placed farthest from the fulcrum, though there are only 2 weights.
 *  1.)  **** How would the results of this experiment have been different if you started with 2 weights placed 30 centimeters to the left of the fulcrum? With 4 weights place 30 centimeters left of the fulcrum? With 2 weights placed 50 centimeters left of the fulcrum? **

For this question, c, b, e, and f work, I subsituted W, and D values with the coordinate pairs on each of the equations, and these four worked. For example, W=120/D, W=4, D=30, 4=120 x 30 is true. And one example that is not true is W=120D, 4=120 x 30 is not true.
 *  2.)  **** Some combinations that balance 3 weights 40 centimeters from the fulcrum are (30, 4), (24, 5), and (20, 6). Which of the following equations do these three data pairs satisfy? Explain. **
 *  a.  **** W=120D **
 *  b.  **** W=120/D **
 *  c.  **** D=120/W **
 *  d.  **** W=D/120 **
 *  e.  **** WD=120 **
 *  f.  **** DW=120 **