Intermediate Algebra
Intermediate Algebra
10th Edition
ISBN: 9781305191495
Author: Jerome E. Kaufmann; Karen L. Schwitters
Publisher: Cengage Learning US
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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Chapter 11.CR, Problem 52CR
To determine

(a)

To find:

The value of the cars after the indicated time P0=25,000, t= 4.

To determine

(b)

To find:

The value of the cars after the indicated time P0=35,000, t= 3

To determine

(c)

To find:

The value of the cars after the indicated time P0=20,000, t= 1.

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Let 2 A = 4 3 -4 0 1 (a) Show that v = eigenvalue. () is an eigenvector of A and find the corresponding (b) Find the characteristic polynomial of A and factorise it. Hint: the answer to (a) may be useful. (c) Determine all eigenvalues of A and find bases for the corresponding eigenspaces. (d) Find an invertible matrix P and a diagonal matrix D such that P-¹AP = D.
(c) Let 6 0 0 A = -10 4 8 5 1 2 (i) Find the characteristic polynomial of A and factorise it. (ii) Determine all eigenvalues of A and find bases for the corresponding eigenspaces. (iii) Is A diagonalisable? Give reasons for your answer.
most 2, and let Let P2 denote the vector space of polynomials of degree at D: P2➡ P2 be the transformation that sends a polynomial p(t) = at² + bt+c in P2 to its derivative p'(t) 2at+b, that is, D(p) = p'. (a) Prove that D is a linear transformation. (b) Find a basis for the kernel ker(D) of the linear transformation D and compute its nullity. (c) Find a basis for the image im(D) of the linear transformation D and compute its rank. (d) Verify that the Rank-Nullity Theorem holds for the linear transformation D. (e) Find the matrix representation of D in the standard basis (1,t, t2) of P2.

Chapter 11 Solutions

Intermediate Algebra

Ch. 11.1 - For Problems 1-10 answer true or false If 2x+1=23x...Ch. 11.1 - Prob. 2CQCh. 11.1 - Prob. 3CQCh. 11.1 - Prob. 4CQCh. 11.1 - Prob. 5CQCh. 11.1 - Prob. 6CQCh. 11.1 - Prob. 7CQCh. 11.1 - Prob. 8CQCh. 11.1 - Prob. 9CQCh. 11.1 - Prob. 10CQ
Ch. 11.1 - Prob. 1PSCh. 11.1 - Prob. 2PSCh. 11.1 - Prob. 3PSCh. 11.1 - Prob. 4PSCh. 11.1 - Prob. 5PSCh. 11.1 - Prob. 6PSCh. 11.1 - Prob. 7PSCh. 11.1 - Prob. 8PSCh. 11.1 - Prob. 9PSCh. 11.1 - Prob. 10PSCh. 11.1 - Prob. 11PSCh. 11.1 - Prob. 12PSCh. 11.1 - Prob. 13PSCh. 11.1 - Prob. 14PSCh. 11.1 - Prob. 15PSCh. 11.1 - Prob. 16PSCh. 11.1 - Prob. 17PSCh. 11.1 - Prob. 18PSCh. 11.1 - Prob. 19PSCh. 11.1 - Prob. 20PSCh. 11.1 - Prob. 21PSCh. 11.1 - Prob. 22PSCh. 11.1 - Prob. 23PSCh. 11.1 - Prob. 24PSCh. 11.1 - Prob. 25PSCh. 11.1 - Prob. 26PSCh. 11.1 - Prob. 27PSCh. 11.1 - Prob. 28PSCh. 11.1 - Prob. 29PSCh. 11.1 - Prob. 30PSCh. 11.1 - Prob. 31PSCh. 11.1 - Prob. 32PSCh. 11.1 - Prob. 33PSCh. 11.1 - Prob. 34PSCh. 11.1 - Prob. 35PSCh. 11.1 - Prob. 36PSCh. 11.1 - Prob. 37PSCh. 11.1 - Prob. 38PSCh. 11.1 - Prob. 39PSCh. 11.1 - Prob. 40PSCh. 11.1 - Prob. 41PSCh. 11.1 - Prob. 42PSCh. 11.1 - Prob. 43PSCh. 11.1 - Prob. 44PSCh. 11.1 - Prob. 45PSCh. 11.1 - Prob. 46PSCh. 11.1 - Prob. 47PSCh. 11.1 - Prob. 48PSCh. 11.1 - Prob. 49PSCh. 11.1 - Prob. 50PSCh. 11.1 - For Problems 35-52, graph each exponential...Ch. 11.1 - For Problems 35-52, graph each exponential...Ch. 11.1 - Prob. 53PSCh. 11.1 - Prob. 54PSCh. 11.1 - Prob. 55PSCh. 11.1 - Prob. 57PSCh. 11.1 - Prob. 58PSCh. 11.1 - Prob. 59PSCh. 11.1 - Prob. 60PSCh. 11.1 - Prob. 61PSCh. 11.2 - For Problems 1-5, match each type of problem with...Ch. 11.2 - Prob. 2CQCh. 11.2 - Prob. 3CQCh. 11.2 - Prob. 4CQCh. 11.2 - Prob. 5CQCh. 11.2 - Prob. 6CQCh. 11.2 - Prob. 7CQCh. 11.2 - Prob. 8CQCh. 11.2 - Prob. 9CQCh. 11.2 - Prob. 10CQCh. 11.2 - Prob. 1PSCh. 11.2 - Suppose it is estimated that the value of a car...Ch. 11.2 - Prob. 3PSCh. 11.2 - Prob. 4PSCh. 11.2 - Prob. 5PSCh. 11.2 - Prob. 6PSCh. 11.2 - Prob. 7PSCh. 11.2 - Prob. 8PSCh. 11.2 - Prob. 9PSCh. 11.2 - Prob. 10PSCh. 11.2 - Prob. 11PSCh. 11.2 - Prob. 12PSCh. 11.2 - Prob. 13PSCh. 11.2 - Prob. 14PSCh. 11.2 - Prob. 15PSCh. 11.2 - Prob. 16PSCh. 11.2 - Prob. 17PSCh. 11.2 - Prob. 18PSCh. 11.2 - Prob. 19PSCh. 11.2 - Prob. 20PSCh. 11.2 - Prob. 21PSCh. 11.2 - Prob. 22PSCh. 11.2 - Prob. 23PSCh. 11.2 - Prob. 24PSCh. 11.2 - Prob. 25PSCh. 11.2 - Prob. 26PSCh. 11.2 - Prob. 27PSCh. 11.2 - Two years ago Daniel invested some money at 8...Ch. 11.2 - What rate of interest to the nearest hundredth of...Ch. 11.2 - Suppose that a certain radioactive substance has a...Ch. 11.2 - Strontium-90 has a half life of 29 years. If there...Ch. 11.2 - The half life of radium is approximately 1600...Ch. 11.2 - For Problems 33-38, graph each of the exponential...Ch. 11.2 - Prob. 34PSCh. 11.2 - Prob. 35PSCh. 11.2 - Prob. 36PSCh. 11.2 - Prob. 37PSCh. 11.2 - Prob. 38PSCh. 11.2 - For Problems 39-44, express your answer to the...Ch. 11.2 - Prob. 40PSCh. 11.2 - Prob. 41PSCh. 11.2 - Prob. 42PSCh. 11.2 - Prob. 43PSCh. 11.2 - Prob. 44PSCh. 11.2 - Prob. 45PSCh. 11.2 - Prob. 46PSCh. 11.2 - Prob. 47PSCh. 11.2 - Prob. 48PSCh. 11.2 - Prob. 49PSCh. 11.2 - Prob. 50PSCh. 11.2 - Graph f(x)=ex. Now predict the graphs for f(x)=ex,...Ch. 11.2 - Prob. 52PSCh. 11.3 - For Problems 1-10, answer true or false. The...Ch. 11.3 - Prob. 2CQCh. 11.3 - Prob. 3CQCh. 11.3 - Prob. 4CQCh. 11.3 - Prob. 5CQCh. 11.3 - Prob. 6CQCh. 11.3 - Prob. 7CQCh. 11.3 - For Problems 1-10, answer true or false....Ch. 11.3 - Prob. 9CQCh. 11.3 - Prob. 10CQCh. 11.3 - Prob. 1PSCh. 11.3 - Prob. 2PSCh. 11.3 - Prob. 3PSCh. 11.3 - Prob. 4PSCh. 11.3 - Prob. 5PSCh. 11.3 - Prob. 6PSCh. 11.3 - Prob. 7PSCh. 11.3 - Prob. 8PSCh. 11.3 - Prob. 9PSCh. 11.3 - Prob. 10PSCh. 11.3 - Prob. 11PSCh. 11.3 - Prob. 12PSCh. 11.3 - Prob. 13PSCh. 11.3 - Prob. 14PSCh. 11.3 - For Problems 11-20, write each of the following in...Ch. 11.3 - Prob. 16PSCh. 11.3 - Prob. 17PSCh. 11.3 - Prob. 18PSCh. 11.3 - Prob. 19PSCh. 11.3 - Prob. 20PSCh. 11.3 - Prob. 21PSCh. 11.3 - Prob. 22PSCh. 11.3 - Prob. 23PSCh. 11.3 - Prob. 24PSCh. 11.3 - Prob. 25PSCh. 11.3 - Prob. 26PSCh. 11.3 - Prob. 27PSCh. 11.3 - Prob. 28PSCh. 11.3 - Prob. 29PSCh. 11.3 - Prob. 30PSCh. 11.3 - Prob. 31PSCh. 11.3 - Prob. 32PSCh. 11.3 - Prob. 33PSCh. 11.3 - Prob. 34PSCh. 11.3 - Prob. 35PSCh. 11.3 - Prob. 36PSCh. 11.3 - Prob. 37PSCh. 11.3 - Prob. 38PSCh. 11.3 - Prob. 39PSCh. 11.3 - Prob. 40PSCh. 11.3 - Prob. 41PSCh. 11.3 - Prob. 42PSCh. 11.3 - Prob. 43PSCh. 11.3 - Prob. 44PSCh. 11.3 - Prob. 45PSCh. 11.3 - Prob. 46PSCh. 11.3 - Prob. 47PSCh. 11.3 - Prob. 48PSCh. 11.3 - Prob. 49PSCh. 11.3 - Prob. 50PSCh. 11.3 - Prob. 51PSCh. 11.3 - Prob. 52PSCh. 11.3 - Prob. 53PSCh. 11.3 - Prob. 54PSCh. 11.3 - Prob. 55PSCh. 11.3 - Prob. 56PSCh. 11.3 - Prob. 57PSCh. 11.3 - Prob. 58PSCh. 11.3 - Prob. 59PSCh. 11.3 - Prob. 60PSCh. 11.3 - Prob. 61PSCh. 11.3 - Prob. 62PSCh. 11.3 - Prob. 63PSCh. 11.3 - Prob. 64PSCh. 11.3 - Prob. 65PSCh. 11.3 - Prob. 66PSCh. 11.3 - Prob. 67PSCh. 11.3 - Prob. 68PSCh. 11.3 - Prob. 69PSCh. 11.3 - Prob. 70PSCh. 11.3 - Prob. 71PSCh. 11.3 - Prob. 72PSCh. 11.3 - For Problems 69-80, express each of the following...Ch. 11.3 - Prob. 74PSCh. 11.3 - Prob. 75PSCh. 11.3 - Prob. 76PSCh. 11.3 - Prob. 77PSCh. 11.3 - Prob. 78PSCh. 11.3 - Prob. 79PSCh. 11.3 - Prob. 80PSCh. 11.3 - Prob. 81PSCh. 11.3 - Prob. 82PSCh. 11.3 - Prob. 83PSCh. 11.3 - Prob. 84PSCh. 11.3 - Prob. 85PSCh. 11.3 - Prob. 86PSCh. 11.3 - Prob. 87PSCh. 11.3 - Prob. 88PSCh. 11.3 - Prob. 89PSCh. 11.3 - Prob. 90PSCh. 11.3 - Prob. 91PSCh. 11.3 - Prob. 92PSCh. 11.3 - Prob. 93PSCh. 11.3 - Prob. 94PSCh. 11.3 - Prob. 95PSCh. 11.3 - Prob. 96PSCh. 11.3 - Prob. 97PSCh. 11.3 - Prob. 98PSCh. 11.3 - Prob. 99PSCh. 11.3 - Prob. 100PSCh. 11.3 - Prob. 101PSCh. 11.3 - Prob. 102PSCh. 11.4 - For Problems 1-10, answer true or false. The...Ch. 11.4 - Prob. 2CQCh. 11.4 - Prob. 3CQCh. 11.4 - Prob. 4CQCh. 11.4 - Prob. 5CQCh. 11.4 - Prob. 6CQCh. 11.4 - For Problems 1-10, answer true or false. If lnx=1...Ch. 11.4 - Prob. 8CQCh. 11.4 - Prob. 9CQCh. 11.4 - Prob. 10CQCh. 11.4 - Prob. 1PSCh. 11.4 - Prob. 2PSCh. 11.4 - Prob. 3PSCh. 11.4 - Prob. 4PSCh. 11.4 - Prob. 5PSCh. 11.4 - Prob. 6PSCh. 11.4 - Prob. 7PSCh. 11.4 - Prob. 8PSCh. 11.4 - For Problems 1-10, use a calculator to find each...Ch. 11.4 - Prob. 10PSCh. 11.4 - Prob. 11PSCh. 11.4 - Prob. 12PSCh. 11.4 - Prob. 13PSCh. 11.4 - Prob. 14PSCh. 11.4 - Prob. 15PSCh. 11.4 - Prob. 16PSCh. 11.4 - Prob. 17PSCh. 11.4 - Prob. 18PSCh. 11.4 - Prob. 19PSCh. 11.4 - Prob. 20PSCh. 11.4 - Prob. 21PSCh. 11.4 - Prob. 22PSCh. 11.4 - Prob. 23PSCh. 11.4 - Prob. 24PSCh. 11.4 - Prob. 25PSCh. 11.4 - Prob. 26PSCh. 11.4 - Prob. 27PSCh. 11.4 - Prob. 28PSCh. 11.4 - For problems 21-30, use your calculator to find...Ch. 11.4 - Prob. 30PSCh. 11.4 - Prob. 31PSCh. 11.4 - Prob. 32PSCh. 11.4 - Prob. 33PSCh. 11.4 - Prob. 34PSCh. 11.4 - Prob. 35PSCh. 11.4 - Prob. 36PSCh. 11.4 - Prob. 37PSCh. 11.4 - Prob. 38PSCh. 11.4 - Prob. 39PSCh. 11.4 - Prob. 40PSCh. 11.4 - Prob. 41PSCh. 11.4 - Prob. 42PSCh. 11.4 - Prob. 43PSCh. 11.4 - Prob. 44PSCh. 11.4 - Prob. 45PSCh. 11.4 - Prob. 46PSCh. 11.4 - For Problems 47-53, graph each of the functions....Ch. 11.4 - Prob. 48PSCh. 11.4 - Prob. 49PSCh. 11.4 - Prob. 50PSCh. 11.4 - Prob. 51PSCh. 11.4 - Prob. 52PSCh. 11.4 - Prob. 53PSCh. 11.4 - Prob. 54PSCh. 11.4 - Prob. 55PSCh. 11.4 - Prob. 56PSCh. 11.4 - Prob. 57PSCh. 11.4 - Prob. 58PSCh. 11.4 - Prob. 59PSCh. 11.4 - Prob. 60PSCh. 11.4 - Prob. 61PSCh. 11.4 - Why is the number 1 excluded from being a base of...Ch. 11.4 - Prob. 63PSCh. 11.4 - Prob. 64PSCh. 11.4 - Prob. 65PSCh. 11.4 - Prob. 66PSCh. 11.4 - Prob. 67PSCh. 11.4 - Prob. 68PSCh. 11.4 - Prob. 69PSCh. 11.5 - For Problems 1-8, answer true or false. The...Ch. 11.5 - For Problems 1-8, answer true or false. All...Ch. 11.5 - Prob. 3CQCh. 11.5 - Prob. 4CQCh. 11.5 - For Problems 1-8, answer true or false. The...Ch. 11.5 - Prob. 6CQCh. 11.5 - For Problems 1-8, answer true or false. The...Ch. 11.5 - Prob. 8CQCh. 11.5 - Prob. 1PSCh. 11.5 - Prob. 2PSCh. 11.5 - Prob. 3PSCh. 11.5 - Prob. 4PSCh. 11.5 - Prob. 5PSCh. 11.5 - Prob. 6PSCh. 11.5 - For problems 1-14, solve each exponential equation...Ch. 11.5 - For problems 1-14, solve each exponential equation...Ch. 11.5 - For problems 1-14, solve each exponential equation...Ch. 11.5 - For problems 1-14, solve each exponential equation...Ch. 11.5 - Prob. 11PSCh. 11.5 - Prob. 12PSCh. 11.5 - Prob. 13PSCh. 11.5 - Prob. 14PSCh. 11.5 - Prob. 15PSCh. 11.5 - Prob. 16PSCh. 11.5 - Prob. 17PSCh. 11.5 - Prob. 18PSCh. 11.5 - Prob. 19PSCh. 11.5 - Prob. 20PSCh. 11.5 - Prob. 21PSCh. 11.5 - Prob. 22PSCh. 11.5 - Prob. 23PSCh. 11.5 - Prob. 24PSCh. 11.5 - Prob. 25PSCh. 11.5 - Prob. 26PSCh. 11.5 - Prob. 27PSCh. 11.5 - Prob. 28PSCh. 11.5 - Prob. 29PSCh. 11.5 - Prob. 30PSCh. 11.5 - Prob. 31PSCh. 11.5 - Prob. 32PSCh. 11.5 - Prob. 33PSCh. 11.5 - For Problems 33-41, solve each problem and express...Ch. 11.5 - Prob. 35PSCh. 11.5 - Prob. 36PSCh. 11.5 - Prob. 37PSCh. 11.5 - Prob. 38PSCh. 11.5 - Prob. 39PSCh. 11.5 - Prob. 40PSCh. 11.5 - Prob. 41PSCh. 11.5 - Prob. 42PSCh. 11.5 - Prob. 43PSCh. 11.5 - Prob. 44PSCh. 11.5 - Prob. 45PSCh. 11.5 - Prob. 46PSCh. 11.5 - Prob. 47PSCh. 11.5 - Prob. 48PSCh. 11.5 - Prob. 49PSCh. 11.5 - Prob. 50PSCh. 11.5 - Prob. 51PSCh. 11.5 - Prob. 52PSCh. 11.5 - Prob. 53PSCh. 11.5 - Prob. 54PSCh. 11.S - Prob. 1SCh. 11.S - Prob. 2SCh. 11.S - Prob. 3SCh. 11.S - Prob. 4SCh. 11.S - Prob. 5SCh. 11.S - Prob. 6SCh. 11.S - Prob. 7SCh. 11.S - Prob. 8SCh. 11.S - Prob. 9SCh. 11.S - Prob. 10SCh. 11.S - Prob. 11SCh. 11.S - Prob. 12SCh. 11.S - Prob. 13SCh. 11.S - Prob. 14SCh. 11.S - Prob. 15SCh. 11.S - Prob. 16SCh. 11.S - Prob. 17SCh. 11.S - Prob. 18SCh. 11.CR - For problems 1 and 2, graph each of the functions....Ch. 11.CR - Prob. 2CRCh. 11.CR - Prob. 3CRCh. 11.CR - Prob. 4CRCh. 11.CR - Prob. 5CRCh. 11.CR - Prob. 6CRCh. 11.CR - Prob. 7CRCh. 11.CR - Prob. 8CRCh. 11.CR - Prob. 9CRCh. 11.CR - Prob. 10CRCh. 11.CR - Prob. 11CRCh. 11.CR - Prob. 12CRCh. 11.CR - Prob. 13CRCh. 11.CR - For problems 11-14, write each of the following in...Ch. 11.CR - Prob. 15CRCh. 11.CR - Prob. 16CRCh. 11.CR - Prob. 17CRCh. 11.CR - Prob. 18CRCh. 11.CR - Prob. 19CRCh. 11.CR - Prob. 20CRCh. 11.CR - Prob. 21CRCh. 11.CR - Prob. 22CRCh. 11.CR - Prob. 23CRCh. 11.CR - Prob. 24CRCh. 11.CR - Prob. 25CRCh. 11.CR - Prob. 26CRCh. 11.CR - Prob. 27CRCh. 11.CR - Prob. 28CRCh. 11.CR - Prob. 29CRCh. 11.CR - Prob. 30CRCh. 11.CR - Prob. 31CRCh. 11.CR - Prob. 32CRCh. 11.CR - Prob. 33CRCh. 11.CR - Prob. 34CRCh. 11.CR - Prob. 35CRCh. 11.CR - Prob. 36CRCh. 11.CR - Prob. 37CRCh. 11.CR - Prob. 38CRCh. 11.CR - Prob. 39CRCh. 11.CR - Prob. 40CRCh. 11.CR - Prob. 41CRCh. 11.CR - Prob. 42CRCh. 11.CR - Prob. 43CRCh. 11.CR - Prob. 44CRCh. 11.CR - Prob. 45CRCh. 11.CR - Prob. 46CRCh. 11.CR - Prob. 47CRCh. 11.CR - Prob. 48CRCh. 11.CR - Prob. 49CRCh. 11.CR - Prob. 50CRCh. 11.CR - Prob. 51CRCh. 11.CR - Prob. 52CRCh. 11.CR - Suppose that 8000 is invested at 6 interest...Ch. 11.CR - If 25, 000 is invested at 4 interest compounded...Ch. 11.CR - How long will it take 1000 to double itself if it...Ch. 11.CR - Prob. 56CRCh. 11.CR - If 3500 is invested at 8 interest compounded...Ch. 11.CR - Prob. 58CRCh. 11.CR - Prob. 59CRCh. 11.CR - Suppose that a certain radioactive substance has a...Ch. 11.CR - Suppose that the present population of a city is...Ch. 11.CR - Prob. 62CRCh. 11.CR - An earthquake in Mexico in 1985 had and intensity...Ch. 11.CR - Prob. 64CRCh. 11.CT - Prob. 1CTCh. 11.CT - Prob. 2CTCh. 11.CT - Prob. 3CTCh. 11.CT - Prob. 4CTCh. 11.CT - Prob. 5CTCh. 11.CT - Prob. 6CTCh. 11.CT - Prob. 7CTCh. 11.CT - Prob. 8CTCh. 11.CT - Prob. 9CTCh. 11.CT - Prob. 10CTCh. 11.CT - Prob. 11CTCh. 11.CT - Prob. 12CTCh. 11.CT - Prob. 13CTCh. 11.CT - Prob. 14CTCh. 11.CT - Prob. 15CTCh. 11.CT - Prob. 16CTCh. 11.CT - Prob. 17CTCh. 11.CT - Prob. 18CTCh. 11.CT - Prob. 19CTCh. 11.CT - Prob. 20CTCh. 11.CT - Prob. 21CTCh. 11.CT - Prob. 22CTCh. 11.CT - Prob. 23CTCh. 11.CT - Prob. 24CTCh. 11.CT - Prob. 25CT
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