[PDF] Additional Vocabulary Support 5. What is the constant

View - Download Additional Vocabulary Support

Previous PDF

Next PDF

Prentice Hall Algebra 2 • Teaching Resources

Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 1

Name Class Date

8-1

Additional Vocabulary Support

Inverse Variation

Choose the expression from the list that best matches each sentence. combined constant of inverse joint variation variation variation variation 1. equations of the form xy5k

2. when one quantity varies with respect to two or more quantities

3. when one quantity varies directly with two or more quantities

4. the product of two variables in an inverse variation

Choose the expression from the list that best matches each sentence. combined constant of inverse joint

variation variation variation variation

5. When one quantity increases and the other quantity decreases proportionally,

the relationship is an .

6. ? e function z5kxy is an example of a .

7. ? e is represented by the variable k.

8. Both functions z5

kx wy and z5kxy are examples of .Multiple Choice

9. Which function would be used to model the relationship x and y vary

inverselyŽ? y5kx z5kxy y5 k x y5 x k

10. Which function would be used to model the relationship z varies jointly with

x and yŽ? y5kxz z5kxy y5 k xz y5xz k inverse variation joint variation constant of variation combined variationinverse variation combined variation joint variation constant of variation C G

Prentice Hall Algebra 2 • Teaching Resources

Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 2

Name Class Date

? e spreadsheet shows data that could be modeled by an equation of the form PV5k. Estimate P when V 5 62.

Understanding the Problem

1. ? e data can be modeled by

z??????z

2. What is the problem asking you to determine?

Planning the Solution

3. What does it mean that the data can be modeled by an inverse variation?

4. How can you estimate the constant of the inverse variation?

5. What is the constant of the inverse variation?

6. Write an equation that you can use to nd P when V562.

Getting an Answer

7. Solve your equation.

8. What is an estimate for P when V562?

8-1

Think About a Plan

Inverse Variation

AB

140.00 1002

3

147.30 95

4

155.60 90

164.70 85

5

175.00 80

6

186.70 75

71
PV PV5k an estimate of the value of P when V562 about 14,000 about 226

62P514,000

The product of each pair of P and V values is approximately the same constant Find PV for each row of the data. It should be approximately the same for each row

62P514,000

P5

14,000

62
N226

Name Class Date

Prentice Hall Gold Algebra 2 • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 3 8-1

Practice Form G

Inverse Variation

Is the relationship between the values in each table a direct variation, an inverse variation, or neither? Write equations to model the direct and inverse variations. 1. x y2 104
55
420
1 2. x y 1 23
87
2010
29
3. x y 1 62
125
307
42
4. x y 0.2 250.5
62.52
2503
375
5. x y31 7 32 1

101232

5 2 6. x y 3 51.5
100.5
300.3
50
Suppose that x and y vary inversely. Write a function that models each inverse variation. Graph the function and nd y when x 5 10.

7. x57 when y52 8. x54 when y50.2 9. x5

1 3 when y5 9 10

10. ? e students in a school club decide to raise money by selling hats with the

school mascot on them. ? e table below shows how many hats they can expect to sell based on how much they charge per hat in dollars.

Price per Hat (p) 5689

72 60 45 40

Hats Sold (

h) a. What is a function that models the data? b. How many hats can the students expect to sell if they charge $7.50 per hat?

11. ? e minimum number of carpet rolls n needed to carpet a house varies

directly as the houses square footage h and inversely with the square footage r in one roll. It takes a minimum of two 1200-ft 2 carpet rolls to cover 2300 ft 2 of oor. What is the minimum number of 1200-ft 2 carpet rolls you would need to cover 2500 ft 2 of oor? Round your answer up to the nearest half roll. y5 14 x 7 5 y5 4 5x ; 0.08 or 2 25
y5 3 10x ; 0.03 or 3 100
ph5360 or h5 360
p 48

2.5inverse;

y5 20 x neither direct; y5125x inverse; y5 15 x direct; y56x neither

Name Class Date

Prentice Hall Gold Algebra 2 • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 4 8-1

Practice (continued) Form G

Inverse Variation

12. On Earth, the mass m of an object varies directly with the objects potential

energy E and inversely with its height above the Earths surface h. What is an equation for the mass of an object on Earth? (Hint: E 5 gmh, where g is the acceleration due to gravity.) Each ordered pair is from an inverse variation. Find the constant of variation.

13. Q3,

1 3

R 14. (0.2, 6) 15. (10, 5) 16. Q

5 7 2 5 R

17. (213, 22) 18. Q

1 2 , 10R 19. Q 1 3 6 7 R

20. (4.8, 2.9) 21. Q

5 8 ,2 2 5

R 22. (4.75, 4)

Write the function that models each variation. Find z when x 5 6 and y 5 4.

23. z varies jointly with x and y. When x 5 7 and y 5 2, z 5 28.

24. z varies directly with x and inversely with the cube of y. When x 5 8 and y 5 2,

z 5 3. Each pair of values is from an inverse variation. Find the missing value.

25. (2, 4), (6, y) 26. Q

1 3 , 6R, Qx, 2 1 2

R 27. (1.2, 4.5), (2.7, y)

28. One load of gravel contains 240 ft

3 of gravel. ? e area A that the gravel will cover is inversely proportional to the depth d to which the gravel is spread. a. Write a model for the relationship between the area and depth for one load of gravel.

b. A designer plans a playground with gravel 6 in. deep over the entire play area. If the play area is a rectangle 40 ft wide and 24 ft long, how many loads of gravel will be needed?

m5 kE h , where k5 1 g

22861 1.2 50

2 7

13.9252

1 42
7 19 242

2 loads

4 3 z 5 2xy; 48 z5 3x y 3 9 32
A5 240
d Prentice Hall Foundations Algebra 2 • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 5

Name Class Date

8-1

Practice Form K

Inverse Variation

Is the relationship between the values in each table a direct variation, an inverse variation, or neither? Write an equation to model the direct and inverse variations. 1. xy 0.1 3 6 243
0.1 0.05

0.0125

2. xy 1 2 5 63
6 15 18 3. xy 0 2 4 61
5 7 8 Suppose that x and y vary inversely. Write a function that models each inverse variation. Graph the function and nd y when x 5 10.

4. x52 when y524 5. x529 when y521 6. x51.5 when y510

7. Suppose the table at the right shows the

time t it takes to drive home when you travel at various average speeds s. a. Write a function that models the relationship between the speed and the time it takes to drive home. b. At what speed would you need to drive to get home in 50 min or 5 6 h?

Time t (h) Speed s (mi/h)

60
40
30
13.3 1 6 1 4 1 3quotesdbs_dbs31.pdfusesText_37

[PDF] 11 5 study guide and intervention dividing polynomials

[PDF] 11 7 study guide and intervention mixed expressions and complex fractions

[PDF] 11 7 study guide and intervention trigonometric ratios

[PDF] 11 8 skills practice rational equations answers

[PDF] 11 alive news anchor faith

[PDF] 11 alive news anchor fired

[PDF] 11 alive news anchor vinny

[PDF] 11 alive news trafficking

[PDF] 11 alive news weather radar

[PDF] 11 alive weather alerts

[PDF] 11 alive weather lady

[PDF] 11 alive weather report

[PDF] 11 pro max 64gb green

[PDF] 11 pro max charger box

[PDF] 11 pro max charger cable