Graphical Reasoning Use the formulas for the area of a circular sector and arc length given in Section 1.1. (a) For θ = 0.8 , write the area and arc length as functions of r . What is the domain of each function? Use a graphing utility to graph the functions. Use the graphs to determine which function changes more rapidly as r increases. Explain. (b) For r = 10 centimeters, write the area and arc length as functions of θ . What is the domain of each function? Use the graphing utility to graph the functions.
Graphical Reasoning Use the formulas for the area of a circular sector and arc length given in Section 1.1. (a) For θ = 0.8 , write the area and arc length as functions of r . What is the domain of each function? Use a graphing utility to graph the functions. Use the graphs to determine which function changes more rapidly as r increases. Explain. (b) For r = 10 centimeters, write the area and arc length as functions of θ . What is the domain of each function? Use the graphing utility to graph the functions.
Solution Summary: The author calculates the area function and the arc length function as r, and determines which function changes more rapidly.
Graphical Reasoning Use the formulas for the area of a circular sector and arc length given in Section
1.1.
(a) For
θ
=
0.8
,
write the area and arc length as functions of
r
. What is the domain of each function? Use a graphing utility to graph the functions. Use the graphs to determine which function changes more rapidly as
r
increases. Explain.
(b) For
r
=
10
centimeters, write the area and arc length as functions of
θ
.
What is the domain of each function? Use the graphing utility to graph the functions.
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
Give an exact expression for y as a function of a, angle B and angle Cif A = 45° and D = 60°.
Simplify your answer, rationalize denominators as needed.
y=
B
A Ferris wheel has a radius of 35 feet. The bottom of the Ferris wheel sits 0.7 feet above the ground. You board the Ferris wheel at the 6 o'clock
position and rotate counter-clockwise.
a. Write a function f that determines your height above the ground (in feet) in terms of the number of radians you have swept out from the 6
o'clock position, a.
f(a) = tan(35)
Preview
b. Write a function g, that determines your height above the ground (in feet) in terms of the number of feet you have traveled since you
started rotating, s.
g(s) :
Preview
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY