1. The problem asks to rearrange formulas to make the specified letter the subject. We will isolate the letter inside the brackets in each formula. 2. (a) For $F = \frac{9}{5} C + 32$ and subject $C$: Subtract 32 from both sides: $$F - 32 = \frac{9}{5} C$$ Multiply both sides by $\frac{5}{9}$: $$C = \frac{5}{9} (F - 32)$$ 3. (b) For $A = 2\pi r^2 + \pi r l$ and subject $l$: Subtract $2\pi r^2$ from both sides: $$A - 2\pi r^2 = \pi r l$$ Divide both sides by $\pi r$: $$l = \frac{A - 2\pi r^2}{\pi r}$$ 4. (c) For $s = ut + \frac{1}{2} at^2$ and subject $u$: Subtract $\frac{1}{2} a t^2$ from both sides: $$s - \frac{1}{2} a t^2 = ut$$ Divide both sides by $t$: $$u = \frac{s - \frac{1}{2} a t^2}{t} = \frac{s}{t} - \frac{1}{2} a t$$ 5. (d) For $s = \frac{n}{2} a + (n-1) d$ and subject $d$: Subtract $\frac{n}{2} a$ from both sides: $$s - \frac{n}{2} a = (n - 1) d$$ Divide both sides by $n - 1$: $$d = \frac{s - \frac{n}{2} a}{n - 1}$$ Final answers: (a) $C = \frac{5}{9} (F - 32)$ (b) $l = \frac{A - 2\pi r^2}{\pi r}$ (c) $u = \frac{s}{t} - \frac{1}{2} a t$ (d) $d = \frac{s - \frac{n}{2} a}{n - 1}$