Wanda and Louise determine that the expression A =-2w^2+36w models the area of a rectangular puppy run, where w is the width in metres and A is the area in square metres. What dimensions produce an area of 112 m2
+14917 Wanda and Louise determine that the expression A =-2w^2+36w models the area of a rectangular puppy run, where w is the width in metres and A is the area in square metres. What dimensions produce an area of 112 m2
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\( A =-2w^2+36w \\ -2w^2+36w -A=0\\ -2w^2+36w -112=0\\ w^2-18w+56=0\)
\(w=-\frac{p}{2}\pm \sqrt{(\frac{p}{2})^2-q}\\ w=9\pm \sqrt{9^2-56}\\ w=9\pm 5\\ \color{blue}w_1=4m\\ \color{blue}l_2=14m\)
\(l_1=A/w_1=112m^2/4m\\ \color{blue}l_1=28m\\ w_2=A/l_2=112m^2/14m\\ \color{blue}w_2=8m\\\)
The dimensions \({\color{blue}4m\times 28m}\ and\ \color{blue}8m\times 14m\) produce an area of \(\color{blue}112 m^2.\)
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