|
Question 1122924: 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 cm2.
a. Use function notation to represent the area of a circle whose circumference is 109 cm.
b. Use function notation to represent the circumference of a circle whose area is 6.75 cm2.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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 cm2.
a. Use function notation to represent the area of a circle whose circumference is 109 cm.
the formula for the area of a circle is A = pi * r^2
you are given that g(c) represents the radius of a circle whose circumference is c.
therefore, replace r with g(c) and the formula becomes:
A = pi * g(c)^2
when the circumference is 109 cm, the formula becomes:
A = pi * g(109)^2
b. Use function notation to represent the circumference of a circle whose area is 6.75 square cm.
the formula for the circumference of a circle is C = 2 * pi * r.
you are given that j(a) represents the radius of a circle whose area is a square centimeters.
therefore, replace r with j(a) to get:
C = 2 * pi * j(a)
when a is 6.75 square centimeters, the formula becomes:
C = 2 * pi * j(6.75)
here's a reference on functional notation you might find useful.
https://mathbitsnotebook.com/Algebra1/Functions/FNNotationEvaluation.html
|
|
|
| |
