Smartboard Notes 2.3 Fundamental Theorem of Variation.notebook
November 10, 2011
2‐3: FUNDAMENTAL THEOREM OF VARIATION
"Osmosis at its finest..."
Smartboard Notes 2.3 Fundamental Theorem of Variation.notebook
November 10, 2011
The area of a pizza varies directly with the square of its
radius with a constant variation of π.
The variation equation for the area of a circle is A = πr2
r
1
3
2
5
4
6
Area
r
1
Area
3
2
1π
4π
4
5
6
7
9π 16π 25π 36π 49π
As the radius doubles, times by 4 = 22
what happens to the area? As the radius triples, times by 9 = 32
what happens to the area?
7
Smartboard Notes 2.3 Fundamental Theorem of Variation.notebook
November 10, 2011
Direct Variation
(MULTIPLY)
n
If y varies directly as x and x is multiplied by c, then
y is MULTIPLIED by Cn
Suppose y varies directly with x3.
Assume a.If x is multiplied by 2,what happens to y?
Smartboard Notes 2.3 Fundamental Theorem of Variation.notebook
November 10, 2011
Suppose y varies directly with x3.
Assume b. If x is multiplied by 4,what happens to y?
Suppose y varies directly with x3.
Assume c. If x is multiplied by 1/3,what happens to y?
Smartboard Notes 2.3 Fundamental Theorem of Variation.notebook
November 10, 2011
Inverse Variation
(DIVIDE)
n
If y varies directly as x , and x is multiplied by c, then
y is DIVIDED by Cn.
Suppose y varies inversely with x3
Assume
a.If x is multiplied by 3, what happens to y?
Smartboard Notes 2.3 Fundamental Theorem of Variation.notebook
Suppose y varies inversely with x3
Assume
b. If x is multiplied by 5, what happens to y?
Suppose y varies inversely with x3
Assume
c. If x is multiplied by 1/4, what happens to y?
November 10, 2011
Smartboard Notes 2.3 Fundamental Theorem of Variation.notebook
November 10, 2011
Suppose y varies inversely with the fifth power of x. How is y changed if x is divided by 2?
Suppose h varies directly with the square of g.
If g is multiplied by ¼, what happens to h?
Smartboard Notes 2.3 Fundamental Theorem of Variation.notebook
November 10, 2011
Suppose r is inversely proportional to the fourth power of s. If s is divided by , what happens to r?
Suppose b is directly proportional to the cube of a.
If a is multiplied by 27, what happened to b?
Smartboard Notes 2.3 Fundamental Theorem of Variation.notebook
November 10, 2011
Smartboard Notes 2.3 Fundamental Theorem of Variation.notebook
November 10, 2011
Smartboard Notes 2.3 Fundamental Theorem of Variation.notebook
November 10, 2011