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:
IQR = 21-8 = 13
Step-by-step explanation:
Answer: (x-1)(3x+8)
Step-by-step explanation:
Slide and divide method
See what multiplies to get -24 (because of 3 and -8) and what adds to get 5
Put those into factoring form (x-3)(x+8) without a number in front of the x’s
Divide the numbers by what isn’t in front of the x’s (-3/3 and 8/3)
Simplify them and if it doesn’t divide perfectly, put the denominator in front of the x
Solution
**I can’t explain it well but watch a video on the method AND ONLY DO IT IF IT WORKS WELL FOR YOU**
Answer:
Problem 10:
Input X: -2, -1, 0, 1, 2
Output Y: -2, 1, 2, 1, -2
Nonlinear, exponential because there's an exponent. Plug the X values in place of X and solve solution to get Y values. Then graph
Problem 11: Linear because there's no exponent
Answer: 54 cm
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula:
Perimeter of a square = side length x4
Replacing with the values given:
72 = 4 s
Solving for s (side length)
72/4=s
s = 18 cm
Since the side length of the square is the length of each rod, and all the rods have the same length, to obtain the perimeter of the triangle we have to apply:
Perimeter of an equilateral triangle: 3 side length
P = 3 (18 ) = 54 cm
Feel free to ask for more if needed or if you did not understand something.