a rope of length 18 m is used to form a sector of a circle of radius 3.5 m on a school field. What is the size of the angle of the sector?​

Step-by-step explanation:

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Perimeter of the sector = 2r + length of arc= 2(3.5)+11= 7+11=18 meters exactly the length of the rope.

Step-by-step explanation:

The perimeter of the sector is equivalent to the length of the rope which is 18 meters

Perimeter of the sector= 2 x radius + length of the arc

But length of arc= radius x central angle in radian

18= 2(3.5)+ 3.5(central angle in radians)

18=7+3.5 (central angle in radians)

18–7=3.5(central angle)

11=3.5(central angle)

central angle =11/3.5=3.14 radians or pi radians

Angle in degrees =pi radians x 360 degrees/2pi radians =pi radians x 180 degrees/pi radians = 180 degrees

Therefore the central angle = 180 degrees because pi radians is half of 2pi radians which is half of 360 degrees

Notes: This sector shape is a semicircle because the central angle is 180 degrees

Check: Length of Arc for semicircle =3.5(pi radians)=11 meters

Perimeter of the sector = 2r + length of arc= 2(3.5)+11= 7+11=18 meters exactly the length of the rope.

the solution is x=1

step-by-step explanation:

we are given our   equation as

let's assume

left side function is

right side function is

now, we can draw graph

and then we can get intersection point

the intersection point will be solution

so, the solution is

x=1