THE COMPOUND // FIELD NOTES // WEEK 21
Mixed systems, double radicals, and force vectors
Field Book
Lessons 76 to 79
Due
Test 18 due · Supplement 21
Method
Paper first, every step
Two radicals in one equation means the squaring move runs twice. Isolate, square, isolate, square.
What you have to be able to do
- Choose substitution or elimination per system, including negative vectors
- Solve equations with more than one radical
- Resolve force vectors and use the 45 45 90 ratios
The procedures
Substitution and elimination togetherField Book Lesson 76
- Pick the tool per equation: substitute where a variable is exposed, eliminate where coefficients align.
- A negative vector points opposite: subtract components accordingly.
Multiple radicalsField Book Lesson 77
- Isolate one radical, square both sides, and simplify.
- If a radical remains, isolate it and square again. Check all answers.
Force vectorsField Book Lesson 78
- Write each force in polar form first, then break into components.
- Sum the components to get the resultant, and convert back if asked.
Metric volume and 45 45 90Field Book Lesson 79
- Metric volume runs in two forms: cubic centimeters and milliliters, one to one.
- In a 45 45 90 triangle the legs match and the hypotenuse is leg times √2.
Worked: 45 45 90
- Each leg of a 45 45 90 triangle is 4.
- Hypotenuse = 4√2.
- Check: √(16 + 16) = √32 = 4√2.
Terms on the record
| Term | Meaning |
|---|
| resultant | the single vector equal to the sum of the forces |
| 45 45 90 triangle | the isosceles right triangle with hypotenuse leg times √2 |
| milliliter | one cubic centimeter of volume |