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y is inversely proportional to the square of x - Edexcel - GCSE Maths - Question 17 - 2019 - Paper 3

Question 17

y is inversely proportional to the square of x. y = 8 when x = 2.5 Find the negative value of x when y = \frac{8}{9}.

Worked Solution & Example Answer:y is inversely proportional to the square of x - Edexcel - GCSE Maths - Question 17 - 2019 - Paper 3

Step 1

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Answer

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

$y = \frac{k}{x^2}$ where k is a constant.

Step 2

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Answer

Substituting the known values into the equation:

$8 = \frac{k}{(2.5)^2}$

We calculate:

$(2.5)^2 = 6.25$

Thus,

$8 = \frac{k}{6.25}$

Multiplying both sides by 6.25 gives:

$k = 8 \times 6.25 = 50$ .

Step 3

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Answer

Substituting y = \frac{8}{9}$ into the relationship:

$\frac{8}{9} = \frac{50}{x^2}$

Rearranging gives:

$x^2 = \frac{50 \times 9}{8} = 56.25$ .

Now taking the square root:

$x = -\sqrt{56.25} = -7.5$ (considering negative value).

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