Task one - fuel cost Key information from the first page is repeated here: - The one-way distance from Northcote College to Tongariro Alpine Crossing is 350 km . - The current fuel price is \( \$ 2.62 \) per litre. - The school vans use 7.2 litres of fuel per 100 km travelled. - Each of the school vans can fit a maximum of 10 people. - The government is considering a \( 17 \% \) fuel tax to be added to the cost of fuel prior to the trip, which could be in place before the camp. 1. Calculate the cost of fuel per person for a return trip to Tongariro Alpine Crossing from Northcote College. 2. If a fuel tax increases the fuel price, then calculate how this could change the total fuel cost. 3. Discuss any assumptions or limitations you have made and how they impact your calculations.

What do you get when you subtract \( 4 \) from \( 10 \)?

Consider the following equilibrium system: \[ \mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \] A 10.00 L evacuated flask is filled with 0.4414 mol \( \mathrm{PCl}_{5}(\mathrm{~g}) \) at \( \mathbf{2 9 8 . 3} \mathrm{K} \). The temperature is then raised to 503.3 K , where the decomposition of \( \mathrm{PCl}_{5} \) gas takes place to an appreciable extent. When equilibrium is established, the total pressure in the flask is \( \mathbf{2 . 5 9 7} \) atm.

Given: \( 2^{m+1}+2^{m}=3^{n+2}-3^{n} \) where \( m \) and \( n \) are integers. Determine the value of \( m+n \).

1. \( \left\{\begin{array}{c}3 x+4 y \leq 12 \\ 2 x+4 y \leq 8 \\ x \geq 0 \\ y \geq 0\end{array}\right. \) dicate the coordinates of the extreme points. 2. \( \left\{\begin{array}{c}4 x+4 y \text { belo } \\ 5 x+3 y \leq 16 \\ x \geq 0 \\ y \geq 0\end{array}\right. \)

Write \( 5^{-3} \) and \( 4^{\frac{3}{2}} \) without using indices.