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Elodia [21]
3 years ago
10

Suppose that circles R and S have a central angle measuring 125°. Additionally, circle R has a radius of 2 3 feet and the radius

of circle S is 3 4 feet. If the length of the intercepted arc for circle R is 4 9 π feet, what is the length of the intercepted arc for circle S?
Mathematics
1 answer:
nikklg [1K]3 years ago
5 0
Let 
rR--------> radius of the circle R
rS-------> radius of the circle S
LR------> the length of the intercepted arc for circle R
LS------> the length of the intercepted arc for circle S

we have that
rR=2/3 ft
rS=3/4 ft
rR/rS=8/9--------> rS/rR=9/8
LR=(4/9)π ft

we know that
if Both circle R and circle S have a central angle , the ratio of the radius of circle R to the radius of circle S is equals to the ratio of the length of circle R to the length of circle S

rR/rS=LR/LS--------> LS=LR*rS/rR-----> [(4/9)π*9/8]----> (1/2)π ft

the answer is
the length of the intercepted arc for circle S is  (1/2)π ft
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The amount of fabric needed for Jimmy's costume is not stated, we can only determine the amount needed for Rob's costume, which makes it impossible to compare the amounts needed for both of their costumes. If this omission was an error, then you can find the difference between these amounts if the amount needed for Jimmy's costume is stated explicitly.

Step-by-step explanation:

The number of yards of fabric needed for Robs costume is (7/8+1/2+1 3/4)÷2

Assuming 1 3/4 is a mixed fraction.

= (7/8 + 1/2 + 7/4) ÷ 2

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Suppose 2 yards of fabric is needed for Jimmy's costume, then comparing with Rob's yards, we see that Jimmy's costume requires (2 - 13/16 = 19/16) more yards than Rob's costume.

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Step-by-step explanation:

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