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y is inversely proportional to $x^2$ and $y = 5$ when $x = 4$ - OCR - GCSE Maths - Question 11 - 2017 - Paper 1

Question 11

y is inversely proportional to $x^2$ and $y = 5$ when $x = 4$. Find a formula linking $x$ and $y$.

Worked Solution & Example Answer:y is inversely proportional to $x^2$ and $y = 5$ when $x = 4$ - OCR - GCSE Maths - Question 11 - 2017 - Paper 1

Step 1

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Answer

Since $y$ is inversely proportional to $x^2$ , we can express this relationship as:

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

where $k$ is a constant.

Step 2

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Answer

Using the information provided ( $y = 5$ when $x = 4$ ), we can substitute these values into the equation to find $k$ :

$5 = \frac{k}{4^2}$

This simplifies to:

$5 = \frac{k}{16}$

Multiplying both sides by 16 gives:

$k = 5 \times 16 = 80.$

Thus, the constant $k$ is 80.

Step 3

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101 rated

Answer

Substituting the value of $k$ back into the original relationship yields the final formula linking $x$ and $y$ :

$y = \frac{80}{x^2}.$

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