How do you write a general formula to describe each variation if y varies inversely with #sqrt x#; y =4 when x=9?

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Answer 1 · 2017-02-11T13:28:31

# color(blue)(y = 12/sqrtx)#

In an inverse variation, as one quantity increases, the other decreases: It is shown as #y prop1/x#

However, in this case the inverse variation is with #sqrtx#

#y prop1/sqrtx#

All variations (also called proportions) are connected by a constant,#k#

#:. color(blue)(y = k/sqrtx)" larr# we need to find the value of #k#

#k = yxx sqrtx" "larr# isolate #k# by cross- multiplying

Use the given values for #x and y#

#k= 4 xx sqrt9= 4xx 3 = 12" "# we now know #k#

Replace #k# by #12#

#:. color(blue)(y = 12/sqrtx)#