/*! 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 74 Write the standard form of the e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 74

Write the standard form of the equation of the circle with the given characteristics. Center: (3,-2)\(;\) Solution point: (-1,1)

Short Answer

Expert verified
The standard form of the equation of the circle with center at (3,-2) and a point at (-1,1) is \((x-3)^2 + (y+2)^2 = 25\).

Step by step solution

01

Calculate the radius of the circle

To calculate the radius \(r\), we can use the distance formula with the coordinates of the center of the circle (h,k) as \((x_1 , y_1)\) and the given point on the circle (-1,1) as \((x_2, y_2)\). Therefore, the radius will be \(r =\sqrt{((-1 - 3)^2 + (1 + 2)^2)}\). Simplifying this, we get \(r = \sqrt{(-4)^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5\).
02

Write the equation of the circle in standard form

After calculating the radius as 5, we can substitute this radius and the center of the circle \((h,k) = (3,-2)\) into the standard form of the circle's equation \((x-h)^2 + (y-k)^2 = r^2\). This will give us our final equation for the circle as \((x-3)^2 + (y+2)^2 = 5^2\).

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

Determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=\sqrt{x-2} $$

Use the given value of \(k\) to complete the table for the direct variation model $$y=k x^{2}$$ Plot the points on a rectangular coordinate system. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=k x^{2} & & & & & \\ \hline \end{array}$$ $$ k=2 $$

The lengths (in feet) of the winning men's discus throws in the Olympics from 1920 through 2008 are listed below. (Source: International Olympic Committee) $$\begin{array}{llllll} 1920 & 146.6 & 1956 & 184.9 & 1984 & 218.5 \\ 1924 & 151.3 & 1960 & 194.2 & 1988 & 225.8 \\ 1928 & 155.3 & 1964 & 200.1 & 1992 & 213.7 \\ 1932 & 162.3 & 1968 & 212.5 & 1996 & 227.7 \\ 1936 & 165.6 & 1972 & 211.3 & 2000 & 227.3 \\ 1948 & 173.2 & 1976 & 221.5 & 2004 & 229.3 \\ 1952 & 180.5 & 1980 & 218.7 & 2008 & 225.8 \end{array}$$ (a) Sketch a scatter plot of the data. Let \(y\) represent the length of the winning discus throw (in feet) and let \(t=20\) represent 1920 (b) Use a straightedge to sketch the best-fitting line through the points and find an equation of the line. (c) Use the regression feature of a graphing utility to find the least squares regression line that fits the data. (d) Compare the linear model you found in part (b) with the linear model given by the graphing utility in part (c). (e) Use the models from parts (b) and (c) to estimate the winning men's discus throw in the year 2012 .

The total numbers of people (in thousands) in the U.S. civilian labor force from 1992 through 2007 are given by the following ordered pairs. $$\begin{array}{ll} (1992,128,105) & (2000,142,583) \\ (1993,129,200) & (2001,143,734) \\ (1994,131,056) & (2002,144,863) \\ (1995,132,304) & (2003,146,510) \\ (1996,133,943) & (2004,147,401) \\ (1997,136,297) & (2005,149,320) \\ (1998,137,673) & (2006,151,428) \\ (1999,139,368) & (2007,153,124) \end{array}$$ A linear model that approximates the data is \(y=1695.9 t+124,320,\) where \(y\) represents the number of employees (in thousands) and \(t=2\) represents 1992 . Plot the actual data and the model on the same set of coordinate axes. How closely does the model represent the data? (Source: U.S. Bureau of Labor Statistics)

Determine if the situation could be represented by a one-to-one function. If so, write a statement that describes the inverse function. The population \(p\) of South Carolina in terms of the year \(t\) from 1960 through 2008
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

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.