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

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Answer 1 · 2017-02-11T13:28:31

$y = \frac{12}{\sqrt{x}}$ $color(blue)(y = 12/sqrtx)$

In an inverse variation, as one quantity increases, the other decreases: It is shown as $y \propto \frac{1}{x}$ $y prop1/x$

However, in this case the inverse variation is with $\sqrt{x}$ $sqrtx$

$y \propto \frac{1}{\sqrt{x}}$ $y prop1/sqrtx$

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

$:. color(blue)(y = k/sqrtx)" larr$ 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 $12$

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

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