Answer:
The area of the grass covered by the sprinkler water is approximately 78.54 feet^2
Answer:
- The quadrilateral is a rectangle
![Perimeter=8\sqrt{2} \,\,Unit](https://tex.z-dn.net/?f=Perimeter%3D8%5Csqrt%7B2%7D%20%5C%2C%5C%2CUnit)
![Area=6\,\,sq.unit](https://tex.z-dn.net/?f=Area%3D6%5C%2C%5C%2Csq.unit)
Step-by-step explanation:
Given,
![A=(0,0)\\B=(1,1)\\C=(4,-2)\\D=(3,-3)](https://tex.z-dn.net/?f=A%3D%280%2C0%29%5C%5CB%3D%281%2C1%29%5C%5CC%3D%284%2C-2%29%5C%5CD%3D%283%2C-3%29)
Now,
![Slope\,\,for\,\,AB=\frac{1-0}{1-0} =1\\\\Slope\,\,for\,\,CD=\frac{-3+2}{3-4} =1\\\\Slope\,\,for\,\,AD=\frac{-3-0}{3-0} =-1\\\\Slope\,\,for\,\,BC=\frac{-2-1}{4-1} =-1\\\\So,AB||CD\,\,and\,\,AD||BC](https://tex.z-dn.net/?f=Slope%5C%2C%5C%2Cfor%5C%2C%5C%2CAB%3D%5Cfrac%7B1-0%7D%7B1-0%7D%20%3D1%5C%5C%5C%5CSlope%5C%2C%5C%2Cfor%5C%2C%5C%2CCD%3D%5Cfrac%7B-3%2B2%7D%7B3-4%7D%20%3D1%5C%5C%5C%5CSlope%5C%2C%5C%2Cfor%5C%2C%5C%2CAD%3D%5Cfrac%7B-3-0%7D%7B3-0%7D%20%3D-1%5C%5C%5C%5CSlope%5C%2C%5C%2Cfor%5C%2C%5C%2CBC%3D%5Cfrac%7B-2-1%7D%7B4-1%7D%20%3D-1%5C%5C%5C%5CSo%2CAB%7C%7CCD%5C%2C%5C%2Cand%5C%2C%5C%2CAD%7C%7CBC)
![AB=\sqrt{(1-0)^2+(1-0)^2}=\sqrt{2}\\BC=\sqrt{(4-1)^2+(-2-1)^2}=3\sqrt{2}\\CD=\sqrt{(3-4)^2+(-3+2)^2}=\sqrt{2}\\AD=\sqrt{(3-0)^2+(-3-0)^2}=3\sqrt{2}\\\\So,\,\,AB=CD,AD=BC\\The\,\,quadrilateral\,\,is\,\,a\,\,rectangle](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%281-0%29%5E2%2B%281-0%29%5E2%7D%3D%5Csqrt%7B2%7D%5C%5CBC%3D%5Csqrt%7B%284-1%29%5E2%2B%28-2-1%29%5E2%7D%3D3%5Csqrt%7B2%7D%5C%5CCD%3D%5Csqrt%7B%283-4%29%5E2%2B%28-3%2B2%29%5E2%7D%3D%5Csqrt%7B2%7D%5C%5CAD%3D%5Csqrt%7B%283-0%29%5E2%2B%28-3-0%29%5E2%7D%3D3%5Csqrt%7B2%7D%5C%5C%5C%5CSo%2C%5C%2C%5C%2CAB%3DCD%2CAD%3DBC%5C%5CThe%5C%2C%5C%2Cquadrilateral%5C%2C%5C%2Cis%5C%2C%5C%2Ca%5C%2C%5C%2Crectangle)
![Perimeter=2*(AB+AD)=2*(BC+CD)\\=2*(\sqrt{2}+3\sqrt{2})=8\sqrt{2} \,\,Unit](https://tex.z-dn.net/?f=Perimeter%3D2%2A%28AB%2BAD%29%3D2%2A%28BC%2BCD%29%5C%5C%3D2%2A%28%5Csqrt%7B2%7D%2B3%5Csqrt%7B2%7D%29%3D8%5Csqrt%7B2%7D%20%5C%2C%5C%2CUnit)
![Area=AB*AD=BC*CD=\sqrt{2} *3\sqrt{2}=6\,\,sq.unit](https://tex.z-dn.net/?f=Area%3DAB%2AAD%3DBC%2ACD%3D%5Csqrt%7B2%7D%20%2A3%5Csqrt%7B2%7D%3D6%5C%2C%5C%2Csq.unit)
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Answer: The amount she pays for admission
Step-by-step explanation:
The answer is the 1st graph. This is because a square have 4 sides and it is all the same. on the x axis (Side length) when it is 4 the perimeter (Length around the outside) will be 4 x 4 which is 16.
Hope this helps?
Step-by-step explanation:
![\csc( - 450 \degree) \\ \\ = - \csc450 \degree \\ \\ = - \csc(360 \degree + 90\degree) \\ \\ = - \csc( 90\degree) \\ \\ = - 1](https://tex.z-dn.net/?f=%20%5Ccsc%28%20-%20450%20%5Cdegree%29%20%5C%5C%20%20%5C%5C%20%20%3D%20%20-%20%20%5Ccsc450%20%5Cdegree%20%5C%5C%20%20%5C%5C%20%20%3D%20%20-%20%20%5Ccsc%28360%20%5Cdegree%20%2B%2090%5Cdegree%29%20%5C%5C%20%20%5C%5C%20%20%3D%20-%20%20%5Ccsc%28%2090%5Cdegree%29%20%5C%5C%20%20%5C%5C%20%20%3D%20%20-%201)