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The table shows a set of values for x and y - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 1

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The table shows a set of values for x and y. | x | 1 | 2 | 3 | 4 | |---|---|---|---|---| | y | 9 | \frac{1}{4} | 1 | \frac{9}{16} | y is inversely proportional to... show full transcript

Worked Solution & Example Answer:The table shows a set of values for x and y - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 1

Step 1

Find an equation for y in terms of x.

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Answer

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

y=kx2y = \frac{k}{x^2}

where k is a constant. To find the value of k, we can use one pair of values from the table. Let's use x = 1 and y = 9:

9=k12⇒k=9.9 = \frac{k}{1^2} \Rightarrow k = 9.

Thus, the equation for y in terms of x is:

y=9x2.y = \frac{9}{x^2}.

Step 2

Find the positive value of x when y = 16.

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Answer

Using the equation derived in part (a):

16=9x2.16 = \frac{9}{x^2}.

To find x, we can rearrange this equation:

x2=916⇒x=916=34.x^2 = \frac{9}{16} \Rightarrow x = \sqrt{\frac{9}{16}} = \frac{3}{4}.

Thus, the positive value of x when y = 16 is:

x=34.x = \frac{3}{4}.

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