Make the variable given after each equation the subject of the formula: a) \( \quad V=\pi r^{2} h \) for \( h \) b) \( \quad V=\pi r^{2} h \) for \( r \) c) \( \quad A=P(1+i n) \) for \( i \) d) \( \quad A=P(1+i)^{n} \) for \( i \) e) \( 3=\frac{-b+\sqrt{b^{2}-4 a c}}{2 a} \) for c f) \( s=u t+\frac{1}{2} a t^{2} \) for a g) \( s=u t+\frac{1}{2} a t^{2} \) for u h) \( \quad S A=2(l b+l h+b h) \) for h i) \( \quad 0=a x^{2}+b x+c \quad \) for \( a \) j) \( \quad T_{n}=a(r)^{n-1} \) for \( r \)

To make the variable the subject of the formulas, we need to isolate it step-by-step. a) For \( V=\pi r^{2} h \) and solving for \( h \): \[ h = \frac{V}{\pi r^{2}} \] b) For \( V=\pi r^{2} h \) and solving for \( r \): \[ r = \sqrt{\frac{V}{\pi h}} \] c) For \( A=P(1+i n) \) and solving for \( i \): \[ i = \frac{A}{Pn} - 1 \] d) For \( A=P(1+i)^{n} \) and solving for \( i \): \[ i = ( \frac{A}{P} )^{\frac{1}{n}} - 1 \] e) For \( 3=\frac{-b+\sqrt{b^{2}-4 a c}}{2 a} \) and solving for \( c \): \[ c = \frac{b^{2}-4 a (3 \cdot 2 a)}{4 a} \] f) For \( s=u t+\frac{1}{2} a t^{2} \) and solving for \( a \): \[ a = \frac{2(s - ut)}{t^{2}} \] g) For \( s=u t+\frac{1}{2} a t^{2} \) and solving for \( u \): \[ u = \frac{s - \frac{1}{2} a t^{2}}{t} \] h) For \( S A=2(l b+l h+b h) \) and solving for \( h \): \[ h = \frac{SA/2 - lb}{b} - l \] i) For \( 0=a x^{2}+b x+c \) and solving for \( a \): \[ a = \frac{-b x - c}{x^{2}} \] j) For \( T_{n}=a(r)^{n-1} \) and solving for \( r \): \[ r = ( \frac{T_{n}}{a} )^{\frac{1}{n-1}} \]