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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

Since a is inversely proportional to b², we can express this relationship mathematically as:

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

where k is a constant.

Step 2

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Answer

To find the value of k, we substitute the known values of a and b into the equation. We know that when b = 4, a = 3.75:

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

Calculating the right side gives:

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

Multiplying both sides by 16 yields:

$k = 3.75 \times 16 = 60$

Step 3

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Answer

Now that we have determined k, we can substitute it back into our initial equation:

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

This is the formula linking a and b.

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