/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 41 Give the center and radius of th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 41

Give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$x^{2}+y^{2}=16$$

Short Answer

Expert verified
The center of the given circle is at the origin (0,0). The radius of the circle is 4 units. The domain and range of the given circle are both from -4 to 4.

Step by step solution

01

Find the Center

Three is no constant term subtracted from x or y in the equation, so the center of the circle is at the origin point (0,0).
02

Determine the Radius

The equation of the circle is in the form \(x^{2}+y^{2}=r^{2}\), where r is the radius of the circle. Therefore, the radius r = \(\sqrt{16}\) = 4 units.
03

Graph the Circle

The graph of the circle can be drawn with radius 4 units and the center at origin. The circle touches the coordinates (4,0), (0,4), (-4,0) and (0,-4).
04

Identify Domain and Range

Once we have the graph, we can identify the domain and range. The domain (set of x-values) and range (set of y-values) of a circle's equation are defined by the radius. Therefore, the domain and range of this circle are from -4 to 4.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Begin by graphing the standard cubic function, \(f(x)-x^{3} .\) Then use transformations of this graph to graph the given function. $$ h(x)-\frac{1}{2} x^{3} $$

If you are given a function's equation, how do you determine if the function is even, odd, or neither?

Show that $$ f(x)=\frac{3 x-2}{5 x-3} $$ is its own inverse.

Begin by graphing the standard cubic function, \(f(x)-x^{3} .\) Then use transformations of this graph to graph the given function. $$ g(x)-(x-3)^{3} $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I noticed that the difference quotient is always zero if \(f(x)=c,\) where \(c\) is any constant.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.