Question $6$

$[$LO$4]$

$($a$)$ Find $\frac{dy}{dx}$

$[5$ marks$]$

$y(x)=\frac{(8-3x{)}^2}{x}$

$($b$)$ The alternating current is given by $i=5sin100t$ amperes, where $t$ is the time in seconds. Determine the rate of change of the current $($i$.$e$.,\frac{di}{dt})$ when $t=0\mathrm{.}02$ seconds.

$[5$ marks$]$

Page $3$ of $4$

$($c$)$ A landscaping team is designing a parabolic flower bed for the university campus, following the curve $y=-2{?}^2+12x-10$ with the edge of the bed along the x $-$axis. To plan for soil and plants, they need to determine the area of the bed. Calculate the area enclosed by the curve and the x axis.

$[10$ marks$]$

${\displaystyle \underset{1}{\overset{5}{}}}(-2x^2+12x-10t)dx$