Definition of Joint Variation
- Joint variation is a variation in which y varies jointly as
x or powers of x () and
y or powers of z ( ), if there is some nonzero constant k such that , where x ≠ 0, z ≠ 0, and n > 0.
Examples of Joint Variation
- y = 7xz, here y varies jointly as x and z.
- , here y varies jointly as and .
Solved Example on Joint Variation
Assume a varies jointly with b and c. If b = 2 and c = 3, find the value of a. Given that a = 12 when b = 1 and
c = 6.
Correct Answer: C
Step 1: Given that a = 12 when b = 1 and c = 6.
Step 2: As a = kbc, .
Step 3: For b = 2 and c = 3, a = k × 2 × 3 = 2 × 2 × 3 = 12.
Related Terms for Joint Variation
Real-world Connections for Joint Variation
- Force = mass × acceleration. The force exerted on an object varies jointly as the mass of the object and the acceleration produced.
Additional Links for Joint Variation