2. Joint and Combined Variation

3. Review of Variations Direct Variation Inverse Variation Formula General Equation

4. Joint Variation  The variable y is said to vary jointly as x and z if y=kxz.  In the equation y=kxz, k is the constant of variation.  Example: y varies jointly as x and z, and y = 54 when x = 2 and z=9.

5. Example  If y varies jointly as x and z, and y = 54 when x = 2 and z=9.  Find the constant of variation

6. Example continued…  If y varies jointly as x and z, and y = 54 when x = 2 and z=9, find y when x = 7 and z = 10.  Since k = 3, then

7. Combined Variation  In combined variation the relation involves both direct and inverse variation.  In the equation, k is the constant of variation.  Example: y varies directly as x and inversely as z, and y = 30 when x = 20 and z = 50.

8. Example  If y varies directly as x and inversely as z, and y = 30 when x = 20 and z = 50, find the constant of variation.

9. Example continued…  If y varies directly as x and inversely as z, and y = 30 when x = 20 and z = 50, find y when x = 40 and z = 25.  Since k = 75, then

10. Examples  If y varies jointly as x and z, and y = 48 when x = 3 and z = 4, find the constant of variation.  If z varies inversely as t 2, and t = 10 when z = 4, then find z when t = 8. K=4 Z = 6.25

11. Examples  If x varies jointly as y and z, and x = 36 when y = 36 and z = 4, find x when y = 12 and z = 8.  If r varies directly as t 2 and inversely as s, and r = 192 when t = 8 and s = 3, find s when t = 9 and r = 486. X =24 S =1.5