h is inversely proportional to p p is directly proportional to \sqrt{t} Given that h = 10 and t = 144 when p = 6 find a formula for h in terms of t - Edexcel - GCSE Maths - Question 21 - 2019 - Paper 1

Since p is directly proportional to \sqrt{t}, we have: $p = k_1 \sqrt{t}$ for some constant k_1.

Given h = 10 and p = 6 when t = 144: Substituting p into the equation for h: $10 = \frac{k}{6} \implies k = 60$ Using p = 6 to find k_1: $6 = k_1 \sqrt{144} \implies k_1 = \frac{6}{12} = 0.5$

Now substituting p = 0.5 \sqrt{t} into h: $h = \frac{60}{0.5 \sqrt{t}} = 120 / \sqrt{t}$ Thus, the formula for h in terms of t is: $h = \frac{120}{\sqrt{t}}$