COMBINED VARIATION.pptx

GRADE 9 MATHEMATICS

1. COMBINED VARIATION

2. Definition The statement “z varies directly as x and inversely as y” means , or , where k is the constant variation.  

3. TRANSLATING STATEMENT TO EQUATION Translating statements into mathematical equations using k as the constant of variation. T varies directly as a and inversely as b Y varies directly as x and inversely as the square of z  

4. Translate each statement into mathematical equation. W varies jointly as c and the square of a and inversely as b P varies directly as the square of x and inversely as s The electrical resistance R of a wire varies directly as its length and inversely as the square of its diameter d The acceleration A of a moving object varies directly as the distance d it travels and inversely as the square of the time t it travels The pressure P of a gas varies directly as its temperature t and inversely as the volume V           ACTIVITY

5. EXAMPLE 1 If z varies directly as x and inversely as y, and z = 9 when x = 6 and y = 2. Find z when x =8 and y = 12. Solution:  

6. EXAMPLE 1 If z varies inversely as x and inversely as y, and z = 9 when x = 6 and y = 2. Find z when x =8 and y = 12. Solution:  

7. EXAMPLE 2 If s varies directly as r and inversely as t, and s=15 when r=20 and t=40, find s when r=12 and t=20. Solution: