Question

#1. if i have a circle with a radius of 6 in and it is cut into 8 equal slices (like a pie) and the coordinates are (8, 5) then what is the central angle, what is the measure of the arc that 2 pieces together would intercept, and the equation that represents as well as the circumference?

I also need the same answers for these:

#2. radius 10 inches, 14 equal pieces, and points of (3, 7)

#3. radius 25 cm, 16 pieces and 14 and 53

#4. radius 12 inches, 8 pieces and points of (2, 5)

#5. radius 4 inches, 12 equal pieces, and points of (3, 6)

Answer 1

part 1)
coordinates of the center (8,5)
radius=6 in
is cut into 8 equal slices-----> 360°/8-----> 45° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-8)²+(y-5)²=6²

b) circumference=2*pi*r-----> 2*pi*6---> 37.68 in
if 360° (full circle) has a length of---------> 37.68 in
90° (2 pieces together)---------> x
x=90*37.68/360-----> x=9.42 in

the measure of the arc that 2 pieces together would intercept is 9.42 in

c) The central angle of one slice is 45 degrees

Part 2)
coordinates of the center (3,7)
radius=10 in
is cut into 14 equal slices-----> 360°/14-----> 25.71° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-3)²+(y-7)²=10²

b) circumference=2*pi*r-----> 2*pi*10---> 62.8 in
if 360° (full circle) has a length of---------> 62.8 in
51.42° (2 pieces together)---------> x
x=51.42*62.8/360-----> x=8.97 in

the measure of the arc that 2 pieces together would intercept is 8.97 in

c) The central angle of one slice is 25.71 degrees

Part 3)
coordinates of the center (14,53)
radius=25 cm
is cut into 16 equal slices-----> 360°/16-----> 22.5° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-14)²+(y-53)²=25²

b) circumference=2*pi*r-----> 2*pi*25---> 157 cm
if 360° (full circle) has a length of---------> 157 cm
45° (2 pieces together)---------> x
x=45*157/360-----> x=19.63 cm

the measure of the arc that 2 pieces together would intercept is 19.63 cm

c) The central angle of one slice is 22.5 degrees

Part 4)
coordinates of the center (2,5)
radius=12 in
is cut into 8 equal slices-----> 360°/8-----> 45° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-2)²+(y-5)²=12²

b) circumference=2*pi*r-----> 2*pi*12---> 75.36 in
if 360° (full circle) has a length of---------> 75.36 in
90° (2 pieces together)---------> x
x=90*75.36/360-----> x=18.84 in

the measure of the arc that 2 pieces together would intercept is 18.84 in

c) The central angle of one slice is 45 degrees

Part 5)
coordinates of the center (3,6)
radius=4 in
is cut into 12 equal slices-----> 360°/12-----> 30° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-3)²+(y-6)²=4²

b) circumference=2*pi*r-----> 2*pi*4---> 25.12 in
if 360° (full circle) has a length of---------> 25.12 in
60° (2 pieces together)---------> x
x=60*25.12/360-----> x=4.19 in

the measure of the arc that 2 pieces together would intercept is 4.19 in

c) The central angle of one slice is 30 degrees