Answer:
(x + 2)² + (y - 5)² = 7²
Step-by-step explanation:
Incomplete question. I believe you meant, "write the equation of the circle with center at (-2, 5) and radius 7.
That would be:
(x + 2)² + (y - 5)² = 7²
Answer:
![A(4)=-4\pi](https://tex.z-dn.net/?f=A%284%29%3D-4%5Cpi%20)
![A(8)=-4\pi +8](https://tex.z-dn.net/?f=A%288%29%3D-4%5Cpi%20%2B8)
![A(12)=-4\pi +16](https://tex.z-dn.net/?f=A%2812%29%3D-4%5Cpi%20%2B16)
![A(14)=-4\pi +15](https://tex.z-dn.net/?f=A%2814%29%3D-4%5Cpi%20%2B15)
Step-by-step explanation:
we are given
![A(x)=\int\limits^x_0 f{x} \, dx](https://tex.z-dn.net/?f=A%28x%29%3D%5Cint%5Climits%5Ex_0%20f%7Bx%7D%20%5C%2C%20dx)
Calculation of A(4):
we can plug x=4
![A(4)=\int\limits^4_0 f{x} \, dx](https://tex.z-dn.net/?f=A%284%29%3D%5Cint%5Climits%5E4_0%20f%7Bx%7D%20%5C%2C%20dx)
Since, this curve is below x-axis
so, the value of integral must be negative
and it is quarter of circle
so, we can find area of quarter circle
radius =4
![A(4)=-\frac{1}{4}\times \pi \times (4)^2](https://tex.z-dn.net/?f=A%284%29%3D-%5Cfrac%7B1%7D%7B4%7D%5Ctimes%20%5Cpi%20%5Ctimes%20%284%29%5E2)
![A(4)=-4\pi](https://tex.z-dn.net/?f=A%284%29%3D-4%5Cpi%20)
Calculation of A(8):
we can plug x=8
![A(8)=\int\limits^8_0 f{x} \, dx](https://tex.z-dn.net/?f=A%288%29%3D%5Cint%5Climits%5E8_0%20f%7Bx%7D%20%5C%2C%20dx)
we can break into two parts
![A(8)=\int\limits^4_0 f{x} \, dx+\int\limits^8_4 f{x} \, dx](https://tex.z-dn.net/?f=A%288%29%3D%5Cint%5Climits%5E4_0%20f%7Bx%7D%20%5C%2C%20dx%2B%5Cint%5Climits%5E8_4%20f%7Bx%7D%20%5C%2C%20dx)
now, we can find area and then combine them
![A(8)=-4\pi +\frac{1}{2}\times 4\times 4](https://tex.z-dn.net/?f=A%288%29%3D-4%5Cpi%20%2B%5Cfrac%7B1%7D%7B2%7D%5Ctimes%204%5Ctimes%204)
![A(8)=-4\pi +8](https://tex.z-dn.net/?f=A%288%29%3D-4%5Cpi%20%2B8)
Calculation of A(12):
we can plug x=12
![A(12)=\int\limits^12_0 f{x} \, dx](https://tex.z-dn.net/?f=A%2812%29%3D%5Cint%5Climits%5E12_0%20f%7Bx%7D%20%5C%2C%20dx)
we can break into two parts
![A(12)=\int\limits^4_0 f{x} \, dx+\int\limits^8_4 f{x} \, dx+\int\limits^12_8 f{x} \, dx](https://tex.z-dn.net/?f=A%2812%29%3D%5Cint%5Climits%5E4_0%20f%7Bx%7D%20%5C%2C%20dx%2B%5Cint%5Climits%5E8_4%20f%7Bx%7D%20%5C%2C%20dx%2B%5Cint%5Climits%5E12_8%20f%7Bx%7D%20%5C%2C%20dx)
now, we can find area and then combine them
![A(12)=-4\pi +\frac{1}{2}\times 8\times 4](https://tex.z-dn.net/?f=A%2812%29%3D-4%5Cpi%20%2B%5Cfrac%7B1%7D%7B2%7D%5Ctimes%208%5Ctimes%204)
![A(12)=-4\pi +16](https://tex.z-dn.net/?f=A%2812%29%3D-4%5Cpi%20%2B16)
Calculation of A(14):
we can plug x=14
![A(14)=\int\limits^14_0 f{x} \, dx](https://tex.z-dn.net/?f=A%2814%29%3D%5Cint%5Climits%5E14_0%20f%7Bx%7D%20%5C%2C%20dx)
we can break into two parts
![A(14)=\int\limits^4_0 f{x} \, dx+\int\limits^8_4 f{x} \, dx+\int\limits^12_8 f{x} \, dx+\int\limits^14_12 f{x} \, dx](https://tex.z-dn.net/?f=A%2814%29%3D%5Cint%5Climits%5E4_0%20f%7Bx%7D%20%5C%2C%20dx%2B%5Cint%5Climits%5E8_4%20f%7Bx%7D%20%5C%2C%20dx%2B%5Cint%5Climits%5E12_8%20f%7Bx%7D%20%5C%2C%20dx%2B%5Cint%5Climits%5E14_12%20f%7Bx%7D%20%5C%2C%20dx)
now, we can find area and then combine them
![A(14)=-4\pi +\frac{1}{2}\times 8\times 4-\frac{1}{2}\times 1\times 2](https://tex.z-dn.net/?f=A%2814%29%3D-4%5Cpi%20%2B%5Cfrac%7B1%7D%7B2%7D%5Ctimes%208%5Ctimes%204-%5Cfrac%7B1%7D%7B2%7D%5Ctimes%201%5Ctimes%202)
![A(14)=-4\pi +16-1](https://tex.z-dn.net/?f=A%2814%29%3D-4%5Cpi%20%2B16-1)
![A(14)=-4\pi +15](https://tex.z-dn.net/?f=A%2814%29%3D-4%5Cpi%20%2B15)
Answer:
64
step by step:
16oz x4= 64
answer= 64
If you want to increase something by 31% then...
100%+31%=131% or 1.31
you multiply it by 131% or 1.31. So for 429 grams...
429*1.31=561.99grams
If you increase 429 by 31%, you get 561.99 grams
Answer=561.99 grams
For this case we have the following system of equations:
![y = -0.25x + 4.7 y = 4.9x-1.64](https://tex.z-dn.net/?f=y%20%3D%20-0.25x%20%2B%204.7%0A%0Ay%20%3D%204.9x-1.64)
When solving the problem graphically we must take into account the following:
1) The solution of the system of equations is given by the intersection of both functions.
2) The solution is an ordered pair of the form (x, y)
For this case we observe that the solution is given by:
![(x, y) = (1.23, 4.39) ](https://tex.z-dn.net/?f=%28x%2C%20y%29%20%3D%20%281.23%2C%204.39%29%0A)
Note: see attached image.
Answer:
The approximate solution to the system is (1.23, 4.39)