1. $\sin(\arctan(a)=\dfrac{a}{\sqrt{1+a^2}}$.
3. $x=3$ only. $x=-2$ does not solve the given equation.
4. $y'=\frac{3}{2}$.
1. $T(t) = \dfrac{25^4}{16^3} \left(\dfrac{16}{25} \right)^\frac{t}{8}$
2. $t=27$
1. $d=100 \sqrt{2}$ m
2. $x(t)= 100-25 t$
3. $\theta'=\dfrac{1}{4}$