9.1 notes
April 03, 2014
Inverse and Joint Variation
Direct Variation: y = kx, k=0
y varies directly with y
k is called the constant of variation. Inverse Variation: y = k
k=0
x
y varies inversely with x
Do the following equations show direct variation, inverse variation or neither?
a. y =x
5
b. y = x+2
c. xy = 4
9.1 notes
April 03, 2014
Writing Inverse and direct Variation Equations
The variables x and y vary inversely, and y = 8 and x = 3
The variables x and y vary directly, and y = 8 and x = 3
Writing Inverse and direct Variation Equations
The variables x and y vary inversely, and y = 3 and x = ­5
The variables x and y vary directly, and y = 3 and x = ­5
9.1 notes
April 03, 2014
Writing Inverse and direct Variation Equations
The variables x and y vary inversely, and y = 12 and x = 1/2
The variables x and y vary directly, and y = 12 and x = 1/2
Writing an Inverse Variation Model
The speed of a whirlpool varies inversely with the distance from the whirlpool's center. The Lofoten Maelstrom is a whirlpool located off the coast of Norway. At a distance of 3 Km (3000 meters) from the center, the speed of the current is about 0.1 m per second. Write and inverse variation equation relating distance from cetner d and speed s. Describe the change in the speed of the current as you move closer to the whirlpool's center. 9.1 notes
April 03, 2014
How can we find K simply given an x and y value?
The variables x and y vary inversely, and y = 12 and x = 1/2
The variables x and y vary directly, and y = 12 and x = 1/2
Checking Data for Inverse or direct Variation
The table compares the wing flapping rate r (in beats per second) to the wing length l (in cm) for several birds. Do these data show inverse or direct variation? If so, find the model. Bird
4(bpersec) l(cm)
Carrion Crow
3.6
32.5
Common Scoter
5
23.5
Great Crested Grebe
6.3
18.7
Curlew
4.0
29.2
Lesser black backed gull
2.8
42.2
9.1 notes
April 03, 2014
Joint Variation
Joint variation occurs when a quantity varies directly as the product of two or more other quantities. if z = kxy, k = 0, z varies jointly with x and y. We can mix and match our variations. Write an equation for the given relationships. a. y varies directly with x
b. y varies inversely with x
c. z varies jointly with x and y
d. y varies inversely with the square of x
e. z varies directly with y and inversely with x.
9.1 notes
April 03, 2014
Variation Models
The law of universal gravitation states that the gravitational force F (in Newtons) between two objects varies jointly with their masses m1 and m2 (in kg) and inversely with the square of the distance d (in m) between the two objects. The constant of variation is denoted by G and is called the Universal Gravitational Constant. a. Write an equation for the law of universal gravitation
b. Estimate the universal gravitational constant given the info for the sun and earth:
Sun Mass: 1.99*1030kg
Earth Mass: 5.98*1024kg
distance between the two: 1.50*1011 m
Force between the two: 3.53*1022N