Question

Explain how to find the constant of proportionality for the ratio of robins to cardinals.

A 2-column table with 4 rows. Column1 is labeled Cardinals with entries 5, 6, 9, 10. Column 2 is labeled Robins with entries 15, 18, 27, 30.

Answer 1

Given :    a table

Cardinals        Robins

5                      15

6                      18

9                       27

10                      30

To Find :  the constant of proportionality  

Solution:

Robins   ∝   Cardinals

=>  Robins   = K    Cardinals

K is the constant of proportionality

Cardinals        Robins

5                      15

6                      18

9                       27

10                      30

=> 15 = k (5)

=> k = 3

constant of proportionality  = 3

Verify other

6(3)  = 18

9(3) = 27

10(3) = 30

Direct variation if a variable increases then other variable also increases with a constant factor   y = kx

inverse variation if a variable increases then other variable decreases with a  constant factor  xy = k

Joint variation is a relationship between atleast three variables, where one variable varies directly with all other variables.

y = kxz

Combined Variation  is a relationship between three or more variables where it is in direct variation with few variable and in inverse  variation with other variable  y = kx/z

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