Question

Write the following statements using the symbol of variation



a. Circumference (C)of a circle is directly proportional to its radius( r).


b. The wavelength of sound ( l ) and its frequency (f) are in inverse

plz answer..!!
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Answer 1

Answer:

a . Circumference (c) of a circle is directly proportional to its radius (r). This statement is written as  

c∝r

b. The wavelength of sound (l) and its frequency (f) are in inverse variation.  

This statement can be written using symbol of variation as  

l∝1/f

Answer 2

Given :  

a. Circumference (C)of a circle is directly proportional to its radius( r).

b) The wavelength of sound ( L) and its frequency (f) are in inverse variation.​

To Find :   Write using symbol of variation.

Solution:

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

a) Circumference (C)of a circle is directly proportional to its radius( r).

C ∝ r

C = 2πr      2π is the constant of proportionality

b) The wavelength of sound ( L) and its frequency (f) are in inverse variation.​

L ∝  1/f

L = c/f  

=> Lf = c    c is the constant of proportionality  ( speed of light)

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