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Algebra And Trigonometry 10th Edition Ron Larson - Solutions

Use matrices to solve the system of linear equations, if possible. Use Gauss-Jordan elimination.1.2.
Use the matrix capabilities of a graphing utility to write the augmented matrix corresponding to the system of linear equations in reduced row-echelon form. Then solve the system, if possible.1.
Solve for x and y.1.2. 3. 4.
If possible, find(a) A + B(b) A - B(c) 4A(d) 2A + 2B1.2.
Evaluate the expression.1.2. 3. 4.
Solve for X in the equation, where1. X = 2A ˆ’ 3B 2. 6X = 4A + 3B
If possible, find AB and state the dimension of the result.1.2. 3. 4.
Write the augmented matrix for the system of linear equations.1.2. Write the system of linear equations represented by the augmented matrix. (Use variables x, y, z, and w, if applicable.) 3. 4.
Use the matrix capabilities of a graphing utility to find AB, if possible.1.2. 3. 4.
If possible, find(a) AB(b) BA(c) A2.1.2.
Find Av, where v = (2, 5), and describe the transformation.1.2. 3. 4.
1. A tire corporation has three factories that manufacture two models of tires. The production levels are represented by A.Find the production levels when production decreases by 5%. 2. The pay-as-you-go charges (per minute) of two cell phone companies for calls inside the coverage area, regional
Show that B is the inverse of A.1.2.
Find the inverse of the matrix, if possible.1.2. 3. 4.
Use the matrix capabilities of a graphing utility to find the inverse of the matrix, if possible.1.2.
Use the formula on page 732 to find the inverse of the 2 Ã— 2 matrix, if possible.1.2. 3. 4.
Use an inverse matrix to solve the system of linear equations, if possible.1.2.3.
Use the matrix capabilities of a graphing utility to solve the system of linear equations, if possible.1.2.3.4.
Write the matrix in row-echelon form. (Remember that the row-echelon form of a matrix is not unique.)1.2.
Find the determinant of the matrix.1.2.3.4.
Find all the(a) Minors(b) Cofactors of the matrix.1.2.
Use the following definition of the arithmetic mean xÌ… of a set of n measurements x1, x2, x3, . . . , xn.1. Find the arithmetic mean of the six checking account balances $327.15, $785.69, $433.04, $265.38, $604.12, and $590.30. Use the statistical capabilities of a graphing utility to verify
The graph represents the first 10 terms of a sequence. Complete each expression for the apparent nth term (an) of the sequence. Which expressions are appropriate to represent the cost an to buy n MP3 songs at a cost of $1 per song? Explain.
Describe the error in finding the sum.1.2.
Find the missing term of the sequence.
Use a graphing utility to graph the first 10 terms of the sequence. (Assume that n begins with 1.) 1. an = 2/3n 2. an = 3n + 3(-1)n 3. an = 16(-0.5)n-1 4. an = 8(0.75)n-1 5. an = 2n/n + 1 6. an = 3n2/n2 + 1
Match the sequence with the graph of its first 10 terms. [The graphs are labeled (a), (b), (c), and (d).](a).(b) (c) (d) 1. an = 8/n + 1 2. an = 8n/n + 1 3. an = 4(0.5)n-1 4. an = n(2 - n/10)
Write an expression for the apparent nth term (an) of the sequence. (Assume that n begins with 1.) 1. 3, 7, 11, 15, 19, . . . 2. 0, 3, 8, 15, 24, . . . 3. 3, 10, 29, 66, 127, . . . 4. 91, 82, 73, 64, 55, . . .
Write the first five terms of the sequence defined recursively. 1. a1 = 28, ak+1 = ak - 4 2. a1 = 3, ak+1 = 2(ak − 1) 3. a1 = 81, ak+1 = 1/3ak
Write the first 12 terms of the Fibonacci sequence whose nth term is an and the first 10 terms of the sequence given by bn = an+1/an, n ≥ 1
Write the first five terms of the sequence. (Assume that n begins with 0.) 1. an = 5/1! 2. an = 1/(n + 1)!
The factorial expression 1. 4! / 6! 2. 12! / 4! · 8! 3. n + 1)! / n!
Find the sum1.2. 3.
Write the first five terms of the sequence. (Assume that n begins with 1.) 1. an = 4n - 7 2. an = −2n + 8 3. an = (-1)n+1 + 4
Use a graphing utility to find the sum.1.2.3.4.
Use sigma notation to write the sum. 1. 1 / 3(1) + 1 / 3(2) + 1 / 3(3) + . . . . + 1 / 3(9) 2. 5 / 1 + 1 + 5 / 1 + 2 + 5 / 1 + 3 + . . . + 5 / 1 + 15 3. [2(1/8) + 3] + [2(2/8) + 3] + . . . . + [2(8/8) + 3] 4. [1 - (1/6)2] + [1 - (2/6)2] + . . . . + [1 - (6/6)2]
Find the(a) Third(b) Fourth,(c) Fifth partial sums of the series1.2.
Find the sum of the infinite series.1.2. 3.
An investor deposits $10,000 in an account that earns 3.5% interest compounded quarterly. The balance in the account after n quarters is given by An = 10,000(1 + 0.035/4)n, n = 1, 2, 3, . . . (a) Write the first eight terms of the sequence. (b) Find the balance in the account after 10 years by
The percent pn of United States adults who met federal physical activity guidelines from 2007 through 2014 can be approximated by pn = 0.0061n3 ˆ’ 0.419n2 + 7.85n + 4.9, n = 7, 8, . . . , 14 where n is the year, with n = 7 corresponding to 2007. (Source: National Center for Health
Determine whether the statement is true or false. Justify your answer.1.2.
Consider the sequencean = n + 1 / n2 + 1a) Use a graphing utility to graph the first 10 terms of the sequence.(b) Use the graph from part (a) to estimate the value of an as n approaches infinity.(c) Complete the table.(d) Use the table from part (c) to determine (if possible) the value of an as n
What conclusion can be drawn about the sequence of statements Pn for each situation? (a) P3 is true and Pk implies Pk + 1. (b) P1, P2, P3, . . . , P50 are all true. (c) P1, P2, and P3 are all true, but the truth of Pk does not imply that Pk + 1 is true. (d) P2 is true and P2k implies P2k+2.
Recall that a fractal is a geometric figure that consists of a pattern that is repeated infinitely on a smaller and smaller scale. One well-known fractal is the Sierpinski Triangle. In the first stage, the midpoints of the three sides are used to create the vertices of a new triangle, which is then $Recall that a fractal is a geometric figure that consists$
You work for a company that pays $0.01 the first day, $0.02 the second day, $0.04 the third day, and so on. If the daily wage keeps doubling, what will your total income be for working 30 days?
1. A multiple choice question has five possible answers. You know that the answer is not B or D, but you are not sure about answers A, C, and E. What is the probability that you will get the right answer when you take a guess?2. You throw a dart at the circular target shown below. The dart is
The odds in favor of an event occurring is the ratio of the probability that the event will occur to the probability that the event will not occur. The reciprocal of this ratio represents the odds against the event occurring. (a) A bag contains three blue marbles and seven yellow marbles. What are
An event A has n possible outcomes, which have the values x1, x2, . . . , xn . The probabilities of the n outcomes occurring are p1, p2, . . . , pn. The expected value V of an event A is the sum of the products of the outcomes' probabilities and their values, V = p1x1 + p2x2 + . . . + pnxn. (a) To
Consider the sequencean = 3 + (-1)n(a) Use a graphing utility to graph the first 10 terms of the sequence.(b) Use the graph from part (a) to describe the behavior of the graph of the sequence.(c) Complete the table.(d) Use the table from part (c) to determine (if possible) the value of an as n
Can the Greek hero Achilles, running at 20 feet per second, ever catch a tortoise, starting 20 feet ahead of Achilles and running at 10 feet per second? The Greek mathematician Zeno said no. When Achilles runs 20 feet, the tortoise will be 10 feet ahead. Then, when Achilles runs 10 feet, the
Let x0 = 1 and consider the sequence xn given by xn = 1/2xn - 1 + 1 / xn - 1, n = 1, 2, . . Use a graphing utility to compute the first 10 terms of the sequence and make a conjecture about the value of xn as n approaches infinity.
Determine whether each operation results in an arithmetic sequence when performed on an arithmetic sequence. If so, state the common difference. (a) A constant C is added to each term. (b) Each term is multiplied by a nonzero constant C. (c) Each term is squared.
The following sequence of perfect squares is not arithmetic. 1, 4, 9, 16, 25, 36, 49, 64, 81, . . . The related sequence formed from the first differences of this sequence, however, is arithmetic. (a) Write the first eight terms of the related arithmetic sequence described above. What is the nth
A sequence can be defined using a piecewise formula. An example of a piecewise-defined sequence is given below.(a) Write the first 20 terms of the sequence. (b) Write the first 10 terms of the sequences for which a1 = 4, a1 = 5, and a1 = 12 (using an as defined above). What conclusion can you make
Let f1, f2, . . . , fn , . . . be the Fibonacci sequence. (a) Use mathematical induction to prove that f1 + f2 + . . . + fn = fn +2 − 1. (b) Find the sum of the first 20 terms of the Fibonacci sequence.
The numbers 1, 5, 12, 22, 35, 51, . . . are called pentagonal numbers because they represent the numbers of dots in the sequence of figures shown below. Use mathematical induction to prove that the nth pentagonal number Pn is given byPn = n(3n - 1)/2
Write the first five terms of the sequence. Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that n begins with 1.)1. an = 5 + 3n2. an = 100 – 3n3. an = 3 – 4(n – 2)4. an = 1 +(n - 1)n
Find a formula for an for the arithmetic sequence. 1. a1 = 1, d = 3 2. a1 = 15, d = 4 3. a1 = 100, d = −8
Write the first five terms of the arithmetic sequence. 1. a1 = 5, d = 6 2. a1 = 5, d = - 3/4 3. a1 = 2, a12 = −64 4. a4 = 16, a10 = 46
Write the first five terms of the arithmetic sequence defined recursively. 1. a1 = 15, an+1 = an + 4 2. a1 = 200, an+1 = an − 10 3. a5 = 7, an+1 = an − 2
The first two terms of the arithmetic sequence are given. Find the missing term. 1. a1 = 5, a2 = −1, a10 = . 2. a1 = 3, a2 = 13, a9 = .
Find the sum of the finite arithmetic sequence. 1. 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 2. 1 + 4 + 7 + 10 + 13 + 16 + 19 3. −1 + (−3) + (−5) + (−7) + (−9) 4. −5 + (−3) + (−1) + 1 + 3 + 5 5. Sum of the first 100 positive odd integers
Determine whether the sequence is arithmetic. If so, find the common difference. 1. 1, 2, 4, 8, 16, . . . 2. 4, 9, 14, 19, 24, . . . 3. 10, 8, 6, 4, 2, . . . 4. 80, 40, 20, 10, 5,... 5. 5/4, 3/2, 7/4, 2, 9/4, . . .
Find the nth partial sum of the arithmetic sequence for the given value of n. 1. 8, 20, 32, 44, . . . , n = 50 2. −6, −2, 2, 6, . . . , n = 100 3. 0, −9, −18, −27,..., n = 40
Find the partial sum.1.2.3.
Match the arithmetic sequence with its graph. [The graphs are labeled (a)-(d).]a.b. c. d. 1. an = -3/4n + 8 2. an = 3n - 5 3. an = 2 + 3/4n
Use a graphing utility to graph the first 10 terms of the sequence. (Assume that n begins with 1.) 1. an = 15 - 3/2n 2. an = - 5 2n 3. an = 0.2n + 3 4. an = 0.3n + 8
Consider a job offer with the given starting salary and annual raise. (a) Determine the salary during the sixth year of employment. (b) Determine the total compensation from the company through six full years of employment. Starting Salary..........................Annual Raise 1.
1. Determine the seating capacity of an auditorium with 36 rows of seats when there are 15 seats in the first row, 18 seats in the second row, 21seats in the third row, and so on.2. A triangular brick wall is made by cutting some bricks in half to use in the first column of every other row (see
An object with negligible air resistance is dropped from the top of the Willis Tower in Chicago at a height of 1451 feet. During the first second of fall, the object falls 16 feet; during the second second, it falls 48 feet; during the third second, it falls 80 feet; during the fourth second, it
A county fair is holding a baked goods competition in which the top eight bakers receive cash prizes. First place receives $200, second place receives $175, third place receives $150, and so on. (a) Write the nth term (an) of a sequence that represents the cash prize received in terms of the place
An entrepreneur sells $15,000 worth of sports memorabilia during one year and sets a goal of increasing annual sales by $5000 each year for the next 9years. Assuming that the entrepreneur meets this goal, find the total sales during the first 10 years of this business. What kinds of economic
You borrow $5000 from your parents to purchase a used car. The arrangements of the loan are such that you make payments of $250 per month toward the balance plus 1% interest on the unpaid balance from the previous month. (a) Find the first year's monthly payments and the unpaid balance after each
The table shows the net numbers of new stores opened by H&M from 2011 through 2015. Year....................................New
There are a total number of 2206 stores at the end of 2010. Write the terms of a sequence that represents the total number of stores at the end of each year from 2011 through 2015. Is the sequence approximately arithmetic? Explain
Determine whether the statement is true or false. Justify your answer. 1. Given an arithmetic sequence for which only the first two terms are known, it is possible to find the nth term. 2. When the first term, the nth term, and n are known for an arithmetic sequence, you have enough information to
(a) Graph the first 10 terms of the arithmetic sequence an = 2 + 3n. (b) Graph the equation of the line y = 3x + 2. (c) Discuss any differences between the graph of an = 2 + 3n and the graph of y = 3x + 2. (d) Compare the slope of the line in part (b) with the common difference of the sequence in
Describe two ways to use the first two terms of an arithmetic sequence to find the 13th term.
Find the first 10 terms of the sequence. a1 = x, d = 2x
1. Describe the error in finding the sum of the first 50 odd integers.
(a) Compute the following sums of consecutive positive odd integers.(b) Use the sums in part (a) to make a conjecture about the sums of consecutive positive odd integers. Check your conjecture for the sum (c) Verify your conjecture algebraically.
1. A sequence is ________ when the ratios of consecutive terms are the same. This ratio is the ________ratio. 2. The term of a geometric sequence has the form an = ________. 3. The sum of a finite geometric sequence with common ratio r ≠ 1 is given by Sn = ________. 4. The sum of the terms of an
Write the first five terms of the geometric sequence. 1. a1 = 4, r - 3 2. a1 = 7, r = 4 3. a1 = 1, r = 1 / 2 4. a1 = 6, r = − 1 / 4
Write an expression for the nth term of the geometric sequence. Then find the missing term. 1. a1 = 4, r = 1 / 2, a10 =? 2. a1 = 5, r = 7 /2, a8 =? 3. a1 = 6, r = - 1 / 3, a12 =? 4. a1 = 64, r = - 1 / 4, a10 =? 5. a1 = 100, r = ex, a9 =?
Find a formula for the nth term of the sequence. 1. 64, 32, 16, . . . 2. 81, 27, 9, . . . 3. 9, 18, 36, . . . 4. 5, -10, 20, . . . 5. 6, - 9, 27 / 2, . . .
Find the specified term of the geometric sequence. 1. 8th term: 6, 18, 54, . . . 2. 7th term: 5, 20, 80, . . . 3. 9th term: 1 / 3, - 1 / 6, 1 / 12, . . . 4. 8th term: 3 / 2, - 1, 2 / 3, . . .
Match the geometric sequence with its graph. [The graphs are labeled (a), (b), (c), and (d).](a)(b) (c) (d) 1. an = 18(2 / 3)n-1 2. an = 18(-2 / 3)n-1 3. an = 18 (3 / 2)n-1 4. an = 18(- 3 / 2)n-1
Determine whether the sequence is geometric. If so, find the common ratio. 1. 3, 6, 12, 24, . . . 2. 5, 10, 15, 20, . . . 3. 1 / 27, 1 / 9, 1 / 3, 1, . . . 4. 27, - 9, 3, -1, . . . 5. 1, 1 / 2, 1 / 3, 1 / 4, . . . 6. 5, 1, 0.2, 0.04, . . . 7. 1, - √7, 7, -7 √7, . . . 8. 2, 4 / √3, 8 / 3,
Use a graphing utility to graph the first 10 terms of the sequence. 1. an = 14 (1.4)n-1 2. an = 18 (0.7)n-1 3. an = 8 (-0.3)n-1 4. an = 11(-1.9)n-1
Find the sum of the finite geometric sequence.1.
Use summation notation to write the sum. 1. 10 + 30 + 90 + . . . + 7290 2. 15 - 3 + 3 / 5 - . . . - 3 / 625
Find the sum of the infinite geometric series.1.2. 3.
Find the rational number representation of the repeating decimal. 1. 0.3̅6̅ 2. 0.3̅1̅8̅
Use a graphing utility to graph the function. Identify the horizontal asymptote of the graph and determine its relationship to the sum.1.2.
1. A tool and die company buys a machine for $175,000 and it depreciates at a rate of 30% per year. (In other words, at the end of each year the depreciated value is 70% of what it was at the beginning of the year.) Find the depreciated value of the machine after 5 full years.2. The table shows the
An investor deposits P dollars on the first day of each month in an account with an annual interest rate r, compounded monthly. The balance A after t years is A = P (1 + r / 12) + . . . + P (1 + r / 12)12t. Show that the balance is A = P [(1 + r / 12)12t - 1] (1 + 12 / r).
1. An investor deposits $100 on the first day of each month in an account that pays 2% interest, compounded monthly. The balance A in the account at the end of 5 years is A = 100 (1 + 0.02 / 12)1 + . . . + 100 (1 + 0.02 / 12)60. Use the following information. A state government gives property
The sides of a square are 27 inches in length. New squares are formed by dividing the original square into nine squares. The center square is then shaded (see figure). This process is repeated three more times. Determine the total area of the shaded region.
A ball is dropped from a height of 6feet and begins bouncing as shown in the figure. The height of each bounce is three-fourths the height of the previous bounce. Find the total vertical distance the ball travels before coming to rest.
1. An investment firm has a job opening with a salary of $45,000 for the first year. During the next 39 years, there is a 5% raise each year. Find the total compensation over the 40-year period.2. Use the figures shown below.(i)(ii) (a) Without performing any calculations, determine which figure

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