Two joggers run 8 miles north and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point?

SULrt \( 5 \quad \) Sebuah mesin memproses minuman mengeluarkan \( 62.92 \mathrm{~m}^{3} \) minuman schari daripada sebuah tangki. Tangki itu mempunyai jejari 2.2 m dan tinggi 4 m . Diberi bahawa isipadu tangki, \( V \) berubah secara langsung dengan kuasa dua jejari, \( j \mathrm{~m} \) dan tinggi, \( t \mathrm{~m} \). A beverage processing machine produces \( 62.92 \mathrm{~m}^{3} \) of beverage per day from a tank. The tank has a radius of 2.2 m and a height of 4 m. Given that the volume of the tank, \( V \) varies directly with the square of the radius, \( j \) mand the height, \( t \mathrm{~m} \). (a) Ungkapkan \( V \) dalam sebutan \( j \) dan \( t \). Express \( V \) in terms of \( j \) and \( t \).

10.A circle, centre \( C \), has a diameter \( P Q \) where \( P \) is the point \( (-1,-1) \) and \( Q \) is the point \( (5,7) \). (a) Show that the equation of the circle is \( x^{2}+y^{2}-4 x-6 y-12=0 \).

7. En cada ítem, estudiar la posición relativa entre las dos rectas dadas y graficar ambas en un mismo sistema de coordenadas cartesianas. a) \( \left\{\begin{array}{l}x=1-5 \lambda \\ y=2+3 \lambda \\ z=-5+\lambda\end{array}\left\{\begin{array}{l}x=1 \\ y=1 \\ z=\mu\end{array}(\lambda, \mu \in \mathbb{R})\right.\right. \) b) \( \left\{\begin{array}{l}x=3+2 \alpha \\ y=1-\alpha \\ z=5\end{array}\left\{\begin{array}{l}x=-1-6 \beta \\ y=3+3 \beta \\ z=5\end{array} \quad(\alpha, \beta \in \mathbb{R})\right.\right. \)

Find the slope of the line passing through the given points. (If an answer is undefined, enter UNDEFINED.) \[ (7,-4) \text { and }(7,-3) \]

7. En cada ítem, estudiar la posición relativa entre las dos rectas dadas y graficar ambas en un mismo sistema de coordenadas cartesianas. a) \( \left\{\begin{array}{l}x=1-5 \lambda \\ y=2+3 \lambda \\ z=-5+\lambda\end{array}\left\{\begin{array}{l}x=1 \\ y=1 \\ z=\mu\end{array}(\lambda, \mu \in \mathbb{R})\right.\right. \)\( \quad \) b) \( \left\{\begin{array}{l}x=3+2 \alpha \\ y=1-\alpha \\ z=5\end{array} \quad\left\{\begin{array}{l}x=-1-6 \beta \\ y=3+3 \beta \\ z=5\end{array} \quad(\alpha, \beta \in \mathbb{R})\right\}\right. \)