College Algebra Essentials
1st Edition
ISBN: 9780078035616
Author: Julie Miller
Publisher: MCG
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Textbook Question
Chapter 4.2, Problem 70PE
Newton’s law of cooling indicates that the temperature of a warm object, such as a cake coming out of the oven, will decrease exponentially with time and will approach the temperature of the surrounding air. The temperature T(t) is modeled by T(t) = Ta +(T0–Ta)e-kt. In this model, Ta represents the temperature of the surrounding air, T0 represents the initial temperature of the object, and t is the time after the object starts cooling. The value of k is the cooling rate and is a constant related to the physical properties of the object. Use this model for Exercises 69–70.
Water in a water heater is originally 122°F. The water heater is shut off and the water cools to the temperature of the surrounding air, which is 60°F. The water cools slowly because of the insulation inside the heater, and the rate of cooling is 0.00351.
a. Write a function that models the temperature T(t) (in °F) of the water t hours after the water heater is shut off.
b. What is the temperature of the water 12 hr after the heater is shut off? Round to the nearest degree.
c. Dominic does not like to shower with water less than 115°F. If Dominic waits 24 hr, will the water still be warm enough for a shower?
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Question 1. Solve the system
-
x1 x2 + 3x3 + 2x4
-x1 + x22x3 + x4
2x12x2+7x3+7x4
Question 2. Consider the system
= 1
=-2
= 1
3x1 - x2 + ax3
= 1
x1 + 3x2 + 2x3
x12x2+2x3
= -b
= 4
1 For what values of a, b will the system be inconsistent?
2 For what values of a, b will the system have only one solution?
For what values of a, b will the saystem have infinitely many solutions?
Chapter 4 Solutions
College Algebra Essentials
Ch. 4.1 - Skill Practice 1 Determine whether function f is a...Ch. 4.1 - Prob. 2SPCh. 4.1 - Prob. 3SPCh. 4.1 - Prob. 4SPCh. 4.1 - Prob. 5SPCh. 4.1 - Prob. 6SPCh. 4.1 - Prob. 7SPCh. 4.1 - Prob. 8SPCh. 4.1 - Prob. 1PECh. 4.1 - Prob. 2PE
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Show that f(x) = 4 x+ 4 defines a one-to-one...Ch. 4.1 - For Exercises 4758, a one-to-one function is...Ch. 4.1 - For Exercises 4758, a one-to-one function is...Ch. 4.1 - For Exercises 4758, a one-to-one function is...Ch. 4.1 - Prob. 50PECh. 4.1 - Prob. 51PECh. 4.1 - Prob. 52PECh. 4.1 - Prob. 53PECh. 4.1 - Prob. 54PECh. 4.1 - Prob. 55PECh. 4.1 - Prob. 56PECh. 4.1 - Prob. 57PECh. 4.1 - Prob. 58PECh. 4.1 - Prob. 59PECh. 4.1 - Prob. 60PECh. 4.1 - Prob. 61PECh. 4.1 - Prob. 62PECh. 4.1 - Prob. 63PECh. 4.1 - Prob. 64PECh. 4.1 - Prob. 65PECh. 4.1 - Prob. 66PECh. 4.1 - Prob. 67PECh. 4.1 - Prob. 68PECh. 4.1 - Prob. 69PECh. 4.1 - Prob. 70PECh. 4.1 - Prob. 71PECh. 4.1 - Prob. 72PECh. 4.1 - Prob. 73PECh. 4.1 - Prob. 74PECh. 4.1 - Prob. 75PECh. 4.1 - Prob. 76PECh. 4.1 - Prob. 77PECh. 4.1 - Prob. 78PECh. 4.1 - Prob. 79PECh. 4.1 - Prob. 80PECh. 4.1 - Prob. 81PECh. 4.1 - Prob. 82PECh. 4.1 - Prob. 83PECh. 4.1 - Prob. 84PECh. 4.1 - Prob. 85PECh. 4.1 - Prob. 86PECh. 4.1 - Prob. 87PECh. 4.1 - Prob. 88PECh. 4.1 - 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Prob. 120PECh. 4.3 - Prob. 121PECh. 4.3 - Prob. 122PECh. 4.3 - Prob. 123PECh. 4.3 - Prob. 124PECh. 4.3 - Prob. 125PECh. 4.3 - Prob. 126PECh. 4.3 - Prob. 127PECh. 4.3 - Prob. 128PECh. 4.3 - Prob. 129PECh. 4.3 - Prob. 130PECh. 4.4 - Prob. 1SPCh. 4.4 - Prob. 2SPCh. 4.4 - Prob. 3SPCh. 4.4 - Prob. 4SPCh. 4.4 - Prob. 5SPCh. 4.4 - Prob. 6SPCh. 4.4 - Prob. 7SPCh. 4.4 - Prob. 8SPCh. 4.4 - Prob. 1PECh. 4.4 - Prob. 2PECh. 4.4 - Prob. 3PECh. 4.4 - Prob. 4PECh. 4.4 - Prob. 5PECh. 4.4 - Prob. 6PECh. 4.4 - Prob. 7PECh. 4.4 - Prob. 8PECh. 4.4 - Prob. 9PECh. 4.4 - Prob. 10PECh. 4.4 - Prob. 11PECh. 4.4 - Prob. 12PECh. 4.4 - Prob. 13PECh. 4.4 - Prob. 14PECh. 4.4 - Prob. 15PECh. 4.4 - Prob. 16PECh. 4.4 - Prob. 17PECh. 4.4 - Prob. 18PECh. 4.4 - Prob. 19PECh. 4.4 - For Exercises 1722, use the product property of...Ch. 4.4 - Prob. 21PECh. 4.4 - Prob. 22PECh. 4.4 - Prob. 23PECh. 4.4 - Prob. 24PECh. 4.4 - Prob. 25PECh. 4.4 - Prob. 26PECh. 4.4 - Prob. 27PECh. 4.4 - Prob. 28PECh. 4.4 - Prob. 29PECh. 4.4 - Prob. 30PECh. 4.4 - 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Prob. 106PECh. 4.5 - Prob. 107PECh. 4.5 - Prob. 108PECh. 4.5 - Prob. 109PECh. 4.5 - Prob. 110PECh. 4.5 - Prob. 111PECh. 4.5 - Prob. 112PECh. 4.5 - Prob. 113PECh. 4.5 - Prob. 114PECh. 4.5 - Prob. 115PECh. 4.5 - Prob. 116PECh. 4.5 - Prob. 117PECh. 4.5 - Prob. 118PECh. 4.5 - Prob. 119PECh. 4.5 - Prob. 120PECh. 4.5 - Prob. 121PECh. 4.5 - Prob. 122PECh. 4.5 - Prob. 123PECh. 4.5 - Prob. 124PECh. 4.5 - Prob. 125PECh. 4.5 - Prob. 126PECh. 4.5 - Prob. 127PECh. 4.5 - Prob. 128PECh. 4.5 - Prob. 129PECh. 4.5 - Prob. 130PECh. 4.6 - Prob. 1SPCh. 4.6 - Prob. 2SPCh. 4.6 - Prob. 3SPCh. 4.6 - Prob. 4SPCh. 4.6 - Prob. 5SPCh. 4.6 - Prob. 6SPCh. 4.6 - Prob. 7SPCh. 4.6 - Prob. 8SPCh. 4.6 - Prob. 1PECh. 4.6 - Prob. 2PECh. 4.6 - Prob. 3PECh. 4.6 - Prob. 4PECh. 4.6 - Prob. 5PECh. 4.6 - Prob. 6PECh. 4.6 - Prob. 7PECh. 4.6 - Prob. 8PECh. 4.6 - Prob. 9PECh. 4.6 - Prob. 10PECh. 4.6 - Prob. 11PECh. 4.6 - Prob. 12PECh. 4.6 - Prob. 13PECh. 4.6 - Prob. 14PECh. 4.6 - Prob. 15PECh. 4.6 - Prob. 16PECh. 4.6 - Prob. 17PECh. 4.6 - Prob. 18PECh. 4.6 - Prob. 19PECh. 4.6 - Prob. 20PECh. 4.6 - Prob. 21PECh. 4.6 - Prob. 22PECh. 4.6 - Prob. 23PECh. 4.6 - Prob. 24PECh. 4.6 - Prob. 25PECh. 4.6 - Prob. 26PECh. 4.6 - Prob. 27PECh. 4.6 - Prob. 28PECh. 4.6 - Prob. 29PECh. 4.6 - Prob. 30PECh. 4.6 - Prob. 31PECh. 4.6 - Prob. 32PECh. 4.6 - Prob. 33PECh. 4.6 - Prob. 34PECh. 4.6 - Prob. 35PECh. 4.6 - Prob. 36PECh. 4.6 - Prob. 37PECh. 4.6 - Prob. 38PECh. 4.6 - Prob. 39PECh. 4.6 - The population of Canada P(t) (in millions) since...Ch. 4.6 - Prob. 41PECh. 4.6 - Prob. 42PECh. 4.6 - Prob. 43PECh. 4.6 - Prob. 44PECh. 4.6 - Prob. 45PECh. 4.6 - Prob. 46PECh. 4.6 - Prob. 47PECh. 4.6 - Prob. 48PECh. 4.6 - Prob. 49PECh. 4.6 - Prob. 50PECh. 4.6 - Prob. 51PECh. 4.6 - Prob. 52PECh. 4.6 - Prob. 53PECh. 4.6 - Prob. 54PECh. 4.6 - Prob. 55PECh. 4.6 - Prob. 56PECh. 4.6 - Prob. 57PECh. 4.6 - The sales of a book tend to increase over the...Ch. 4.6 - Prob. 59PECh. 4.6 - Prob. 60PECh. 4.6 - Prob. 61PECh. 4.6 - Prob. 62PECh. 4.6 - Prob. 63PECh. 4.6 - Prob. 64PECh. 4.6 - Prob. 65PECh. 4.6 - Prob. 66PECh. 4.6 - Prob. 67PECh. 4 - Prob. 1PRECh. 4 - Prob. 2PRECh. 4 - Prob. 3PRECh. 4 - Prob. 4PRECh. 4 - Prob. 5PRECh. 4 - Prob. 6PRECh. 4 - Prob. 7PRECh. 4 - Prob. 8PRECh. 4 - Prob. 9PRECh. 4 - Prob. 10PRECh. 4 - Prob. 11PRECh. 4 - Prob. 12PRECh. 4 - Prob. 13PRECh. 4 - Prob. 14PRECh. 4 - Prob. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - For Exercises 1819, use the formulas on page 450....Ch. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - Prob. 57RECh. 4 - Prob. 58RECh. 4 - Prob. 59RECh. 4 - Prob. 60RECh. 4 - Prob. 61RECh. 4 - Prob. 62RECh. 4 - Prob. 63RECh. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Prob. 69RECh. 4 - Prob. 70RECh. 4 - Prob. 71RECh. 4 - Prob. 72RECh. 4 - Prob. 73RECh. 4 - Prob. 74RECh. 4 - Prob. 75RECh. 4 - Prob. 76RECh. 4 - Prob. 77RECh. 4 - Prob. 78RECh. 4 - Prob. 79RECh. 4 - Prob. 80RECh. 4 - Prob. 81RECh. 4 - Prob. 82RECh. 4 - Prob. 83RECh. 4 - Prob. 84RECh. 4 - Prob. 85RECh. 4 - Prob. 86RECh. 4 - Prob. 87RECh. 4 - Prob. 88RECh. 4 - Prob. 89RECh. 4 - Prob. 90RECh. 4 - Prob. 91RECh. 4 - Prob. 92RECh. 4 - Prob. 1TCh. 4 - Prob. 2TCh. 4 - Prob. 3TCh. 4 - Prob. 4TCh. 4 - Prob. 5TCh. 4 - Prob. 6TCh. 4 - Prob. 7TCh. 4 - Prob. 8TCh. 4 - Prob. 9TCh. 4 - Prob. 10TCh. 4 - Prob. 11TCh. 4 - Prob. 12TCh. 4 - Prob. 13TCh. 4 - Prob. 14TCh. 4 - Prob. 15TCh. 4 - Prob. 16TCh. 4 - Prob. 17TCh. 4 - Prob. 18TCh. 4 - Prob. 19TCh. 4 - Prob. 20TCh. 4 - Prob. 21TCh. 4 - Prob. 22TCh. 4 - Prob. 23TCh. 4 - Prob. 24TCh. 4 - Prob. 25TCh. 4 - Prob. 26TCh. 4 - Prob. 27TCh. 4 - Prob. 28TCh. 4 - Prob. 29TCh. 4 - Prob. 30TCh. 4 - Prob. 31TCh. 4 - Prob. 32TCh. 4 - Prob. 33TCh. 4 - Prob. 34TCh. 4 - Prob. 35TCh. 4 - Prob. 36TCh. 4 - Prob. 37TCh. 4 - Prob. 38TCh. 4 - Prob. 39TCh. 4 - Prob. 40TCh. 4 - Prob. 41TCh. 4 - Prob. 42TCh. 4 - Prob. 1CRECh. 4 - Prob. 2CRECh. 4 - Prob. 3CRECh. 4 - Prob. 4CRECh. 4 - Prob. 5CRECh. 4 - Prob. 6CRECh. 4 - Prob. 7CRECh. 4 - Prob. 8CRECh. 4 - Prob. 9CRECh. 4 - Prob. 10CRECh. 4 - Prob. 11CRECh. 4 - Prob. 12CRECh. 4 - Prob. 13CRECh. 4 - Prob. 14CRECh. 4 - Prob. 15CRECh. 4 - Prob. 16CRECh. 4 - Prob. 17CRECh. 4 - Prob. 18CRECh. 4 - Write the expression as a single logarithm and...Ch. 4 - Prob. 20CRE
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