MATH SOLVE

5 months ago

Q:
# #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

c) The central angle of one slice is 30 degrees

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