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°.

the answer is thin because within context, the stanza concludes the and frail tone the people have toward each other, and the fact that it would be thin, makes the most sense compared to "pliable" or "not hard or firm to the touch". hope this , good luck.

step-by-step explanation:

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the diameter is 16 cm. are you a teacher?

step-by-step explanation: