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Variation Functions - Advanced Algebra - Practice Problems, Exercises of Calculus

Birla Institute of Technology and ScienceCalculus

This lecture is from Advanced Algebra. Key important points are: Variation Functions, Linear Equations, Algebraic Solutions, Variation, Subtraction

Typology: Exercises

2012/2013

Uploaded on 01/31/2013

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Advanced Algebra Ch. 9 Name__________________
Chapter Review Worksheet
1. If y varies directly as x, and y = 3 when x = 2, find k.
2. Suppose x varies inversely as y. Find k when x = 10 and y = 3.
3. If y varies directly as x, and y = 6 when x = 3, find y when x = 2.
4. Suppose y varies inversely as z. Find z when y = 2, if z = 4 when y = 5.
5. Suppose x varies jointly as y and z. If x = 24 when y = 2 and z = 4, find x when y = 3 and
z = 5.
Simplify each expression completely.
6.
2 32
3
6xy 21x yz
7yz 8y
7. 2
22
x 2x x
x 4y x 2y
+÷
−+
pf3
pf4

Partial preview of the text

Download Variation Functions - Advanced Algebra - Practice Problems and more Exercises Calculus in PDF only on Docsity!

Advanced Algebra Ch. 9 Name__________________ Chapter Review Worksheet

  1. If y varies directly as x, and y = 3 when x = 2, find k.
  2. Suppose x varies inversely as y. Find k when x = 10 and y = 3.
  3. If y varies directly as x, and y = 6 when x = 3, find y when x = 2.
  4. Suppose y varies inversely as z. Find z when y = 2, if z = 4 when y = 5.
  5. Suppose x varies jointly as y and z. If x = 24 when y = 2 and z = 4, find x when y = 3 and z = 5.

Simplify each expression completely.

2 3 2 3

6xy 21x yz 7yz 8y

2 2 2

x 2x x x 4y x 2y

+ ÷

2 2 2 2

x 4x x 16 x 8x 16 x 2x 8

2 2 2 2

x 5x 6 x 3x 28 x 3x 10 x 13x 36

2 2 2 2

2x 5x 12 2x 5x 3 6x 2x 3x 4x 1

− − ÷ + +

Simplify each expression using addition and subtraction.

  1. 3 2 x xy

x 4 x 2

  1. 5x^2 4x^5 x 4 4 x
  1. 2 6y^3 y 9 y 3

3x 6 x 2x 8

  1. A tank can be filled by a hose in 10 hours. It can be emptied by a drainpipe in 15 hours. If the drainpipe is open while the tank is being filled, how long does it take to fill the tank?
  2. Working together Jake and Dylan can clean the garage in 3 hours. Alone, Dylan can clean it in 8 hours. How long would it take Jake to clean it by himself?
  3. Katy takes twice as long as Meg to make the display case at school. Together it takes 4 hours to do the display case. How long does it take Meg to do it herself?

Answers: 1. k 3 2

= 2. k = 30 3. y = 4 4. z = 10 5. x = 45 6. 9x y^4 4z

  1. x^2 x 2y
  1. x x − 2

9. (^ )(^ )

x 3 x 7 x 5 x 9

  1. x^4 2x

− (^) 11. 3y 2 xy

12. (^ )

3 x 6 x 4 x 2

  1. x^3 x 4

y − 3

3 x − 4

  1. y 15 7

= 17. x = 3

  1. x = − 3 19. x = − 4,3 20. x 5 , 3

= − 21. 6 or 1.2 hours 5

  1. 30 or 2.3 hours 13
    1. 30 hours 24. 24 or 4.8 hours 5
      1. 6 hours