THE COMPOUND // FIELD NOTES // WEEK 16
Variation, complex roots, and vectors
Field Book
Lessons 60 to 63
Due
Test 14 due ยท Supplement 16
Method
Paper first, every step
Escape 4 posts this week. Direct and inverse variation join the case file, and quadratics grow complex roots.
What you have to be able to do
- Set up direct and inverse variation with the constant k
- Recognize complex solutions of quadratics
- Add vectors by components
The procedures
Direct and inverse variationField Book Lesson 60
- Direct: y = kx. Inverse: y = kx.
- Use the given pair to find k, then answer the question with the finished equation.
Mixture, second typeField Book Lesson 61
- When liquid evaporates or drains, total volume decreases while pure substance holds.
- Track the pure amount and the new total separately.
Complex rootsField Book Lesson 62
- A negative under the square root means complex solutions.
- Write the root of the negative as i times the root of the positive.
Vector additionField Book Lesson 63
- Write each vector in component form first.
- Add the x parts and the y parts separately.
Worked: inverse variation
- y varies inversely as x, and y = 6 when x = 2.
- k = xy = 12, so y = 12x.
- When x = 4, y = 3.
Terms on the record
| Term | Meaning |
|---|
| direct variation | y = kx, quantities growing in proportion |
| inverse variation | y = k over x, one grows as the other shrinks |
| vector | a quantity with both magnitude and direction |