# 3.2.1 Algebraic Formulae, PT3 Practice

3.2.1 Algebraic Formulae, PT3 Practice

Question 1:
Given m2+ 7 = k, express m in terms of k.

Solution:
$\begin{array}{l}{m}^{2}+7=k\\ \text{}{m}^{2}=k-7\\ \text{}m=\sqrt{k-7}\end{array}$

Question 2:
Given 5km = mn – 2k, express k in terms of m and n.

Solution:
$\begin{array}{l}5km=mn-2k\\ 5km+2k=mn\\ k\left(5m+2\right)=mn\\ \text{}k=\frac{mn}{5m+2}\end{array}$

Question 3:
Given $2k-\frac{m}{2n}=m$ , express m in terms of k and n.

Solution:
$\begin{array}{l}2k-\frac{m}{2n}=m\\ -m-\frac{m}{2n}=-2k\\ \text{}m+\frac{m}{2n}=2k\\ \frac{2nm+m}{2n}=2k\\ \frac{m\left(2n+1\right)}{2n}=2k\\ \text{}m=\frac{4kn}{2n+1}\end{array}$

Question 4:
Given $\frac{4m}{\sqrt{T}-k}=\frac{3h}{m}$  , express T in terms of h and m.

Solution:
$\begin{array}{l}\frac{4m}{\sqrt{T}-k}=\frac{3h}{m}\\ \text{}4{m}^{2}=3h\sqrt{T}-3hk\\ \text{}3h\sqrt{T}=4{m}^{2}+3hk\\ \text{}\sqrt{T}=\frac{4{m}^{2}+3hk}{3h}\\ \text{}T={\left(\frac{4{m}^{2}+3hk}{3h}\right)}^{2}←\overline{)\text{Square both sides}}\end{array}$