#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)
Accepted Solution
A:
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