Transcript Lesson 8-7 Quadratic Variation

Lesson 8-7
Quadratic Variation
Objectives:
Students will:
Be able to find equations of direct, inverse, and joint
quadratic variation
Solving problems involving quadratic variation
Quadratic Variation
3 possibilities
1) Direct
→
y = kx2
“y varies directly with the square of x”
k
y

2) Inverse
→
x2
“y varies inversely with the square of x”
3) Joint
→
y = kxz
“y varies jointly with x and z”
Or Combos of these!!
Writing Variation Equations
1) Choose equation
2) Plug in values
3) Solve for k
4) Re-write equation with k-value
Example 1
Find the equation of variation where y varies inversely as the square of x, and y =
2 when x = 3.
k
y 2
x
k
2 2
3
18  k
so
18
y 2
x
Example 2
Find an equation of variation where y varies jointly as x
and z, and y = 2, when x = 3, and z = 4.
y  kxz
2  k (3)(4)
2  12k
1
k
6
1
y  xz
6
Example 3 The intensity I of the light from a lamp varies directly as the wattage W
of the lamp and inversely as the square of the distance D from the lamp. The
intensity is 10 units when a 100-watt bulb is used at a distance of 20 feet. What is
the intensity if a 75-watt bulb is used at 25 feet.
kw
I 2
d
100 k
10 
20 2
1k
10  4   4
4
40  k
40  75
I
25 2
I  4.8units
•
Example 4 The force of attraction F between two magnets varies inversely
as the square of the distance D between them. The force is 5 newtons
when the magnets are 2 cm apart. What is the force when the magnets are
5 cm apart?
Assignment
8-7/370-371/1-15o, 25, 31,33