3.2.1 Algebraic Formulae, PT3 Practice - Mathematics

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 \\ m^{2} = k - 7 \\ m = \sqrt{k - 7} \end{array}

Question 2:

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

Solution:

\begin{array}{l} 5 k m = m n - 2 k \\ 5 k m + 2 k = m n \\ k (5 m + 2) = m n \\ k = \frac{m n}{5 m + 2} \end{array}

Question 3:

Given

2 k - \frac{m}{2 n} = m

, express m in terms of k and n.

Solution:

\begin{array}{l} 2 k - \frac{m}{2 n} = m \\ - m - \frac{m}{2 n} = - 2 k \\ m + \frac{m}{2 n} = 2 k \\ \frac{2 n m + m}{2 n} = 2 k \\ \frac{m (2 n + 1)}{2 n} = 2 k \\ m = \frac{4 k n}{2 n + 1} \end{array}

Question 4:

Given

\frac{4 m}{\sqrt{T} - k} = \frac{3 h}{m}

, express T in terms of h and m.

Solution:

\begin{array}{l} \frac{4 m}{\sqrt{T} - k} = \frac{3 h}{m} \\ 4 m^{2} = 3 h \sqrt{T} - 3 h k \\ 3 h \sqrt{T} = 4 m^{2} + 3 h k \\ \sqrt{T} = \frac{4 m^{2} + 3 h k}{3 h} \\ T = {(\frac{4 m^{2} + 3 h k}{3 h})}^{2} \leftarrow Square both sides \end{array}