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y is inversely proportional to the square of x - OCR - GCSE Maths - Question 12 - 2017 - Paper 1

Question 12

y is inversely proportional to the square of x. Complete the table.

Worked Solution & Example Answer:y is inversely proportional to the square of x - OCR - GCSE Maths - Question 12 - 2017 - Paper 1

Step 1

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Answer

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

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

where k is a constant. To find k, we use the given value when x = 10, y = 9:

$9 = \frac{k}{10^2} \\ k = 9 \times 100 = 900$ .

Now, using k to find y when x = 10:

$y = \frac{900}{10^2} = \frac{900}{100} = 9$ .

Step 2

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Answer

Using the value of k we previously calculated:

$y = \frac{900}{6^2} = \frac{900}{36} = 25$ .

Step 3

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Answer

Using the same value of k again:

$y = \frac{900}{4^2} = \frac{900}{16} = 56.25$ .

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