Need help with theses plz

Mathematics

1 answer:

Sergeeva-Olga [200]2 years ago

8 0

Answer:

7. x=19 2x=38

8.x=23 3x=69

9.x=12 (50-2)/4=12

10.x=15 (31-1)/2

11.x=16 (84-4)/5

12.x=27 (55-1)/2

Step-by-step explanation:

if 2 angles are opposite, it's the same

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The owner of a cattle ranch would like to fence in a rectangular area of 3000000 m^2 and then divide it in half with a fence dow

Reika [66]

If you notice the picture below, the amount of fencing, or perimeter, that will be used will be 3w + 2l

now $\bf \begin{cases}
A=l\cdot w\\\\\
A=3000000\\
----------\\
3000000=l\cdot w\\\\
\frac{3000000}{w}=l
\end{cases}\qquad thus
\\\\\\
P=3w+2l\implies P=3w+2\left( \cfrac{3000000}{w} \right)\implies P=3w+\cfrac{6000000}{w}
\\\\\\
P=3w+6000000w^{-1}\\\\
-----------------------------\\\\
now\qquad \cfrac{dP}{dw}=3-\cfrac{6000000}{w^2}\implies \cfrac{dP}{dw}=\cfrac{3w^2-6000000}{w^2}
\\\\\\
\textit{so the critical points are at }
\begin{cases}
0=w^2\\\\
0=\frac{3w^2-6000000}{w^2}
\end{cases}$

solve for "w", to see what critical points you get, and then run a first-derivative test on them, for the minimum

notice the $0=w^2\implies 0=w$ so. you can pretty much skip that one, though is a valid critical point, the width can't clearly be 0

so.. check the critical points on the other