Warm up. Solve 12y = 3x. Decide whether each equation is true

Transcription

1 Warm up Solve 12 = 3x Decide whether each equation is true

2 Section 9-1

3 Assignment 2/10/15 Section 9-1 (p 499): 8 26 (E) (E)

4 Objective We are going to use inverse and joint variation

5 A linear function defined b an equation of the form =kx, where k is not equal to 0, represents direct variation In direct variation, varies directl as x or varies directl with x If a linear function of the form =kx represent a direct variation, then there is a constant of variation k.

6 Identifing direct variation from a table x k kx 5 20 x

7 Identifing direct variation from a table x k kx 5 16 x

8 Identifing direct variation from a table x k kx 12 4 x

9 Identifing direct variation from a table x k kx 6 7 x

10 Identifing direct variation from an equation 3=2x Write the equation in the form =kx.

11 Identifing direct variation from an equation Y=2x+3 Write the equation in the form =kx.

12 Determine whether varies directl with x. if so, find the constant variation x 2

13 Determine whether varies directl with x. if so, find the constant variation 2 1 x

14 Determine whether varies directl with x. if so, find the constant variation 5 x 6 1 3

15 Determine whether varies directl with x. if so, find the constant variation 7x 4 10

16 Using proportion suppose varies directl with x, and x=27 when =-51. find x when =-17. Let (x 1, 1 )=(27,-51) and let (x 2, 2 )=(x2,-17) Write a proportion x 1 1 x x 2

17 Find the missing value for the direct variation If =4 when x=3, find when x=6

18 Find the missing value for the direct variation If =7 when x=2, find when x=8

19 Inverse variation We can model an inverse variation with an of the equations x k k k,, or x, where k x 0.

20 In inverse variation, varies inversel as x or as inversel proportional to x

21 Modeling inverse variation Suppose that x and var inversel, and x=3 when =-5. write the function that models the inverse variation

22 Modeling inverse variation Suppose that x and var inversel, and x=0.3 when =1.4. write the function that models the inverse variation

23 Identifing direct and inverse variation Is the relationship between the variables in each table a direct variation, an inverse variation, or neither? Write functions to model the direct and inverse variations. x As x increases, increases k kx x

24 Identifing direct and inverse variation Is the relationship between the variables in each table a direct variation, an inverse variation, or neither? Write functions to model the direct and inverse variations. x As x increases, decreases k k x x

25 Identifing direct and inverse variation Is the relationship between the variables in each table a direct variation, an inverse variation, or neither? Write functions to model the direct and inverse variations. x As x increases, decreases k k x x

26 Identifing direct and inverse variation Is the relationship between the variables in each table a direct variation, an inverse variation, or neither? Write functions to model the direct and inverse variations. x

27 Identifing direct and inverse variation Is the relationship between the variables in each table a direct variation, an inverse variation, or neither? Write functions to model the direct and inverse variations. x

28 Identifing direct and inverse variation Is the relationship between the variables in each table a direct variation, an inverse variation, or neither? Write functions to model the direct and inverse variations. x

29 Quantities can var with respect to each other in different was. For example, can var directl with x 3 (=kx 3 ) or inversel with x 2 (=k/x 2 ) It is possible for three or more variables to be related. When one quantit varies with respect to two or more other quantities, the result is a combined variation. For example variable z can var directl with both x and. we can model such a joint variation with the equation z=kx, where k is not equal to 0.

30 Newton s Law of Universal Gravitational is Gm modeled b the formula 1m2 F 2 d F is the gravitational force between two objects with masses m 1 and m 2, and d is the distance between the objects. G is the gravitational constant. Describe Newton s Law as a combined variation. F Gm m d F varies jointl with the masses m 1 and m 2 F varies inversel with the distance between the mass of the objects

31 For the formula for the area of a trapezoid is A 1 2 h( b 1 b 2 ) Describe this relationship as a combined variation A varies jointl with the height and the sum of the bases.

32 The volume V of a tetrahedron varies jointl with its altitude h and base area B. A tetrahedron with a 5-cm altitude and 6-in 2. base has volume of 10 cm 3. write a formula that models this joint variation. V = kbh