Point P=(8,17) and Q=(-2,17) are the endpoints of the diameter of a circle a) what is the equation of the circle
b) what is the length of the arc of the circle between Point P and Point R=(0,13)
c) what is the angle formed by a sector whose area is 25/12pi

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  a) (x -3)^2 +(y -17)^2 = 25

  b) ≈ 11.07

  c) π/6 radians

Step-by-step explanation:

a) The center of the circle is the midpoint of the given segment, so is ...

  A = (P +Q)/2 = ((8, 17) +(-2, 17))/2 = (6, 34)/2 = (3, 17) . . . center

The radius is the difference between center and end coordinates: 8 -3 = 5.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)^2 +(y -k)^2 = r^2

This circle's equation is ...

  (x -3)^2 +(y -17)^2 = 25

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b) The length of the arc is given by ...

  s = rθ

where r is the circle radius and θ is the central angle in radians.

We can find the central angle using a little trigonometry. Point R differs from point A by ...

  R -A = (0, 13) -(3, 17) = (-3, -4)

so is 4 units below and 3 units left of the center of the circle. The sine of this angle QAR is 4/5, so its value is ...

  angle QAR = arcsin(4/5) ≈ 53.13°

Then angle PAR is the supplement of this, so about 126.87°, or 2.2143 radians. Then the arc length is ...

  s = (5)(2.2143 radians)

  s ≈ 11.07

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c) The area of a sector is given by ...

  A = (1/2)r^2·θ

Then the angle is ...

  θ = (2A)/r^2

For the given values and r=5, we have ...

  θ = 2(25/12π)/25

  θ = π/6

The sector with that area will have a central angle of π/6 radians, or 30°.

(0,,,0)

step-by-step explanation:

the table of x and y values is shown in the attached pic(part of question)

we have to decide according that graph

given points are (0, 0) (–1, 0), (2, 0)

when we graph these points on graph they show an increasing line as shown in the attached pic

a long term investor

step-by-step explanation:

because he is a long term investor