Suppose f, g, h, and j are functions such that: f(r) represents the circumference (in cm) of a circle whose radius is r cm. g(C) represents the radius (in cm) of a circle whose circumference is C cm . h(r) represents the area (in cm2) of a circle whose radius is r cm. j(A) represents the radius (in cm) of a circle whose area is A cm^2. a. Use function notation to represent the area of a circle whose circumference is 140 cm. b. Use function notation to represent the circumference of a circle whose area is 5.18 cm^2.

Answer:Part a) [tex]h(g(140))=\frac{4,900}{\pi}\ cm^2[/tex]Part b) [tex]f(j(5.18))=2\pi\sqrt{\frac{5.18}{\pi}}\ cm[/tex]Step-by-step explanation:we know thatThe circumference of a circle is [tex]C=2\pi r[/tex]Solve for r[tex]r=\frac{C}{2\pi}[/tex]so[tex]f(r)=2\pi r[/tex] ---> represents the circumference (in cm) of a circle whose radius is r cm[tex]g(C)=\frac{C}{2\pi}[/tex] ---> represents the radius (in cm) of a circle whose circumference is C cm The area of a circle is [tex]A=\pi r^{2}[/tex]solve for r[tex]r=\sqrt{\frac{A}{\pi}}[/tex]so[tex]h(r)=\pi r^{2}[/tex] ---->represents the area (in cm2) of a circle whose radius is r cm [tex]j(A)=\sqrt{\frac{A}{\pi}}[/tex] ---> represents the radius (in cm) of a circle whose area is A cm^2.Part a. Use function notation to represent the area of a circle whose circumference is 140 cm[tex]h(g(C))=\pi (\frac{C}{2\pi})^{2}=\frac{C^2}{4\pi}[/tex]substitute the valueC=140 cm[tex]h(g(140))=\frac{140^2}{4\pi}[/tex][tex]h(g(140))=\frac{4,900}{\pi}\ cm^2[/tex]Part b. Use function notation to represent the circumference of a circle whose area is 5.18 cm^2.[tex]f(j(A))=2\pi\sqrt{\frac{A}{\pi}}[/tex]substitute the valueA=5.18 cm^2[tex]f(j(5.18))=2\pi\sqrt{\frac{5.18}{\pi}}\ cm[/tex]