example of joint variation
Answer (1)
Answer:Joint variation, also known as direct variation, occurs when two or more quantities increase or decrease together in a constant ratio.*Examples:*1. Area of a circle and radius:A = πr^2 (Area varies directly with the square of the radius)1. Volume of a sphere and radius:V = (4/3)πr^3 (Volume varies directly with the cube of the radius)1. Speed, distance, and time:s = d/t (Speed varies directly with distance and inversely with time)1. Force and acceleration:F = ma (Force varies directly with mass and acceleration)1. Pressure and force:P = F/A (Pressure varies directly with force and inversely with area)1. Cost, quantity, and price:C = qp (Cost varies directly with quantity and price)*Real-life examples:*1. Cooking: The amount of ingredients needed varies directly with the number of servings.2. Travel: The distance traveled varies directly with the speed and time.3. Finance: The interest earned varies directly with the principal amount and interest rate.4. Physics: The kinetic energy of an object varies directly with its mass and velocity squared.*Mathematical representation:*y = kx (Direct variation)y = k/x (Inverse variation)where:- y is the dependent variable- x is the independent variable- k is the constant of variationDo you have any specific questions or need further clarification?
