Math Pre Calc

Card Set Information

Author:
Jense133
ID:
71932
Filename:
Math Pre Calc
Updated:
2011-03-09 20:10:13
Tags:
Math modeling variation
Folders:

Description:
Modeling Variation
Show Answers:

Home > Flashcards > Print Preview

The flashcards below were created by user Jense133 on FreezingBlue Flashcards. What would you like to do?


  1. Direct variation
    when one quantity is a constant multiple of another quantity, we say that the quantities are directly proportional to one another
  2. Direct variation variables
    • y=kx, where k is a nonzero constant
    • y varies directly with x
    • y is directly proportional to x

    constant k is called the constant of variation or constant of proportionality.
  3. Finding the Constant of Variation
    • 1) write direct variation model
    • y=kx
    • 2) label the variables and constant
    • (usually will be solving for k)
    • example:
    • x= number of kWh
    • y= cost (increases with x)
    • k= cost per kWh

    3) Substitute variables, and SOLVE FOR K
  4. Direct Variation with Powers
    • Let x and y represent 2 quantities
    • y=kxn where k is a nonzero constant
    • y varies directly with the nth power of x
    • y is directly proportional to the nth power of x (however many times x occurs, y varies)
  5. What is an example of Direct Variation with Powers?
    W=kH3 (equivalent to y=kx3)

    Statistics shows that weight in lbs is directly proportional to the cube of height (feet).
  6. Inverse Variation
    When one variable increased, the other decreased.

    ex: supply & demand (when price increased, demand decreases & vice versa.)
  7. Formula and quantities
    • y= k
    • x

    where k is a nonzero constant

    y varies inversely with x

    y is inversely proportional to x

    the constant k is called the constant of variation or constant of proportionality.
  8. Solving inverse variation
    • y=k
    • x

    • x= price of houses in thousands of dollars
    • y=number of buyers



    select any point on the curve

    plug in points

    solve for k (x multiplied times y)

    plug back into original formula

    • y= 100,000 = 50
    • 2000 <---original question
  9. Joint variation
    one quantity is proportional to the product of two or more other quantities
  10. Example of joint variation
    I=Prt

    • I = interest in dollars
    • P= initial amount in dollars
    • r= nterest rate (expressed in decimal form)
    • t= time in years

    total interest is proportional to these quantities
  11. Combined variation
    when direct variation and inverse variation occur at the same time
  12. Example of combined variation
    combined gas law in chemistry

    • P=k T
    • V
    • P= pressure
    • T= temp
    • V= volume
    • k= gas constant

    • volume is inverse- volume decreases, pressure increases
    • temp is direct- temp increases, pressure increases

What would you like to do?

Home > Flashcards > Print Preview