Question

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 1

Answer:

Part a) $h(g(140))=\frac{4,900}{\pi}\ cm^2$

Part b) $f(j(5.18))=2\pi\sqrt{\frac{5.18}{\pi}}\ cm$

Step-by-step explanation:

we know that

The circumference of a circle is

$C=2\pi r$

Solve for r

$r=\frac{C}{2\pi}$

so

$f(r)=2\pi r$ ---> represents the circumference (in cm) of a circle whose radius is r cm

$g(C)=\frac{C}{2\pi}$ ---> represents the radius (in cm) of a circle whose circumference is C cm

The area of a circle is

$A=\pi r^{2}$

solve for r

$r=\sqrt{\frac{A}{\pi}}$

so

$h(r)=\pi r^{2}$ ---->represents the area (in cm2) of a circle whose radius is r cm

$j(A)=\sqrt{\frac{A}{\pi}}$ ---> 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

$h(g(C))=\pi (\frac{C}{2\pi})^{2}=\frac{C^2}{4\pi}$

substitute the value

C=140 cm

$h(g(140))=\frac{140^2}{4\pi}$

$h(g(140))=\frac{4,900}{\pi}\ cm^2$

Part b. Use function notation to represent the circumference of a circle whose area is 5.18 cm^2.

$f(j(A))=2\pi\sqrt{\frac{A}{\pi}}$

substitute the value

A=5.18 cm^2

$f(j(5.18))=2\pi\sqrt{\frac{5.18}{\pi}}\ cm$

Answer 2

Answer:

A. H(g(140))

B. F(j(5.18)

Step-by-step explanation:

That’s how you write a FUNCTION NOTATION ...