Joint and Combined Variation PDF

Joint and Combined Variation Joint Variation ▪ It occurs when one quantity varies directly as the product of two or more other quantities Joint Variation y varies jointly as x and z if there exists a nonzero number k such that y = kxz, where x≠0 and z≠0 Joint Variation Example: The area of a...

Joint and Combined Variation Joint Variation ▪ It occurs when one quantity varies directly as the product of two or more other quantities Joint Variation y varies jointly as x and z if there exists a nonzero number k such that y = kxz, where x≠0 and z≠0 Joint Variation Example: The area of a rectangle varies jointly as its length and width. Find the equation of joint variation if A = 60 sq.ft, l = 15 ft, and w = 4 ft Joint Variation Solution: The area (A) Varies jointly = (K) as its length (h) and (.) Width (W) Joint Variation Solution: A = klw 60 = k (15)(4) 60 = 60 k=1 Combined Variation ▪ It describes a situation where a variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others (when the rest of the variables are held constant). Combined Variation If a situation is modelled by an equation of the form: y= Where k is a nonzero constant, we say that y varies directly as x and inversely as z. The number (k) is called the constant variation Combined Variation Example: If y varies directly as x and inversely as z, and y = 22 when x = 4 and z = 6, find y when x = 10 and z = 25 Combined Variation Solution: Step 1: y = Step 2: 22 = 132 = 4k 33 = k Combined Variation Solution: Step 3: y = Step 4: y = Final Answer: y =