The height of a firework is modeled by $h(t)=u{t}^2+vt+4$, where $h$ is in metres and $t$ is in seconds. The firework reaches its maximum height of $9$ m at $t=1$ s.

Lina is cycling to a campsite located 8 km from where she starts. The distance, $s$, in kilometres, that Lina has travelled from her starting point can be modelled by the exponential function $s(t)=a+b(k^{-t})$, where $t\ge 0$ and $t$ is the time in minutes since Lina started cycling.

The graph below shows the vertical displacement, $D$ (in metres), of a camera drone relative to the level of a bridge deck against $t$, the time in minutes after filming begins.

This data is fitted by a cubic function given by $D=a{t}^3+b{t}^2+ct+d$, where $a$, $b$, $c$ and $d$ are constants. The curve passes through the following points.

Values of $D<0$ indicate that the drone is below the level of the bridge deck.

A logistics company provides three types of parcel delivery services: Standard, Express, and Overnight. The costs per parcel for each service are shown in the table below.

On a specific day:

• A total of 250 parcels were delivered.
• The total revenue collected from these deliveries was $2010.
• There were 30 more Standard deliveries than Overnight deliveries.

Let $x,y,$ and $z$ represent the number of Standard, Express, and Overnight deliveries respectively.

In this question, provide all final values rounded to two decimal places.

A decorator is repainting a community hall. One litre of paint covers 6.8 m${}^2$. The hall has 145 m${}^2$ of wall area to paint. The decorator buys 7% extra paint to allow for wastage.

For a mural, the area covered is modelled by $A=Ly$, where $A$ is the area in m${}^2$ and $L$ is the number of litres of paint used. The decorator uses 18.5 L of paint to cover 127.31 m${}^2$.