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dolphi86 [110]
3 years ago
10

It is given that y varies inversely as x^2. If x is decreased by 50%, find the percentage change in y.

Mathematics
1 answer:
vova2212 [387]3 years ago
7 0

Answer:

300%

Step-by-step explanation:

Given

y\ \alpha\ \frac{1}{x^2}

Required

Find the percentage change in y when x decreased by 50%

First, convert to equation

y\ = \ \frac{k}{x^2}

Where k is the constant of proportionality

When x decreased by 50%

Y = \frac{k}{(x - 0.5x)^2}

Y = \frac{k}{(0.5x)^2}

Y = \frac{k}{0.25x^2}

Expand

Y = \frac{1}{0.25} * \frac{k}{x^2}

Substitute \frac{k}{x^2} for y

Y = \frac{1}{0.25} * y

Y = 4 * y

Y = 4 y

The percentage change is then calculated as:

\%Change = \frac{Y - y}{y} * 100\%

\%Change = \frac{4y - y}{y} * 100\%

\%Change = \frac{3y}{y} * 100\%

\%Change = 3 * 100\%

\%Change = 300\%

<em>The percentage in y is 300%</em>

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