Download presentation

Presentation is loading. Please wait.

1
**Mathematical Modeling**

PRECALCULUS I Mathematical Modeling Direct, inverse, joint variations; Least squares regression Dr. Claude S. Moore Danville Community College

2
**Direct Variation Statements**

1. y varies directly as x. 2. y is directly proportional to x. 3. y = kx for some nonzero constant m. NOTE: k is the constant of variation or the constant of proportionality. Example: If y = 3 when x = 2, find k. y = kx yields 3 = m(2) or m = 1.5. Thus, y = 1.5x.

3
**Direct Variation as nth Power**

1. y varies directly as the nth power of x. 2. y is directly proportional to the nth power of x. 3. y = kxn for some nonzero constant k. NOTE: k is the constant of variation or constant of proportionality.

4
**Inverse Variation Statements**

1. y varies inversely as x. 2. y is inversely proportional to x. 3. y = k / x for some nonzero constant k. NOTE: k is the constant of variation or the constant of proportionality. Example: If y = 3 when x = 2, find k. y = k / x yields 3 = k / 2 or k = 6. Thus, y = 6 / x.

5
**Joint Variation Statements**

1. z varies jointly as x and y. 2. z is jointly proportional to x and y. 3. z = kxy for some nonzero constant k. NOTE: k is the constant of variation. Example: If z = 15 when x = 2 and y = 3, find k. z = kxy yields 15 = k(2)(3) or k = 15/6 = 2.5. Thus, z = 2.5xy.

6
**USING DIRECT AND INVERSE VARIATION IN REAL LIFE**

Writing and Using a Model BICYCLING A bicyclist tips the bicycle when making turn. The angle B of the bicycle from the vertical direction is called the banking angle. banking angle, B

7
**Writing and Using a Model**

Turning Radius Banking angle (degrees) Find an inverse variation model that relates B and r. SOLUTION From the graph, you can see that B = 32° when r = 3.5 feet. B = k r Write direct variation model. 32 = k 3.5 Substitute 32 for B and 3.5 for r. 112 = k Solve for k. The model is B = , where B is in degrees and r is in feet. 112 r

8
**Writing and Using a Model**

Turning Radius Banking angle (degrees) Use the model to find the banking angle for a turning radius of 5 feet. SOLUTION Substitute 5 for r in the model you just found. B = 112 5 = 22.4 When the turning radius is 5 feet, the banking angle is about 22°.

Similar presentations

Presentation is loading. Please wait....

OK

1.11 Modeling Variation.

1.11 Modeling Variation.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on p&g products brands list Lc esi ms ppt online Ppt on web designing with html Animated ppt on solar system Ppt on limits and derivatives class Ppt on 21st century skills rubric Ppt on major domains of the earth for class 6 Ppt on views in dbms definition Ppt on id ego superego diagram Ppt on 3 r's of environment