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a is inversely proportional to b² and a = 3.75 when b = 4 - OCR - GCSE Maths - Question 18 - 2019 - Paper 4

Question 18

a is inversely proportional to b² and a = 3.75 when b = 4. Find a formula linking a and b.

Worked Solution & Example Answer:a is inversely proportional to b² and a = 3.75 when b = 4 - OCR - GCSE Maths - Question 18 - 2019 - Paper 4

Step 1

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Answer

Inversely proportional means that as one variable increases, the other decreases. We can express this relationship mathematically as:

$a = \frac{k}{b^2}$

where k is a constant.

Step 2

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Answer

We know that when b = 4, a = 3.75. We can substitute these values into the equation to find k:

$3.75 = \frac{k}{4^2}$

This simplifies to:

$3.75 = \frac{k}{16}$

Multiplying both sides by 16 gives:

$k = 3.75 \times 16 = 60$ .

Step 3

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Answer

Now that we have found k, we can write the final formula linking a and b:

$a = \frac{60}{b^2}$ .

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