Precalculus
Precalculus
9th Edition
ISBN: 9780321716835
Author: Michael Sullivan
Publisher: Addison Wesley
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Question
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Chapter 2.4, Problem 49AYU

(a)

To determine

To find: the charge for using 50 therms in a month.

(a)

Expert Solution
Check Mark

Answer to Problem 49AYU

The charge for using therms in one month is $52.

Explanation of Solution

Given information:

Monthly service charge $15.95.

Per therm service charge

1st 50 therms     $0.33606/therm

Over 50 therms      $0.10580/therm

Gas charge      $0.3940/therm

Calculation:

For using 50 therms in a month, the rate of service charge $0.33606/therm applied.

In addition monthly service charge $15.95 and gas charge $0.3940/therm also applied.

Monthly service charge = $15.95

Gas charge

  50×$0.3940=$19.7000

Therm service charge

  50×$0.33606=$16.80300

Total charge

  $15.95+$19.7000+$16.80300=$52.45300

Therefore, the charge for using therms in one month is $52.45300.

(b)

To determine

To find: the charge for using 500 therms in a month.

(b)

Expert Solution
Check Mark

Answer to Problem 49AYU

The charge for using therms in one month is $277.363.

Explanation of Solution

Given information:

Monthly service charge $15.95.

Per therm service charge

1st 50 therms     $0.33606/therm

Over 50 therms      $0.10580/therm

Gas charge      $0.3940/therm

Calculation:

For using 500 therms in a month, the rate of service charge $0.33606/therm applied for initial 50 therms and the rate of the service charge $0.10580/therm applied for 450 therms in exceed of 50 therms.

In addition monthly service charge $15.95 and gas charge $0.3940/therm also applied.

Monthly service charge = $15.95

Gas charge

  500×$0.3940=$197.000

Therm service charge

  50×$0.33606+450×$0.10580=$16.80300+$47.61=$64.413

Total charge

  $15.95+$197.000+$64.413=$277.363

Therefore, the charge for using therms in one month is $277.363.

(c)

To determine

To develop: a model that relates the monthly charge C for x therms of gas.

(c)

Expert Solution
Check Mark

Answer to Problem 49AYU

  C(x)={$(15.95+0.73006x)     if  0≤x≤50$(27.463+0.4998x)     if  x>50

Explanation of Solution

Given information:

Monthly service charge $15.95.

Per therm service charge

1st 50 therms     $0.33606/therm

Over 50 therms      $0.10580/therm

Gas charge      $0.3940/therm

Calculation:

For using x therms in a month, the rate of service charge $0.33606/therm applied for initial 50 therms and the rate of the service charge $0.10580/therm applied for remaining therms in exceed of 50 therms.

In addition monthly service charge $15.95 and gas charge $0.3940/therm also applied.

Monthly service charge = $15.95

Gas charge

  $0.3940

Therm service charge

  {$0.33606x                  if  0≤x≤5050×$0.33606+$0.10580(x−50)  if x>50

When 0≤x≤50 :

Total charge

  C(x)=$15.95+$0.3940x+$0.33606=$(15.95+0.73006x)

When x>50 :

Total charge

  C(x)=$15.95+$0.3940x+50×$0.33606+$0.10580(x−50)=$(27.463+0.4998x)

Therefore, the change in one month for using x therms is

  C(x)={$(15.95+0.73006x)     if  0≤x≤50$(27.463+0.4998x)     if  x>50

(d)

To determine

To sketch: the graph of the function which is found in part (c).

(d)

Expert Solution
Check Mark

Explanation of Solution

Given information:

Monthly service charge $15.95.

Per therm service charge

1st 50 therms     $0.33606/therm

Over 50 therms      $0.10580/therm

Gas charge      $0.3940/therm

Calculation:

The graph of the function C(x) is shown below:

  Precalculus, Chapter 2.4, Problem 49AYU

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Chapter 2 Solutions

Precalculus

Ch. 2.1 - The inequality 1x3 can be written in interval...Ch. 2.1 - If x=2 , the value of the expression 3 x 2 5x+ 1 x...Ch. 2.1 - The domain of the variable in the expression x3...Ch. 2.1 - Solve the inequality: 32x5 . Graph the solution...Ch. 2.1 - Prob. 5AYUCh. 2.1 - Prob. 6AYUCh. 2.1 - Prob. 7AYUCh. 2.1 - Prob. 8AYUCh. 2.1 - Prob. 9AYUCh. 2.1 - Prob. 10AYU
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True or False Even functions have graphs that...Ch. 2.3 - In Problems 13-24, use the graph of the function f...Ch. 2.3 - In Problems 13-24, use the graph of the function f...Ch. 2.3 - In Problems 13-24, use the graph of the function f...Ch. 2.3 - In Problems 13-24, use the graph of the function f...Ch. 2.3 - In Problems 13-24, use the graph of the function f...Ch. 2.3 - In Problems 13-24, use the graph of the function f...Ch. 2.3 - In Problems 13-24, use the graph of the function f...Ch. 2.3 - In Problems 13-24, use the graph of the function f...Ch. 2.3 - In Problems 13-24, use the graph of the function f...Ch. 2.3 - In Problems 13-24, use the graph of the function f...Ch. 2.3 - In Problems 25-32, the graph of a function is...Ch. 2.3 - In Problems 25-32, the graph of a function is...Ch. 2.3 - In Problems 25-32, the graph of a function is...Ch. 2.3 - In Problems 25-32, the graph of a function is...Ch. 2.3 - In Problems 25-32, the graph of a function is...Ch. 2.3 - In Problems 25-32, the graph of a function is...Ch. 2.3 - In Problems 25-32, the graph of a function is...Ch. 2.3 - In Problems 25-32, the graph of a function is...Ch. 2.3 - In Problems 33-36, the graph of a function f is...Ch. 2.3 - In Problems 33-36, the graph of a function f is...Ch. 2.3 - In Problems 33-36, the graph of a function f is...Ch. 2.3 - In Problems 33-36, the graph of a function f is...Ch. 2.3 - In Problems 37-48, determine algebraically whether...Ch. 2.3 - In Problems 37-48, determine algebraically whether...Ch. 2.3 - In Problems 3748, determine algebraically whether...Ch. 2.3 - In Problems 37-48, determine algebraically whether...Ch. 2.3 - In Problems 3748, determine algebraically whether...Ch. 2.3 - In Problems 37-48, determine algebraically whether...Ch. 2.3 - In Problems 37-48, determine algebraically whether...Ch. 2.3 - In Problems 37-48, determine algebraically whether...Ch. 2.3 - In Problems 3748, determine algebraically whether...Ch. 2.3 - In Problems 37-48, determine algebraically whether...Ch. 2.3 - In Problems 37-48, determine algebraically whether...Ch. 2.3 - In Problems 37-48, determine algebraically whether...Ch. 2.3 - In Problem 49-56, for each graph of a function...Ch. 2.3 - In Problem 49-56, for each graph of a function...Ch. 2.3 - In Problem 49-56, for each graph of a function...Ch. 2.3 - In Problem 49-56, for each graph of a function...Ch. 2.3 - In Problem 49-56, for each graph of a function...Ch. 2.3 - In Problems 49-56, for each graph of a function...Ch. 2.3 - In Problems 49-56, for each graph of a function...Ch. 2.3 - In Problems 49-56, for each graph of a function...Ch. 2.3 - In Problems 57-64, use a graphing utility to graph...Ch. 2.3 - In Problems 57-64, use a graphing utility to graph...Ch. 2.3 - In Problems 57-64, use a graphing utility to graph...Ch. 2.3 - In Problems 57-64, use a graphing utility to graph...Ch. 2.3 - In Problems 57-64, use a graphing utility to graph...Ch. 2.3 - In Problems 57-64, use a graphing utility to graph...Ch. 2.3 - In Problems 57-64, use a graphing utility to graph...Ch. 2.3 - In Problems 57-64, use a graphing utility to graph...Ch. 2.3 - Prob. 61AYUCh. 2.3 - Prob. 62AYUCh. 2.3 - Prob. 63AYUCh. 2.3 - Prob. 64AYUCh. 2.3 - Prob. 65AYUCh. 2.3 - Prob. 66AYUCh. 2.3 - Prob. 67AYUCh. 2.3 - Prob. 68AYUCh. 2.3 - Prob. 69AYUCh. 2.3 - Prob. 70AYUCh. 2.3 - Prob. 71AYUCh. 2.3 - Prob. 72AYUCh. 2.3 - Prob. 73AYUCh. 2.3 - Prob. 74AYUCh. 2.3 - Prob. 75AYUCh. 2.3 - 80. 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Prob. 38AYUCh. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems graph each function using the...Ch. 2.5 - In Problems 3760, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - In Problems 39-62, graph each function using the...Ch. 2.5 - Prob. 61AYUCh. 2.5 - Prob. 62AYUCh. 2.5 - In Problems 63-66, the graph of a function f is...Ch. 2.5 - In Problems 63-66, the graph of a function f is...Ch. 2.5 - In Problems 63-66, the graph of a function f is...Ch. 2.5 - In Problems 63-66, the graph of a function f is...Ch. 2.5 - In Problems 69-76, complete the square of each...Ch. 2.5 - In Problems 69-76, complete the square of each...Ch. 2.5 - In Problems 69-76, complete the square of each...Ch. 2.5 - In Problems 69-76, complete the square of each...Ch. 2.5 - In Problems 69-76, complete the square of each...Ch. 2.5 - In Problems 69-76, complete the square of each...Ch. 2.5 - In Problems 69-76, complete the square of each...Ch. 2.5 - In Problems 69-76, complete the square of each...Ch. 2.5 - Prob. 75AYUCh. 2.5 - Prob. 76AYUCh. 2.5 - Prob. 77AYUCh. 2.5 - Prob. 78AYUCh. 2.5 - Prob. 79AYUCh. 2.5 - Prob. 80AYUCh. 2.5 - Prob. 81AYUCh. 2.5 - Prob. 82AYUCh. 2.5 - Prob. 83AYUCh. 2.5 - Prob. 84AYUCh. 2.5 - Prob. 85AYUCh. 2.5 - Prob. 86AYUCh. 2.5 - Prob. 87AYUCh. 2.5 - Prob. 88AYUCh. 2.5 - Prob. 89AYUCh. 2.5 - Prob. 90AYUCh. 2.5 - Prob. 91AYUCh. 2.5 - Prob. 92AYUCh. 2.5 - Prob. 93AYUCh. 2.5 - Prob. 94AYUCh. 2.6 - 1. P=( x,y ) be a point on the graph of y= x 2 8 ....Ch. 2.6 - 2. P=( x,y ) be a point on the graph of y= x 2 8 ....Ch. 2.6 - 3. P=( x,y ) be a point on the graph of y= x . (a)...Ch. 2.6 - 4. P=( x,y ) be a point on the graph of y= 1 x ....Ch. 2.6 - 5. A right triangle has one vertex on the graph of...Ch. 2.6 - 6. A right triangle has one vertex on the graph of...Ch. 2.6 - 7. A rectangle has one corner in quadrant I on the...Ch. 2.6 - 8. A rectangle is inscribed in a semicircle of...Ch. 2.6 - 9. A rectangle is inscribed in a semicircle of...Ch. 2.6 - 10. A circle of radius r is inscribed in a square....Ch. 2.6 - 11. Geometry A wire 10 meters long is to be cut...Ch. 2.6 - Prob. 12AYUCh. 2.6 - 13. Geometry A wire of length x is bent into the...Ch. 2.6 - Prob. 14AYUCh. 2.6 - 15. Geometry A semicircle of radius r is inscribed...Ch. 2.6 - 16. Geometry An equilateral triangle is inscribed...Ch. 2.6 - 17. Geometry An equilateral triangle is inscribed...Ch. 2.6 - 18. Uniform Motion Two cars leave an intersection...Ch. 2.6 - 19. Uniform Motion Two cars are approaching an...Ch. 2.6 - 20. Inscribing a Cylinder in a Sphere Inscribe a...Ch. 2.6 - 21. Inscribing a Cylinder in a Cone Inscribe a...Ch. 2.6 - 22. Installing Cable TV MetroMedia Cable is asked...Ch. 2.6 - 23. Time Required to Go from an Island to a Town...Ch. 2.6 - Prob. 24AYUCh. 2.6 - Prob. 25AYUCh. 2.6 - Prob. 26AYUCh. 2 - Prob. 1RECh. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Prob. 31RECh. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - Prob. 35RECh. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - Prob. 40RECh. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Prob. 49RECh. 2 - Prob. 50RECh. 2 - Prob. 51RECh. 2 - Prob. 52RECh. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Prob. 55RECh. 2 - Prob. 56RECh. 2 - Prob. 57RECh. 2 - Prob. 58RECh. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 63RECh. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - Prob. 68RECh. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Prob. 73RECh. 2 - Prob. 74RECh. 2 - 1. Find the domain and range of each relation....Ch. 2 - In Problems find the domain of each function and...Ch. 2 - In Problems 24, find the domain of each function...Ch. 2 - In Problems 24, find the domain of each function...Ch. 2 - Consider the graph of the function f below. Find...Ch. 2 - 6. Graph the function on the interval using a...Ch. 2 - Consider the function g(x)={2x+1ifx1x4ifx1 Graph...Ch. 2 - For the function f(x)=3x23x+4, Find the average...Ch. 2 - For the functions f(x)=2x2+1 and g(x)=3x2, find...Ch. 2 - Graph each function using the techniques of...Ch. 2 - Find the difference quotient of f(x)=x23x.Ch. 2 - 12. A community skating rink is in the shape of a...Ch. 2 - In Problems 1-6, find the real solutions of each...Ch. 2 - In Problems 1-6, find the real solutions of each...Ch. 2 - In Problems 1-6, find the real solutions of each...Ch. 2 - In Problems 1-6, find the real solutions of each...Ch. 2 - In Problems 1-6, find the real solutions of each...Ch. 2 - In Problems 1-6, find the real solutions of each...Ch. 2 - In Problems 7-9, solve each ineQuality. Graph the...Ch. 2 - In Problems 7-9, solve each ineQuality. Graph the...Ch. 2 - In Problems 7-9, solve each ineQuality. Graph the...Ch. 2 - (a) Find the distance from P 1 =( 2,3 )to P 2 =(...Ch. 2 - In problems 11-14, graph each equation. 3x2y=12Ch. 2 - In problems 11-14, graph each equation. x= y 2Ch. 2 - In problems 11-14, graph each equation. x 2 + ( y3...Ch. 2 - In problems 11-14, graph each equation. y= xCh. 2 - Prob. 15CRCh. 2 - Find the slope-intercept form of the equation of...Ch. 2 - In problems 17-19, graph each function. f( x )= (...Ch. 2 - In problems 17-19, graph each function. f( x )= 1...Ch. 2 - In problems 17-19, graph each function. f( x )={...

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