A carpenter is building a rectangular shed with a fixed perimeter of 42 feet. Find the dimensions of the largest floor area of the shed that can be built and find the maximum floor area of the shed. Side length:

(b) A swimming pool is being filled. At the deepest point, the depth of the water in the pool at any instant is \( h \mathrm{~m} \). The volume of water in the pool \( V \mathrm{~m}^{3} \) is given by \[ (h)=20 h^{2}+40 h \] Find the rate at which the volume of water is changing with respect to the depth when the water in the pool is 0.75 m deep.

(iii) \( \left\{\begin{aligned} x_{1}-5 x_{2}-x_{3}+12 x_{4}-x_{5} & =-4 \\ -2 x_{1}+10 x_{2}+3 x_{3}-33 x_{4}+2 x_{5}+x_{6} & =4 \\ x_{3}-9 x_{4}+x_{5} & =8 \\ x_{1}-5 x_{2}+2 x_{3}-15 x_{4}+2 x_{5}+x_{6} & =14\end{aligned}\right. \)

When is an observed effect statistically significant? when it is "loo large" to be due to chance when it is "loo small" to be due to chance when it is "about what we expect" due to chance

11) \( \left((-3)^{2}\right)^{-2}= \) a) 81 b) \( \frac{1}{81} \) c) -81 d) \( \frac{1}{-81} \)

Besponder \( v \) of justifican lo resprunta a) Elcuciente que se obtiene de la siguierte divisió \( \left(6 x^{4}-2 x^{3}+x-1\right):\left(x^{3}-2\right) \) es \( 6 x-2 \)