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grigory [225]
2 years ago
10

Find the length of the arc on a circle with a radius of 2.4 kilometers and is intercepted by a central angle measuring 150°. lea

ve your answer in terms of π.
Mathematics
1 answer:
Kaylis [27]2 years ago
4 0

If the radius of the circle exists 2.4 kilometers and is intercepted by a central angle measuring 150° then the length of the arc exists 5π inches.

<h3>What was the relation between the central angle and its intercepted arc?</h3>
  • If the vertex of an angle exists in the center of the circle and the two sides of the angle are radii in the circle, then this angle exists named a central angle.
  • Each central angle exists subtended by the opposite arc, the name of the arc exists the starting point and the finish point of the angle.
  • There exists a relation between the central angle and its subtended arc the measure of the central angle equals half the measure of its subtended arc.
  • The length of the subtended arc relies on the measurement of its central angle and the length of the radius and the measure of the arc.
  • The measurement of the circle exists at 360°.
  • The length of the circle exists at 2πr.

The radius of the circle r = 2.4 kilometers

The measure of the central angle exists at 150°.

The length of the arc = central angle/360 × 2πr

The length of the arc = 150°/360° × 2 × π × 2.4 = 2π

The length of the arc exists 2π kilometers.

To learn more about arc length refer to:

brainly.com/question/11134371

#SPJ4

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\sqrt{136} = 11.66 units

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= \sqrt{((-8)^{2}-(-2)^{2} ) + ((-6)^{2}-4^{2})   }

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3 years ago
B is the midpoint of AC. If Ab= x +5 and BC = 2x-11, find the measure of Ab.
LuckyWell [14K]

__________________________

Measurement of "AC" :

(x + 5) + (2x <span>− 11) ;
________________________

Find the measurement of "AB" [which is: "(x+5)" ]: 
______________________________________________
First, simplify to find the measurement of "AC" :
________________________________________
 </span>(x + 5) + (2x − 11) ;

=  (x + 5) + 1(2x − 11) ;

=   x + 5 + 2x − 11 ;

 → Combine the "like terms" ; 

   x + 2x = 3x ;
   
   5 − 11 = - 6 ;
______________
to get:  3x − 6 ; 
_______________
So,  (x + 5) + (2x − 11) =  3x − 6 ;
_______________________________
Solve for:  "(x + 5)"
_______________________________

We have: 
_______________________________

(x + 5) + (2x − 11) =  3x − 6  ;

Subtract:  "(2x − 11)" ;  from EACH SIDE of the equation ;
                                      to isolate "(x + 5)" on one side of the equation; 
                                      and to solve for "(x + 5)" ;
________________________________________________________
    →  (x + 5) + (2x − 11) − (2x − 11) =  (3x − 6) − (2x − 11) ;
  
         → (x + 5)  = (3x − 6) − (2x − 11) ;
_________________________________________________
  Note:  Simplify:  "(3x − 6) − (2x − 11)" ;

     →  (3x − 6) − (2x − 11)  ;
 
         =  (3x − 6) − 1(2x − 11) ;
 
         =   3x − 6 − 2x + 11 ;
__________________________
   →  Combine the "like terms" :
_____________________________
         +3x − 2x = 1x = x ;
  
          -6 + 11 = 5 ; 
_____________________________
To get:  x + 5 ; 

So we have:
______________________________
 x + 5 = x + 5 ; 
______________________________

So, x = all real numbers.

x = <span>ℝ </span>
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