Answer:
1)54° 2)5π 3)a=3π 4)b 5)(x – 11)^2+ (y – 6)^2=36 6)center=(7,-6) radius=5 8)b
Explanation:
1- π radians = 180°
so 3π/10=(3*180)/10=54°
2- in order to find arc length we need to find the ratio of the angles then make that equal to the ratio of the arc length to the perimeter:
x=arc length of HN
150/360=x/2πr
5/12=x/2*6π
5/12=x/12π
12*5π=12x
x=5π
3- in order to find the area of the shaded region we have to take the ratio of the angles and make that equal to the ratio of the area of the shaded region to the whole area:
a=area of the shaded region
30/360=a/πr^2
1/12=a/36π
36π=12a
a=3π
4- a slice of a 16 inch pizza has an area of 64π/8=8π
two slices of a 10 inch pizza has an area of 2*(25π/8)= 6.25π
therefore we would be more satisfied with a slice of an 16 inch pizza, which is b.
5- the formula for the equation of a circle is: (x – h)^2+ (y – k)2 = r2
h=x-coordinate of the center point k= y-coordinate of the center r=radius
in this question the center is (11,6) so h=11, k=6 and the radius is 6 so r=6
we plug in
(x – 11)^2+ (y – 6)^2=36
6- h=7 k=-6 so the center is (7,-6)
radius=5
8- center=(1,3) and radius=2
so the graph that corresponds to these values is b