\begin{align*} y & = kx^2 \\ \\ \text{When } x = 2, y & = k(2)^2 \\ & = k(4) \\ & = 4k \\ \\ \text{When } x = 4, y & = k(4)^2 \\ & = k(16) \\ & = 16k \\ \\ 16k - 4k & = 72 \\ 12k & = 72 \\ k & = {72 \over 12} \\ k & = 6 \\ \\ y & = 6x^2 \\ \\ \text{When } & x = 5, \\ y & = 6(5)^2 \\ & = 150 \end{align*}

\begin{align*} y & = {k \over x^3} \\ \\ \text{Let particular value of } x & = a \\ \\ \text{When } x = a & \text{ and } y = 10, \\ 10 & = {k \over a^3} \\ {10 \over 1} & = {k \over a^3} \\ 10a^3 & = k \phantom{0000000} [\text{Cross-multiply}] \\ \\ y & = {10a^3 \over x^3} \\ \\ \text{When } & x = 2a, \phantom{0000} [\text{Doubled from } a \text{ to } 2a] \\ y & = {10a^3 \over (2a)^3} \\ & = {10a^3 \over 8a^3} \\ & = {10 \over 8} \\ & = 1.25 \end{align*}

\begin{align*} z & = k y^2 \\ \\ \text{Let initial value of } y & = a \\ \\ \text{When } y = a, z & = ka^2 \\ \\ \text{New value of } y & = a \times {100 + 10 \over 100} \\ & = a \times 1.1 \\ & = 1.1a \\ \\ \text{When } y = 1.1a, z & = k(1.1a)^2 \\ & = k(1.21a^2) \\ & = 1.21 ka^2 \\ \\ \text{Percentage change} & = { \text{Final} - \text{Initial} \over \text{Initial} } \times 100 \\ & = {1.21ka^2 - ka^2 \over ka^2} \times 100 \\ & = {0.21ka^2 \over ka^2} \times 100 \\ & = {0.21 \over 1} \times 100 \\ & = 21 \% \end{align*}