THE COMPOUND // FIELD NOTES // WEEK 14
Mixture problems, metric conversions, and polar coordinates
Field Book
Lessons 52 to 55
Due
Test 12 due · Supplement 14
Method
Paper first, every step
Vocab 2 runs in the Yard. The mixture template R1V1 + R2V2 = RMVM is the week's machine: feed it carefully.
What you have to be able to do
- Solve mixture problems with the rate times volume template
- Convert metric and English measures through the base units
- Plot points in polar form and convert to rectangular
The procedures
Mixture problemsField Book Lesson 52
- Strength times volume gives the amount of pure substance.
- R1V1 + R2V2 = RMVM: the pure amounts add across the mix.
Metric conversionsField Book Lesson 53
- Route every metric conversion through meters, liters, or grams.
- English weight and percent problems ride the same unit multiplier chains.
Polar coordinatesField Book Lesson 54
- A point is a distance r at an angle θ.
- x = r cos θ and y = r sin θ convert to rectangular.
Advanced abstract equationsField Book Lesson 55
- Clear fractions, collect the target variable, factor, divide.
- Quadratic word problems: set up, factor or complete the square, reject impossible roots.
Worked: mixing strengths
- Mix 10 mL of 20 percent solution with V mL of 60 percent to get 50 percent.
- Pure amounts: 0.2(10) + 0.6V = 0.5(10 + V). Times 10: 20 + 6V = 50 + 5V.
- V = 30 mL.
Terms on the record
| Term | Meaning |
|---|
| mixture equation | pure amounts add: strength times volume, summed, equals the mix |
| polar coordinates | locating a point by distance and angle |
| base unit | the meter, liter, or gram every metric conversion routes through |