Circle O shown below has a radius of 29 inches. To the nearest tenth of an inch, determine the length of the arc, xx, subtended by an angle of 106^{\circ}106 ∘ .

The length of the arc, xx subtended by an angle of 106° and has a radius of 29 inches is; 53.67 inches

The length of an arc is a fraction of the circumference of the circle which the arc is a part of.

In essence, the length of an arc is give mathematically as;

Length of an arc,

where, r = radius

and the symbol, infinity = angle subtended by the arc = 106°

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1537/90 * pi

Step-by-step explanation:

Even without seeing the circle you can answer.

If you know what the central angle of an arc is you can figure out what portion of the circumference it is.

A super quick, easy example.  Say the circumference of a circle is 5 inches.  if you have a semicircle it is literally half of a circle, or 180 degrees of the 360 degrees.  Since it is half that means the arc of this semicircle is half of the total circumference.  so there are two parts, what portion is the arc, and then what is the total circumference to take that portion of.

the arc is 106 degrees.  what portion of 360 is this?  well, 180/360=1/2 that gets us that 180 is half of 360.  so just do the same 106/360 = 53/180 or in decimal form is .2944 so 29.44%  Almost 30%  Since the decimal form is repeating though I am going to use the simplified fraction form 53/180.  so in other words this says 106 is fifty three one hundred eighths of 360.

Now, we want the length of the arc, which is basically the circumference of it.  To do this find the whole circumference and multiply it by the fraction.  Again, say the circumference was 5 inches, cutting it in half makes it 2.5 inches.  So let's find the circumference.  circumference is 2*pi*r.  the question tells us the radius is 29, so let's just plug in.

2 * pi * r

2 * pi * 29

2 * 29 * pi

58*pi

So now we multiply by the fraction we found.

58*pi * 53/180 = 1537/90 * pi

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional