Write an equation for a circle centered at (2,0) and tangent to y=x+2

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  (a)  (x -2)² +y² = 8

Step-by-step explanation:

The distance between the center and the point of tangency at (0, 2) is ...

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((0 -2)² +(2 -0)²) = √8

This is the radius of the circle. The circle centered at (h, k) with radius r has equation ...

  (x -h)² +(y -k)² = r²

For the given values (h, k) = (2, 0) and r = √8, the equation of the circle is ...

  (x -2)² +y² = 8

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Additional comment

The tangent line has a slope of 1. The radius to the point of tangency will be perpendicular, so will have a slope of -1. The point of tangency will be where the lines y=x+2 and y=-(x-2) meet, at the point (0, 2).

Above, we found the radius using the distance formula. You can also find it using the "distance to a line" formula:

  d = |ax +by +c|/√(a²+b²)

where d is the distance from (x, y) to line ax+by+c = 0. Our given line is x-y+2=0, so the distance from point (2, 0) to the tangent line is ...

  d = |1(2)-1(0)+2|/√(1²+(-1)²) = 4/√2 = √8

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation:

if i'm not wrong, i would say that the third angle has (72) because the three sides of all triangles have 180 degrees and if we subtract 180 - 62 - 40 = (72) / but i'm not sure about 40 yd.