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14 y is inversely proportional to x² y = 44 when x = a Show that y = 5.5 when x = 2a - Edexcel - GCSE Maths - Question 15 - 2018 - Paper 3

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14--y-is-inversely-proportional-to-x²----y-=-44-when-x-=-a----Show-that-y-=-5.5-when-x-=-2a-Edexcel-GCSE Maths-Question 15-2018-Paper 3.png

14 y is inversely proportional to x² y = 44 when x = a Show that y = 5.5 when x = 2a

Worked Solution & Example Answer:14 y is inversely proportional to x² y = 44 when x = a Show that y = 5.5 when x = 2a - Edexcel - GCSE Maths - Question 15 - 2018 - Paper 3

Step 1

Express the relationship between y and x

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Answer

Since y is inversely proportional to x², we can express this relationship mathematically as:

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

where k is a constant.

Step 2

Substitute known values to find k

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Answer

We know that y = 44 when x = a. Substituting these values into the equation gives us:

44=ka244 = \frac{k}{a^2}

From this, we can solve for k:

k=44a2.k = 44a^2.

Step 3

Show that y = 5.5 when x = 2a

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Answer

Next, we need to find y when x = 2a. Using our equation again:

y=k(2a)2y = \frac{k}{(2a)^2}

Substituting k:

y=44a24a2y = \frac{44a^2}{4a^2}

This simplifies to:

y=444=11.y = \frac{44}{4} = 11.

However, we need to show that y equals 5.5.

If we reconsider the inversion:

y=44x2y = \frac{44}{x^2}

Thus:

When x = 2a, substituting into the original equation gives:

y=44(2a)2=444a2y = \frac{44}{(2a)^2} = \frac{44}{4a^2}

Reevaluating this as:

y=444=11.y = \frac{44}{4} = 11.

This leads to an inconsistency; however, further checks or interpretations within the context of the problem may yield the intended target value more accurately.

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