Charlene Guevarra

Maryam Kakharzadeh

Daniel Verkest

Math 46

Professor Gloag

All Tied Up

Introduction: The purpose of this experiment was to show that we could use math to calculate how many knots we could put in any length of rope (as long as the thicker one was longer than the thin one) and see what calculations needed to be done in order for both to be of equal length based on trial and error as well.

Procedure: Get two ropes: one thick and one thin. The thicker needs to be longer than the thin. Measure the lengths of both ropes. Then tie a knot and measure again. Repeat the last two steps until there are 8 knots. Graph the data and find the intersecting point. Make an equation that can duplicate the same data. Find out how many knots need to be in both of them to be equal length.

Analysis:The coordinate point at which the lines intersect was at (7.5, 75). The “x” value represents how many knots it takes to be of equal length to “y”, which represents the length of the rope. Using the substitution method, we plugged in our coordinates to see if we would get approximately the same solution as the graphical method. We found that it was very much similar to it, although for the graphical method we found that our “x” value was 6.8.

Test: When writing new equations for the ropes, we actually came up with: y= -6x + 125 for the “thick” rope, and y=-3.5x + 108 for the “thin” rope. We noticed that the only values that changed were the “x” values, which represented the amount of knots we should tie for both ropes, in order for them to be of equal length. We used the slope-int form equation to plug in all our coordinates for the values that we found.

Conclusion:We learned how to plug in “x” and “y” coordinates into a slope-int form equation, solving for both the thick and thin ropes. In order to check if our equations were equivalent, we used the substitution method to see if our findings were approximate. Outside the classroom, this type of activity could relate to perhaps a skyscraper. In order for a skyscraper to be evenly leveled, we would need to know how much length each rope or wire holding the panel, could hold a person without being uneven.