1. Chapter 3.1
Variation

2. Other Type of Direct Variation
General equation, y = f(x) = kxn
y = kx2 K> 0
= kx
K> 0
y= kx3 K > 0
Inverse Variation
y = n where k is positive constant and n> 0
y is inversely proportional to xn

3. Inverse Variation
y varies inversely with x if
y = , x = 0 where k is a positive
constant 40 30 20 10 R T 10 60 15 40 20 30 50 12
200 3
400
1.5
f(R) =

4. No 4, Ex 3.1 ( pg 247) The force of gravity( F ) on a 1-kg mass is inversely proportional to the square of the object’s distance (D) from the center of the earth F F=
Fd2 = k
= 9.8(1)2
K = 9.8
b) F= substitute k 2
Distance Earth Radii
Force (Newtons) 1 2 4
9.8
2.45
0.6125 8 6 4 2
Graph
Force
Distance d

5. Pg 249, No 13 The weight of an object on the moon varies directly with its weight on earth
a) m w where m = weight of object, on
moon and w= wt . Of object on earth
m = kw
m = pounds, w = 150 pounds
K = 24.75/150 = 0.165
m = 0.165w , substitute k
b) m = 0.165( 120) = 19.8 pounds
c) w= = 30/0.165 = pound
Wt. on earth (W) w
100
150
200
400 m
16.5
24.75 33 66
Wt. on moon (m)

6. No No 26
y varies directly with x y varies inversely with the square of x
y = kx y = y = 1.25 when x = 4, so
y = 1.5, when x = 5
So 1.5 = k(5) = and k = 1.25(4) 2
k = 1.5/5 = 0.3 x y 2 5
1.5
2.4 12
4.5 x y
0.2 80 2 4
1.25
0.8