9.2 Direct, inverse and joint variation
Definitions:
Direct Variation:
A type of variation where y varies directly as x if there is
some constant k such that y = kx.
Direct Variation:
y = kx
ex: JOB: hrs , $ ; hrs , $
What is the constant?
Inverse Variation:
A type of variation where y varies inversely as x if there is
some constant k such that y = k .
x
Inverse Variation: y = k or y = k 1
x
x
ex: car - yrs old , value
Joint Variation:
A type of variation where y varies jointly as x and z if there is
some constant k such that y = kxz.
Joint Variation: y =kxz
ex: Area of a trapezoid A = (1/2)h(b1 + b2)
What is the constant?
Examples:
1.
If y varies directly as x and y=6 when x=11, find y when x=3.
2.
If y varies inversely as x and y=10 when x=20, find x when y=16.
3.
The volume (V) of a cone varies jointly as the square of the
radius of the base (r2) and the height (h). Find the equations
of joint variation if V=285, r=4 and h=17.