aa section 2-2
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Section 2-2Inverse Variation
Warm-upy varies directly as the square of x. If y = 63 when x = 3,
a. Find y when x = 9
Warm-upy varies directly as the square of x. If y = 63 when x = 3,
a. Find y when x = 9
y = kx2
Warm-upy varies directly as the square of x. If y = 63 when x = 3,
a. Find y when x = 9
y = kx2 63 = k(3)2
Warm-upy varies directly as the square of x. If y = 63 when x = 3,
a. Find y when x = 9
y = kx2 63 = k(3)2 63 = 9k
Warm-upy varies directly as the square of x. If y = 63 when x = 3,
a. Find y when x = 9
y = kx2 63 = k(3)2 63 = 9k k = 7
Warm-upy varies directly as the square of x. If y = 63 when x = 3,
a. Find y when x = 9
y = kx2 63 = k(3)2 63 = 9k k = 7
y = 7x2
Warm-upy varies directly as the square of x. If y = 63 when x = 3,
a. Find y when x = 9
y = kx2 63 = k(3)2 63 = 9k k = 7
y = 7x2 y = 7(9)2
Warm-upy varies directly as the square of x. If y = 63 when x = 3,
a. Find y when x = 9
y = kx2 63 = k(3)2 63 = 9k k = 7
y = 7x2 y = 7(9)2 = 7(81)
Warm-upy varies directly as the square of x. If y = 63 when x = 3,
a. Find y when x = 9
y = kx2 63 = k(3)2 63 = 9k k = 7
y = 7x2 y = 7(9)2 = 7(81) = 567
Warm-upy varies directly as the square of x. If y = 63 when x = 3,
a. Find y when x = 9
y = kx2 63 = k(3)2 63 = 9k k = 7
y = 7x2 y = 7(9)2 = 7(81) = 567
b. Find y when x = 5
Warm-upy varies directly as the square of x. If y = 63 when x = 3,
a. Find y when x = 9
y = kx2 63 = k(3)2 63 = 9k k = 7
y = 7x2 y = 7(9)2 = 7(81) = 567
b. Find y when x = 5
y = 7x2
Warm-upy varies directly as the square of x. If y = 63 when x = 3,
a. Find y when x = 9
y = kx2 63 = k(3)2 63 = 9k k = 7
y = 7x2 y = 7(9)2 = 7(81) = 567
b. Find y when x = 5
y = 7x2 y = 7(5)2
Warm-upy varies directly as the square of x. If y = 63 when x = 3,
a. Find y when x = 9
y = kx2 63 = k(3)2 63 = 9k k = 7
y = 7x2 y = 7(9)2 = 7(81) = 567
b. Find y when x = 5
y = 7x2 y = 7(5)2 = 7(25)
Warm-upy varies directly as the square of x. If y = 63 when x = 3,
a. Find y when x = 9
y = kx2 63 = k(3)2 63 = 9k k = 7
y = 7x2 y = 7(9)2 = 7(81) = 567
b. Find y when x = 5
y = 7x2 y = 7(5)2 = 7(25) = 175
Review: Direct Variation
Review: Direct Variation
Wording for Direct Variation
Review: Direct Variation
Wording for Direct Variation
General Equation
Review: Direct Variation
Wording for Direct Variation
General Equation
Constant of Variation
Review: Direct Variation
Wording for Direct Variation
General Equation
Constant of Variation
Steps to solve
“t Varies Inversely as s”:
“t Varies Inversely as s”: When t goes up, s goes down; when t goes down, s goes up
“t Varies Inversely as s”: When t goes up, s goes down; when t goes down, s goes up
Inverse Variation Function:
“t Varies Inversely as s”: When t goes up, s goes down; when t goes down, s goes up
Inverse Variation Function:
A function of the form with k ≠ 0 and n > 0 y =
k
xn
“t Varies Inversely as s”: When t goes up, s goes down; when t goes down, s goes up
Inverse Variation Function:
A function of the form with k ≠ 0 and n > 0 y =
k
xn
“t Varies Inversely as s”: When t goes up, s goes down; when t goes down, s goes up
Inverse Variation Function:
A function of the form with k ≠ 0 and n > 0 y =
k
xn
“ is inversely proportional to”
“t Varies Inversely as s”: When t goes up, s goes down; when t goes down, s goes up
Inverse Variation Function:
A function of the form with k ≠ 0 and n > 0 y =
k
xn
“ is inversely proportional to”
***The intensity of the light varies inversely as the square of the distance from the light source
Example 1Rewrite the statement, “The intensity of the light
varies inversely as the square of the distance from the light source.”
Example 1Rewrite the statement, “The intensity of the light
varies inversely as the square of the distance from the light source.”
The intensity of the light is inversely proportional to the square of the distance from the light source
Example 2In a room, the floor space F per person varies inversely
as the square of the number of people P in the room. Write an equation to represent this situation.
Example 2In a room, the floor space F per person varies inversely
as the square of the number of people P in the room. Write an equation to represent this situation.
F =
k
p2
Example 3The time T required to do a job varies inversely as the number of workers w. It takes 5 hours for 8 cement
workers to do a job. How long would it take 12 workers to do the same job?
Example 3The time T required to do a job varies inversely as the number of workers w. It takes 5 hours for 8 cement
workers to do a job. How long would it take 12 workers to do the same job?
T =
k
w
Example 3The time T required to do a job varies inversely as the number of workers w. It takes 5 hours for 8 cement
workers to do a job. How long would it take 12 workers to do the same job?
T =
k
w 5 =
k
8
Example 3The time T required to do a job varies inversely as the number of workers w. It takes 5 hours for 8 cement
workers to do a job. How long would it take 12 workers to do the same job?
T =
k
w 5 =
k
8k = 40
Example 3The time T required to do a job varies inversely as the number of workers w. It takes 5 hours for 8 cement
workers to do a job. How long would it take 12 workers to do the same job?
T =
k
w 5 =
k
8k = 40
T =
40
w
Example 3The time T required to do a job varies inversely as the number of workers w. It takes 5 hours for 8 cement
workers to do a job. How long would it take 12 workers to do the same job?
T =
k
w 5 =
k
8k = 40
T =
40
w
T =
40
12
Example 3The time T required to do a job varies inversely as the number of workers w. It takes 5 hours for 8 cement
workers to do a job. How long would it take 12 workers to do the same job?
T =
k
w 5 =
k
8k = 40
T =
40
w
T =
40
12 = 3 13 hours
Steps to solving an inverse variation problem
Steps to solving an inverse variation problem
1. Write an equation to describe the variation
Steps to solving an inverse variation problem
1. Write an equation to describe the variation
2. Find k
Steps to solving an inverse variation problem
1. Write an equation to describe the variation
2. Find k
3. Rewrite the function using k
Steps to solving an inverse variation problem
1. Write an equation to describe the variation
2. Find k
3. Rewrite the function using k
4. Evaluate
Example 4g is inversely proportional to h. If g = 3 when h = 6,
find g when h = 9.
Example 4g is inversely proportional to h. If g = 3 when h = 6,
find g when h = 9.
g =
k
h
Example 4g is inversely proportional to h. If g = 3 when h = 6,
find g when h = 9.
g =
k
h 3 =
k
6
Example 4g is inversely proportional to h. If g = 3 when h = 6,
find g when h = 9.
g =
k
h 3 =
k
6k = 18
Example 4g is inversely proportional to h. If g = 3 when h = 6,
find g when h = 9.
g =
k
h 3 =
k
6k = 18
g =
18
h
Example 4g is inversely proportional to h. If g = 3 when h = 6,
find g when h = 9.
g =
k
h 3 =
k
6k = 18
g =
18
h
g =
18
9
Example 4g is inversely proportional to h. If g = 3 when h = 6,
find g when h = 9.
g =
k
h 3 =
k
6k = 18
g =
18
h
g =
18
9= 2
Homework
Homework
p. 81 #1 - 23
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