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JayDelV

  • one year ago

What is the arc length of a circle that has a 7-centimeter radius and a central angle that is 40 degrees? Use 3.14 for π and round your answer to the nearest hundredth.

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  1. arindameducationusc
    • one year ago
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    theta=L/R

  2. UsukiDoll
    • one year ago
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    hmmm my textbook is like this though for arc length \[s = \theta r \]

  3. arindameducationusc
    • one year ago
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    where L = arc legth and r radius... Now I hope you can solve it.... if not, ask me

  4. UsukiDoll
    • one year ago
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    s - arc length theta - the angle r - radius

  5. UsukiDoll
    • one year ago
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    I think we need to convert 40 degrees to radians \[40 \times \frac{\pi}{180} \rightarrow \frac{40 \pi}{180}\]

  6. UsukiDoll
    • one year ago
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    simplify that fraction first ^_^

  7. arindameducationusc
    • one year ago
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    Awesome @UsukiDoll Good job.. @JayDelV just follow @UsukiDoll

  8. UsukiDoll
    • one year ago
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    or we can reduce later.... \[s = \theta r \rightarrow s = \frac{40 \pi}{180} \times 7\]

  9. JayDelV
    • one year ago
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    I'm actually confused, sorry was eating.

  10. UsukiDoll
    • one year ago
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    you're looking for the arc length of a circle The arc length of a circle formula is \[s = \theta r \] where s - arc length theta - the angle r - radius we are given the angle which is 40 degrees, but it looks like we have to convert to radians so multiply 40 by \[\frac{\pi}{180} \] \[\frac{40 \pi}{180}\] this fraction is reducible. afterwards, multiply by 7 and you have your s which is the arc length

  11. UsukiDoll
    • one year ago
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    you were given an angle in degree mode. We can't use degree mode for this formula, so conversion to radians is necessary

  12. UsukiDoll
    • one year ago
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    it's best to reduce that fraction first.. otherwise you will be stuck with an even bigger fraction to reduce.

  13. UsukiDoll
    • one year ago
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    \[s = \theta r \rightarrow s =\frac{40 \pi}{180} \times 7 \rightarrow s = \frac{280 \pi}{180}\] now that's a monster fraction to be reduced.

  14. UsukiDoll
    • one year ago
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    what is 280 divided by 10 what is 180 divided by 10

  15. JayDelV
    • one year ago
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    28 and 18

  16. UsukiDoll
    • one year ago
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    ok.. we still need to reduce further \[s= \frac{28 \pi}{18}\] but this time by 2 what is 28 divided by 2 what is 18 divided by 2

  17. JayDelV
    • one year ago
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    14 and 9

  18. UsukiDoll
    • one year ago
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    yes so we have \[s= \frac{14 \pi}{9}\] we can't reduce anymore, so we got our arc length ;)

  19. JayDelV
    • one year ago
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    Thank you so much for your time I really appreciate it!

  20. JayDelV
    • one year ago
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    Oh wait, the answers are in decimals.

  21. UsukiDoll
    • one year ago
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    ah no problem we can convert to decimals XD

  22. UsukiDoll
    • one year ago
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    \[s= \frac{14 \pi}{9} \rightarrow s =\frac{14(3.14)}{9} \rightarrow s =\frac{43.96}{9}\] \[s=4.8844444444444444444444\] the 4 after the second 8 is repeating, so it's considered a repeating decimal.

  23. JayDelV
    • one year ago
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    Thank you !

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