MATH SOLVE

2 months ago

Q:
# Please someone explain to me how to do this question??

Accepted Solution

A:

Answer:a) x = 6b) 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 = 10Фarc TS = 10*3Ф = 30Фarc PT = 10Ф+30Ф = 40Ф.arc QR = (10 + x)ФQR/PT = 2/5 so:2/5 = (10 + x)Ф / 40ФCross multiply:80Ф = 50Ф + 5xФ5xФ = 30Фx = 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 Фx = 6 so:16^2 Ф - 100 Ф = 31.2 Ф = 31.2 / 156= 0.2 radians.