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y is inversely proportional to the square root of x; y = 5 when x = 36 - OCR - GCSE Maths - Question 14 - 2021 - Paper 1

Question 14

y is inversely proportional to the square root of x; y = 5 when x = 36. (a) Find a formula linking x and y. (b) Find the value of x when y = 20.

Worked Solution & Example Answer:y is inversely proportional to the square root of x; y = 5 when x = 36 - OCR - GCSE Maths - Question 14 - 2021 - Paper 1

Step 1

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Answer

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

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

where k is a constant.

To find k, we use the given values y = 5 when x = 36:

$5 = \frac{k}{\sqrt{36}}$

Since (\sqrt{36} = 6), we have:

$5 = \frac{k}{6}$

Multiplying both sides by 6 gives:

$k = 30$

Thus, the formula linking x and y is:

$y = \frac{30}{\sqrt{x}}$

Step 2

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Answer

We will use the formula derived in part (a):

$y = \frac{30}{\sqrt{x}}$

Substituting y = 20 into the equation gives:

$20 = \frac{30}{\sqrt{x}}$

To isolate (\sqrt{x}), we rearrange the equation:

$\sqrt{x} = \frac{30}{20} = 1.5$

Now, squaring both sides to find x leads to:

$x = (1.5)^2 = 2.25$

Hence, the value of x when y = 20 is:

x = 2.25

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