You have seen many variation formulas in geometry. Some, like the formula for the perimeter of a square, are simple direct variations. Others, like the volume of a cone, relate three or more variables.
When one quantity varies with respect to two or more quantities, you have a combined variation. When one quantity varies directly with two or more quantities, you have joint variation. The volume of a cone varies jointly with the area of the base and the height of the cone,
Take Note Key Concept: Combined Variations
| Combined Variation | Equation Form |
|---|---|
| z varies jointly with x and y. |
|
| z varies jointly with x and y and inversely with w. |
|
| z varies directly with x and inversely with the product wy. |
|
Problem 4 Using Combined Variation
Multiple Choice The number of bags of grass seed n needed to reseed a yard varies directly with the area a to be seeded and inversely with the weight w of a bag of seed. If it takes two 3-lb bags to seed an area of
- 3 bags
- 4 bags
- 5 bags
- 6 bags
Plan
How can you write the model?
Write the constant of variation and direct variation variable in the numerator. Write the inverse variation variable in the denominator.
Th e combined variation equation is
You need five 3-lb bags to seed
✓ Got It?
- The number of bags of mulch you need to cover a planting area varies jointly with the area to be mulched a in square feet and the depth of the mulch d in feet. If you need 10 bags to mulch
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions