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# pls help

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If the degree measure of an arc of a circle is increased by 20% and the radius of the circle is increased by 25% , by what percent does the length of the arc increase?

Mar 3, 2021

#1
+485
+1

lets say the length radius is r, and the degree measure is d. we know that the length of the arc is 2$\pi$r$\cdot$d/360=d$\pi$r/180, so increasing the degree measure of the arc makes 2$\pi$r$\cdot$(6d/5)/360, and increasing the radius by 25%, we get 5$\pi$r/2$\cdot$(6d/5)/360 and we get:

$\frac{5\pi r \cdot \frac{6d}5}{720}=\frac{d\pi r}{120}$

$\frac{\frac{d\pi r}{180}}{\frac{d\pi r}{120}}=\frac32$

$\frac{3}{2} - 1=\frac{1}{2}=\boxed{50\%}$

Mar 3, 2021
#2
+118069
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Call  the original  arc length, S

Call the orignal arc measure , T

So

S =  RT

And  when the arc measure  increases by 20%  and the  radius increases by 25%  we have

(1.20)R * ( 1.25) T  =

1.5  RT

So .....  the  arc length  increases  by   (1.5 -  1) * 100%  =  .5 * 100%  =   50%

Mar 3, 2021
#3
+31281
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Original arc length would be    x / 360   pi  2r

now multiply  x by 1.2   and   r by 1.25

1.2x / 360   pi  2 r * 1.25   =      1/2 * 1.25  x/360 pi 2r

= 1.5  *  original                        so 50% longer

Mar 3, 2021
#4
+118069
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By unanimous consent......50%  it is    !!!!!

Mar 3, 2021