The concentric circles [tex](x-3)^2+(y-5)^2=64[/tex] and [tex](x-3)^2+(y-5)^2=25[/tex] form a ring. The lines [tex]y=\frac{2}{3} x+3[/tex] and [tex]y=5[/tex] intersect the ring, making four sections. Find the area of each section. Round your answers to the nearest tenth of a square unit.

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Hi,

Please check the attached picture of the explanation...

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Answer:

11.5 square unit, 11.5 square wnit
49.8 squave unit, 49.8 square unit

Step-by-step explanation:

[tex]When\ x=3,y=\frac{2}{3}\times3+3=5.[/tex]

[tex]\tan{\theta}=\frac{2}{3}\Rightarrow{\theta}=33.69\ degrees[/tex]

[tex]A_1=\pi(R^2-r^2)\bullet\frac{33.69\ degrees}{360\ degrees}\\ =\pi(64-25)\bullet\frac{33.69\ degrees}{360\ degrees}\\ =11.5[/tex]

[tex]A_2=\pi(R^2-r^2)\bullet\frac{180\ degrees-33.69\ degrees}{360\ degrees}\\ =\pi(64-25)\bullet\frac{146.31\ degrees}{360\ degrees}=49.8[/tex]

[tex]A_3=A_1=11.5\\ A_4=A_2=49.8[/tex]

                  [tex]elementany\ calculation[/tex]

I hope this helps you

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