Below are circles , , and . A central angle of is shown in each.
Answer the following.
When applicable, give the exact answer in terms of in simplest form.
(a) For each circle, find the length of the arc that is intercepted by the central angle.
Length of :

Length of :
Length of :
(b) For each circle, find the ratio of the arc length to the radius.
Length of
Radius of circle
Length of
Radius of circle
Length of
Radius of circle
(c) The ratios suggest which of the following?

The ratios increase by one unit as the lengths of the intercepted arcs increase by units.

The length of the arc intercepted by a central angle is proportional to the radius.

The length of the arc intercepted by a central angle is units more than the radius.

The ratios increase by units as the radii increase by one unit.

None of these.

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step-by-step explanation:

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step-by-step explanation:

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week