THE COMPOUND // FIELD NOTES // WEEK 20
Data lines, conjugates continued, and both-distance motion
Field Book
Lessons 72 to 75
Due
Test 17 due · Quiz 4 · Supplement 20
Method
Paper first, every step
Escape 5 posts this week. Draw the line of best fit before you compute anything: the pencil line is the model.
What you have to be able to do
- Fit a line to fairly linear data and read its equation
- Rationalize with conjugates fluently
- Solve motion problems where both distances are given
The procedures
Lines from dataField Book Lesson 72
- Draw the best-fit line through the cloud first.
- Pick two points on your line, not on the data, to compute slope. Negative angles sweep clockwise.
Conjugates, continuedField Book Lesson 73
- Same move as Lesson 67: multiply top and bottom by the conjugate of the denominator.
- Simplify fully: the denominator should leave with no radicals.
Motion with both distancesField Book Lesson 74
- When both distances are stated, write each as rate times time.
- Link the times or the rates with the story's condition, then solve.
Factorable denominatorsField Book Lesson 75
- Factor every denominator before hunting the LCD.
- Watch sign changes: factoring out a negative flips the fraction's sign.
Worked: out and back
- Out for 2 hours at r mph, back the same distance in 3 hours at r - 10 mph.
- Equal distances: 2r = 3(r - 10).
- 2r = 3r - 30, so r = 30 mph.
Terms on the record
| Term | Meaning |
|---|
| line of best fit | the drawn line that follows the trend of the data |
| negative angle | an angle measured clockwise from the reference ray |
| sign change rule | factoring a negative from top or bottom flips the sign of the fraction |