Variation

1
Chapter 3.6

• Variation

2
Definitons

• Write and equation expressing direct
  variation.The circumference of a circle is given
  by the formula
• As the radius increases the circumference
  increases
• As the radius decreases the circumference
  decreases

3
Definitons

• Direct Variation
• y varies directly as x if there exists a real
  number k such that
• y kx

4
Definitons

• Direct Variation
• Also y is said to be proportional to x. The
  number k is called the constant of variation.

5
Definitons

• We can write the equation
• y 1.60 x to describe the cost y to buy x
  gallons of gas at 1.60 per gallon.

6
Definitons

• Stephen Pusztai is paid an hourly wage. On week
  he worked 43 hours and was paid 795.50.
• How much does he earn per hour.
• P kh

7
Definitons

• Hookes law for an elastic spring states that the
  distance a spring stretches is proportional to
  the force applied .
• If a force of 150 newtons stretches a certain
  spring 8 cm how much will a force of 400 newtons
  stretch the spring?
• d kf

8
Definitons

• Direct variation of a power
• y kxn

9
Definitons

• The area of a circle varies directly with the
  square of the radius
• A kr2
• Here the constant of variation is a special
  number pi so

10
Definitons

• The distance a body falls from rest varies
  directly as the square of the time it falls
• If a skydiver falls 64 feet in 2 seconds, how far
  will she fall in 8 seconds
• d kt2

11
Definitons

• The distance a body falls from rest varies
  directly as the square of the time it falls
• If a skydiver falls 64 feet in 2 seconds, how far
  will she fall in 8 seconds
• d kt2

12

• Inverse variation can be illustrated by a trash
  compactor.
• As the compactor pressed down, the pressure on
  the trash increases. The volume of the trash
  decreases

13

• y varies inversely as x
• y varies inversely as the nth power of x

14

• In the manufacturing of a certain medical
  syringe, the cost of producing the syringe varies
  inversely as the number produced. If 10,000
  syringes are produced, the cost is 2 per
  syringe.
• Find the cost of producing 25,000 syringes.

15

• The weight of an object above Earth varies
  inversely as the square of its distance from the
  center of the Earth.

16

• A space shuttle in an elliptical orbit has a
  maximum distance from the center of Earth
  (apogee) of 6700 miles. Its minimum distance
  from the center of the Earth (perigee) is 4090
  miles. If an astronaut in the shuttle weighs 57
  pounds at its apogee, what does the astronaut
  weigh at the perigee?

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• y varies jointly as x and z
• y kxz

18

• The interest on a loan is given by the formula I
  prt
• If an investment earns 100 interest at 5 for 2
  years, how much interest will the same principal
  earn at 4.5 for 3 years?
• We use the formula I prt where p is the
  constant of variation.

19

• Body mass index or BMI is used by physicians to
  assess a persons level of fatness. A BMI from
  19 to 25 is considered desirable. BMI varies
  directly as an individuals weight in pounds and
  inversely as the square of an individuals height
  in inches.

20

• A person who weights 118 lb and is 64 inches tall
  has a BMI of 20.
• Find the BMI of a person who weighs 165 pounds
  with a height of 70 inches.

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• Lesson 3.6 1 - 54