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°.

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle

Aand b are correctly balanced reactions. they have the same number of atoms in both sides of the reaction