2.5.10
Inverse Proportion
Inverse Proportion
Inverse Proportion
Two variables are inversely proportional to one another if the size of one variable decreases when the size of other increases.
![Illustrative background for Inversely proportional](https://image-v2.cdn.app.senecalearning.com/2020-01/817bc822-8edc-44f1-8c81-50d9e8d353ba/Screenshot%202020-01-30%20at%2011.32.23-min,h_400,q_80,w_640.png)
![Illustrative background for Inversely proportional ?? "content](https://image-v2.cdn.app.senecalearning.com/2020-01/817bc822-8edc-44f1-8c81-50d9e8d353ba/Screenshot%202020-01-30%20at%2011.32.23-min,h_400,q_80,w_640.png)
Inversely proportional
Inversely proportional
- If two numbers are inversely proportional, we write:
- We can always write the equation:
- Where is the constant of proportionality and is a non-zero number.
![Illustrative background for Example](https://image-v2.cdn.app.senecalearning.com/2018-03/09fc14aa-c3e7-4d4c-9ea1-b2682506124b/shutterstock_445430830,h_400,q_80,w_640.jpg)
![Illustrative background for Example ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-03/09fc14aa-c3e7-4d4c-9ea1-b2682506124b/shutterstock_445430830,h_400,q_80,w_640.jpg)
Example
Example
- 3 builders take 12 days to build a wall. How long does it take 4 builders to build an identical wall?
- We expect the time taken to build the wall to decrease as the number of builders increase.
- This means the time taken and the number of builders are inversely proportional.
![Illustrative background for Days taken are inversely proportional to builders](https://image-v2.cdn.app.senecalearning.com/2018-04/fb2b4948-c729-4177-a535-120121fe0aec/Screen%20Shot%202018-04-17%20at%2017.17.28,h_400,q_80,w_640.png)
![Illustrative background for Days taken are inversely proportional to builders ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-04/fb2b4948-c729-4177-a535-120121fe0aec/Screen%20Shot%202018-04-17%20at%2017.17.28,h_400,q_80,w_640.png)
Days taken are inversely proportional to builders
Days taken are inversely proportional to builders
- d = number of days taken
- b = number of builders
![Illustrative background for Sub in b = 4](https://image-v2.cdn.app.senecalearning.com/2018-04/9cc6ef92-570c-4a4f-8a9c-8a42880becd9/Screen%20Shot%202018-04-17%20at%2017.17.56,h_400,q_80,w_640.png)
![Illustrative background for Sub in b = 4 ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-04/9cc6ef92-570c-4a4f-8a9c-8a42880becd9/Screen%20Shot%202018-04-17%20at%2017.17.56,h_400,q_80,w_640.png)
Sub in b = 4
Sub in b = 4
- We want to know the days taken for 4 builders to build the wall.
1Proof
1.1Types of Numbers
1.2Notation
2Algebra & Functions
2.1Powers & Roots
2.2Quadratic Equations
2.3Inequalities
2.4Polynomials
2.5Graphs
2.7Transformation of Graphs
3Coordinate Geometry
3.1Straight Lines
3.2Circles
3.2.1Equations of Circles centred at Origin
3.2.2Finding the Centre & Radius
3.2.3Equation of a Tangent
3.2.4Circle Theorems - Perpendicular Bisector
3.2.5Circle Theorems - Angle at the Centre
3.2.6Circle Theorems - Angle at a Semi-Circle
3.2.7Equation of a Perpendicular Bisector
3.2.8Equation of a Circumcircle
3.2.9Circumcircle of a Right-angled Triangle
3.3Parametric Equations (A2 only)
4Sequences & Series
4.1Binomial Expansion
5Trigonometry
5.2Trigonometric Functions
5.3Triangle Rules
6Exponentials & Logarithms
6.1Exponentials & Logarithms
7Differentiation
7.1Derivatives
7.2Graphs & Differentiation
7.3Differentiation With Trigonometry and Exponentials
7.4Rules of Differetiation (A2 only)
7.5Parametric & Implicit Differentiation
8Integration
8.1Integration
9Numerical Methods
9.1Finding Solutions
9.2Finding the Area
10Vectors
10.12D Vectors
10.23D Vectors
10.3Vector Proofs
Jump to other topics
1Proof
1.1Types of Numbers
1.2Notation
2Algebra & Functions
2.1Powers & Roots
2.2Quadratic Equations
2.3Inequalities
2.4Polynomials
2.5Graphs
2.7Transformation of Graphs
3Coordinate Geometry
3.1Straight Lines
3.2Circles
3.2.1Equations of Circles centred at Origin
3.2.2Finding the Centre & Radius
3.2.3Equation of a Tangent
3.2.4Circle Theorems - Perpendicular Bisector
3.2.5Circle Theorems - Angle at the Centre
3.2.6Circle Theorems - Angle at a Semi-Circle
3.2.7Equation of a Perpendicular Bisector
3.2.8Equation of a Circumcircle
3.2.9Circumcircle of a Right-angled Triangle
3.3Parametric Equations (A2 only)
4Sequences & Series
4.1Binomial Expansion
5Trigonometry
5.2Trigonometric Functions
5.3Triangle Rules
6Exponentials & Logarithms
6.1Exponentials & Logarithms
7Differentiation
7.1Derivatives
7.2Graphs & Differentiation
7.3Differentiation With Trigonometry and Exponentials
7.4Rules of Differetiation (A2 only)
7.5Parametric & Implicit Differentiation
8Integration
8.1Integration
9Numerical Methods
9.1Finding Solutions
9.2Finding the Area
10Vectors
10.12D Vectors
10.23D Vectors
10.3Vector Proofs
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