Answer:
![108\ \text{m}^2](https://tex.z-dn.net/?f=108%5C%20%5Ctext%7Bm%7D%5E2)
Step-by-step explanation:
The sides are rectangle is shown in the diagram
The perimeter of the fence will be
![3x+2y=36\\\Rightarrow x=\dfrac{36-2y}{3}](https://tex.z-dn.net/?f=3x%2B2y%3D36%5C%5C%5CRightarrow%20x%3D%5Cdfrac%7B36-2y%7D%7B3%7D)
Area of the smaller section of the garden
![A=xy\\\Rightarrow A=\dfrac{36-2y}{3}y\\\Rightarrow A=\dfrac{36y-2y^2}{3}](https://tex.z-dn.net/?f=A%3Dxy%5C%5C%5CRightarrow%20A%3D%5Cdfrac%7B36-2y%7D%7B3%7Dy%5C%5C%5CRightarrow%20A%3D%5Cdfrac%7B36y-2y%5E2%7D%7B3%7D)
Differentiating with respect to y we get
![\dfrac{dA}{dy}=\dfrac{1}{3}(36-4y)](https://tex.z-dn.net/?f=%5Cdfrac%7BdA%7D%7Bdy%7D%3D%5Cdfrac%7B1%7D%7B3%7D%2836-4y%29)
Equating with zero we get
![\dfrac{1}{3}(36-4y)=0\\\Rightarrow 36-4y=0\\\Rightarrow y=\dfrac{36}{4}\\\Rightarrow y=9](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B3%7D%2836-4y%29%3D0%5C%5C%5CRightarrow%2036-4y%3D0%5C%5C%5CRightarrow%20y%3D%5Cdfrac%7B36%7D%7B4%7D%5C%5C%5CRightarrow%20y%3D9)
Double derivative of area
![\dfrac{d^2A}{dy^2}=-4](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%5E2A%7D%7Bdy%5E2%7D%3D-4%3C0)
at y = 9 the area is maximum
![x=\dfrac{36-2y}{3}=\dfrac{36-2\times 9}{3}\\\Rightarrow x=6](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B36-2y%7D%7B3%7D%3D%5Cdfrac%7B36-2%5Ctimes%209%7D%7B3%7D%5C%5C%5CRightarrow%20x%3D6)
The sides of the entire garden are
and ![6\ \text{m}](https://tex.z-dn.net/?f=6%5C%20%5Ctext%7Bm%7D)
The maximum area of the natural fertilizer garden is ![18\times 6=108\ \text{m}^2](https://tex.z-dn.net/?f=18%5Ctimes%206%3D108%5C%20%5Ctext%7Bm%7D%5E2)
Answer:
I hope this helps:D
SA : 600 Cm2
LA : 500 Cm2
V. : 500 Cm3
and these are all rounded to the nearest hundredth
C hope this helps................
Answer:
![\frac{1}{r^{42} }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Br%5E%7B42%7D%20%7D)
Step-by-step explanation:
Using the rules of exponents
⇔ ![a^{mn}](https://tex.z-dn.net/?f=a%5E%7Bmn%7D)
⇔ ![\frac{1}{a^{m} }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Ba%5E%7Bm%7D%20%7D)
Given
![(r^{-7}) ^{6}](https://tex.z-dn.net/?f=%28r%5E%7B-7%7D%29%20%5E%7B6%7D)
= ![r^{-7(6)}](https://tex.z-dn.net/?f=r%5E%7B-7%286%29%7D)
= ![r^{-42}](https://tex.z-dn.net/?f=r%5E%7B-42%7D)
= ![\frac{1}{r^{42} }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Br%5E%7B42%7D%20%7D)