4. Write using symbol of variation. a) Area of a circle (A) is directly proportional to the square of its radius (r) b) The wavelength of sound ( L) and its frequency (f) are in inverse variation.
Answers
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Given :
a) Area of a circle (A) is directly proportional to the square of 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) Area of a circle (A) is directly proportional to the square of its radius (r)
A ∝ r²
A = πr² π 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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