Jointly Proportional

Jointly Proportional Jointly proportional is also known as joint variation. It is very much like a direct variation with a difference that the joint proportional involves more than one variable.If the ratio of a variable y to the product of two or more variables is constant, then y varies jointly. In other words we can say that it is jointly proportional to other variables. This can be represented mathematically as y = k * x* z where the variable k is the constant of variation. Example 1: The volume of wood in a tree varies jointly as the height and inversely as the square of the girth. The volume of a tree is 144 cubic meterswhen the height is 20 meters and the girth is 1.5 meters. What will be the height of a tree with a volume of 1000 cubic metersand girth of 2 meters? Solution: We set up the equation according to the problem V = (k * height)/ girth ^2 We plug in the value of V, height and girth to find k 144 = (k * 20)/ 1.5 ^2 k = (144 * 1.5 ^2) / 20 = 16.2 Now we can plug in the new values to find the new height. 1000 = (16.2 * height)/ 2 ^2 Height = (1000 * 4)/ 16.2 = 246.91meters Example 2: Given that a varies jointly with b and c. If a = 45 when b= 5 and c = 3 then find the constant of variation? Solution: a = k * b * c 45 = k * 5* 3 k = 45 / 15 = 3