Someone explain to me how to do this question? ?

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.

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1