Let x, y, and z denote three quantities. You say that y varies jointly as x and z, or y varies directly as x and z if there exists a nonzero number k such that y = Joint variatio dependent varia kxz. %3D Likewise, you say that y varies directly as x and inversely a constant and as z if there exists a nonzero number k such that variables. In rea product of con: patience, perseve %3D Note that in the aforementioned variables, y is the dependent variable, x and z are the independent variables, and k is the constant of variation. Similar to direct and inverse variations, joint and combined variations o between quantities such that these quantities vary together at a certain con combined variations, three or more variables are involved. In this worksheet, yo and combined variations are applied in real life, like in designing product conta a park; and work-related scenarios, such as the number of people to finish a jc to finish a job, and the amount of work to be done. Take the Written Assignments A. Determine the equation of variation when y varies jointly as x and z. * 1. y= 16, x= 2, and z= 4 %3D / 2. y= 25, x= 1, and z= 5 %3D 3. y= 10, x=-5, and z=-2 4. y= 98, x=-7, and z= 14 %3D 5. y=1 000, x= 25 and z=-4 %3D %3D 6. y= 18, x= 9, and z= 4 7. y=24, x =-8, and z= 5 %3D 8. y= 26, x= 3, and z=-13 %3D Dynamic Minds: A Math Workbook 9 40