Origin (0,0), x-axis left to right, y-axis up and down (vertical)
Answer:
![y = -0.75x + 9.5](https://tex.z-dn.net/?f=y%20%3D%20-0.75x%20%2B%209.5)
Step-by-step explanation:
Equation of a circle is given as :
![(x-a)^{2} + (y-b)^2 = r^{2} \\(x-6)^{2} + (y-5)^2 = 4^{2}\\x^{2} - 12x + 36 + y^{2} -10y + 25 = 16\\x^{2} - 12x + y^{2} -10y + 45 = 0\\](https://tex.z-dn.net/?f=%28x-a%29%5E%7B2%7D%20%2B%20%28y-b%29%5E2%20%3D%20r%5E%7B2%7D%20%5C%5C%28x-6%29%5E%7B2%7D%20%2B%20%28y-5%29%5E2%20%3D%204%5E%7B2%7D%5C%5Cx%5E%7B2%7D%20-%2012x%20%2B%2036%20%2B%20y%5E%7B2%7D%20-10y%20%2B%2025%20%3D%2016%5C%5Cx%5E%7B2%7D%20-%2012x%20%20%2B%20y%5E%7B2%7D%20-10y%20%2B%2045%20%3D%200%5C%5C)
Take the derivative of the above with respect to x
![2x - 12 + 2y dy/dx - 10 dy/dy = 0\\\frac{dx}{dy} = \frac{6 - x}{y-5} \\At (2,8) dy/dx = (6-2)/(8-5) = 4/3\\dy/dx = 4/3\\The slope of the tangent to the circle, m = \frac{-1}{dy/dx} \\m = \frac{-1}{4/3}\\m= -0.75](https://tex.z-dn.net/?f=2x%20-%2012%20%2B%202y%20dy%2Fdx%20-%2010%20dy%2Fdy%20%3D%200%5C%5C%5Cfrac%7Bdx%7D%7Bdy%7D%20%3D%20%5Cfrac%7B6%20-%20x%7D%7By-5%7D%20%5C%5CAt%20%282%2C8%29%20dy%2Fdx%20%3D%20%286-2%29%2F%288-5%29%20%3D%204%2F3%5C%5Cdy%2Fdx%20%3D%204%2F3%5C%5CThe%20slope%20of%20the%20tangent%20to%20the%20circle%2C%20m%20%3D%20%5Cfrac%7B-1%7D%7Bdy%2Fdx%7D%20%5C%5Cm%20%3D%20%5Cfrac%7B-1%7D%7B4%2F3%7D%5C%5Cm%3D%20-0.75)
The equation of the tangent is given by :
![y - y_{1} = m(x - x_{1})\\ y - 8 = -0.75(x - 2)\\y - 8 = -0.75x + 1.5\\y = -0.75x + 9.5](https://tex.z-dn.net/?f=y%20-%20y_%7B1%7D%20%3D%20m%28x%20-%20x_%7B1%7D%29%5C%5C%20y%20-%208%20%3D%20-0.75%28x%20-%202%29%5C%5Cy%20-%208%20%3D%20-0.75x%20%2B%201.5%5C%5Cy%20%3D%20-0.75x%20%2B%209.5)
Hey there! :D
1. c - 7 = 32
To solve this problem, add the difference and the subtrahend of the given equation.
![32 + 7 = \boxed{\sf 39}](https://tex.z-dn.net/?f=32%20%2B%207%20%3D%20%5Cboxed%7B%5Csf%2039%7D)
Checking:
To check, simply substitute the conclusion on the unknown quantity.
39 (c) - 7 = 32
Thus, the equation was correct which gives us the answer that:
![\large \boxed{ \sf {\: c = 39}}](https://tex.z-dn.net/?f=%5Clarge%20%5Cboxed%7B%20%5Csf%20%7B%5C%3A%20c%20%3D%2039%7D%7D)
![\begin{gathered} \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5C%5C%20%5Cend%7Bgathered%7D)
2. r + 4 = 39
To solve this problem, subtract the sum and the addend of the given equation.
![39 - 4 = \boxed{\sf 35}](https://tex.z-dn.net/?f=39%20-%204%20%3D%20%5Cboxed%7B%5Csf%2035%7D)
Checking:
To check, simply substitute the conclusion on the unknown quantity.
35 (r) + 4 = 39
Thus, the equation was correct which gives us the answer that:
![\large\boxed{ \sf {r \: = \: 35}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%20%5Csf%20%7Br%20%5C%3A%20%3D%20%5C%3A%2035%7D%7D)
Answer:
113.04 cm squared
Step-by-step explanation:
the area of a circle is:
A=πr2
so as you written before the pi must be 3.14
and the radius is the diameter/2(12/2=6)
A= 3.14 x 6 x 6
A= 113.04 cm squared