Section 2.5 - Variation - Summary
I. Direct Variation
- Quantity y is said to be in direct variation of quantity x if y = kx .
- k is called the constant on variation.
- y varies directly as x also means y is proportional to x
- Exercise 1: C varies as L . Suppose that C=12 when L=8. Determine k and
find L when C=16.
II. Direct Variation as a Power
n
- y is said to be in direct variation of nth power of x if y = kx .
- k is called the constant on variation.
n
n
- y varies directly as x also means y is proportional to x .
- Exercise 2: y varies as the cube of x . Suppose that y=24 when x=2.
Determine k and find y when x=3.
III. Inverse Variation
-
If y varies inversely as x then y =
k
.
x
- k is called the constant on variation.
- Exercise 3: C varies inversely as L . Suppose that C=1 when L=8. Determine
k and find L when C=10.
IV. Joint Variation
- z varies jointly as x and y if z = kxy .
- k is called the constant on variation.
- Exercise 4: I varies jointly as P and t. Suppose that I=1755 when P=13000 and
t=3. Determine k and find I when P=2500 and t=8.
Answers:
3
32
, C=
2
3
2. k = 3, y = 81
1. k =
4
5
4. k = .045, I = 900
3. k = 8, L =