How do you find the variation constant and an equation of variation where y varies inversely as x and y = 6 when x = 14?

1 Answer
May 20, 2016

Answer:

Variation constant is #84#

Explanation:

The maths symbol for proportional to is:#" "alpha#

Given that #" "y color(white)(.) alpha color(white)(.) 1/x#

Let #k# be the constant of variation giving

#y" "=" "kxx1/x" "=" "k/x#
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Given condition #color(blue)(" if "x=14" then "y=6)#

So by substitution

#color(brown)(y=k/x" "->" "color(blue)(6)=k/(color(blue)(14))#

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Multiply both sides by #color(green)(14)#

#=>color(blue)(6color(green)(xx14) color(brown)(=) (color(brown)(k))/14color(green)(xx14))#

#=>84=kxx14/14#
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But #14/14=1#

#84=kxx1#

#color(magenta)(k=84 -> "variation constant")#

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So #" "color(brown)(y color(white)(.) alpha color(white)(.) 1/x)" "->" "color(blue)(y=84/x)#