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y is inversely proportional to the square root of x - OCR - GCSE Maths - Question 14 - 2018 - Paper 4

Question 14

y is inversely proportional to the square root of x. y is 40 when x is 9. Find a formula linking x and y.

Worked Solution & Example Answer:y is inversely proportional to the square root of x - OCR - GCSE Maths - Question 14 - 2018 - Paper 4

Step 1

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Answer

Since y is inversely proportional to the square root of x, we can express this as:

$y = \frac{k}{\sqrt{x}}$

where k is a constant.

Step 2

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Answer

Given that y is 40 when x is 9, we can substitute these values into the equation:

$40 = \frac{k}{\sqrt{9}}$

Calculating ( \sqrt{9} = 3 ), we have:

$40 = \frac{k}{3}$

Multiplying both sides by 3 gives:

$k = 120$ .

Step 3

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Answer

Substituting k back into the equation gives:

$y = \frac{120}{\sqrt{x}}$ .

This is the formula linking x and y.

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