Find the radius of a circle in which a central angle of startfraction pi over 7 endfraction radian determines a sector of area 77 square meters. round to the nearest hundredth.

Step-by-step explanation:

The formula for determining the the area of a sector is expressed as

Area of Sector = θ/360 × πr²

Where

θ represents the central angle.

π is a constant whose value is 3.14

r represents the radius of the circle.

From the information given,

The central angle is π/7 radian. Converting to degrees, it becomes

π/7 × 180/π = 180/7 = 25.714 degrees.

Area of sector = 77 square meters

Therefore

77 = 25.714/360 × 3.14 × r²

77 = 0.2243r²

r² = 77/0.2243 = 343.29

r = √343.29 = 18.53 meters

x > 10/7 or x > 1 3/7

Step-by-step explanation:

First simplify the left side of the inequality.

6x+ 1/4 (4x+8)> 12

6x+x+2>12

7x+2>12  Next, using the property of inequality, subtract two from both sides.

7x>10 Now divide by 7 to solve for x.

x>10/7 or x> 1 3/7