What is the range of the relation? {(1, 2), (2, 4), (3, 2), (4, 6)}

{1, 2, 3, 4}

{1, 2, 3, 4, 6}

{2, 4}

{2, 4, 6}

a)    x = 6

b)  0.2 radians.

Step-by-step explanation:

I ran out of time and the system logged me out so I'll start again:

a) Find the lengths of the arcs in terms of x and Ф:

arc SP = radius * Ф = 10Ф

arc TS = 10*3Ф = 30Ф

arc PT = 10Ф+30Ф = 40Ф.

arc QR = (10 + x)Ф

QR/PT = 2/5 so:

2/5 =  (10 + x)Ф / 40Ф

Cross multiply:

80Ф = 50Ф + 5xФ

5xФ =  30Ф

x = 6.

b)

The area of a sector = radius^2 * angle in radians.

The shaded area = area of arc QOR - area of arc POS:

31.2 = (10 + x)^2 Ф - 10^2 Ф

x = 6 so:

16^2  Ф - 100 Ф = 31.2

Ф = 31.2 / 156

= 0.2 radians.