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

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

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

From this, we can solve for k:

$k = 44a^2.$

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

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

Substituting k:

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

This simplifies to:

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

However, we need to show that y equals 5.5.

If we reconsider the inversion:

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

Thus:

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

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

Reevaluating this as:

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

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