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# Algebra

### Writing and Solving Equations from Word Problems

Sam lives on a lot that he thought was a square, 157 feet by 157 feet. When he had it surveyed, he discovered that one side was actually 2 feet longer than he thought and the other was actually 2 feet shorter than he thought. How much less area does he have than he thought he had?

### Sequences and Series: Using the index of a series as the domain and the value of the series as the range, is a series a function?

Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence? Which one of the basic functions (linear, quadrati

### Please solve these equations related to arithmetic sequence and geometric sequence

1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,...to find the following: a) What is d, the difference between any 2 terms? Answer: Show work in this space. b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: Show work in this space. c) Using the formula for the

### Let {x_n} be a sequence of positive numbers and suppose that he sequence {x_n+1/x_n} converges to L.

Let {x_n} be a sequence of positive numbers and suppose that he sequence {x_n+1/x_n} converges to L. Suppose L <1. Prove that the sequence {x_n} converges to 0.

### The Maximum Height on a Building the Ladder Can Reach

A 30 feet ladder is used by fire fighters is a safe only when it leans against a building at an angle of 60 degrees or less to the ground. What is the maximum height on a building the ladder can reach? Round to the nearest hundredth.

### Recurrence relation

1. If a person invests in a tax-sheltered annuity, the money invested, as well as the interest earned, is not subject to taxation until withdrawn from the account. Assume that a person invests \$2000 each year in a tax-sheltered annuity at 10 percent interest compounded annually. Let An represent the amount at the end of n year

### Graphing and Solving Systems of Inequalities

18. Graph this inequality 2y - 3x > 6 19. Graph this system of inequalities: { 8x + 5y &#8805; 40 x + 2y &#8804; 8 Find the coordinates of any vertices formed.

### Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?

Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence? Which one of the basic functions (linear, quadratic,

### Factor Groups of Non-Abelian Groups

Let G be a nonabelian group and Z(G) be its center. Show that the factor group G/Z(G) is not a cyclic group. We know if G is abelian, Z(G)=G. But now if it is not abelian, can we simply say because G is not cyclic, then any factor group will not be cyclic either? or is there more to it?

### Solving an Initial value problem by using Taylor's method

Use Taylor's method with h = 0.05 to approximate the solution, and compare it with, actual values of y. See attached file for full problem description. (5.3) 6. Given the initial-value problem , , with exact solution : a. Use Taylor's method with h = 0.05 to approximate the solution, and compare it with, actual va

### Contour Integrals

Calculate the integral using contour integration. Complete explanation is required. integral(0-> &#8734;)logxdx/(1+x^2)^2 keywords: integration, integrates, integrals, integrating, double, triple, multiple

### Sequences and Series

1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following: a) What is d, the difference between any 2 terms? b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms? d)

### Maximal Ideals

A commutative ring is called a local ring if it has a unique maximal ideal. Prove that if R is a local ring with maximal ideal M then every element of R-M is a unit. Prove conversely that if R is commutative ring with one in which the set of nonunits forms an ideal M, then R is a local ring with unique maximal ideal M.

### Systems of Congruences : Simultaneous Solutions

1. Prove that gcd (a, lcm[b, c]) = lcm[gcd(a,b), gcd(a,c)]. 2. Find the simultaneous solutions of the following congruences: 2x &#8801; 1(mod 5) 3x &#8801; 9 (mod 6) 4x &#8801; 1 (mod 7) 5x &#8801; 9 (mod 11)

### Fibonacci Sequences

Fibonacci posed the following problem: Suppose that rabbits live forever and that every month each pair produces a new pair which becomes productive at age 2 months. If we start with one newborn pair, how many pairs of rabbits will we have in the nth month? Show that the answer is fn, where {fn} is the Fibonacci sequence defined

### Solve each system by the addition method.

Indicate whether each system is independent, inconsistent or dependent 4 ( 1-x) + y = 3 3 (1-y) - 4x = -=4y 1/3x - 1/6y = 1/3 1/6x + 1/4y= 0

Factor 25-9z^2

### Problem set in group project 4

See attached file for full problem description. 1) An open-top box is to be constructed from a 4 by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of th

b/3=-3/4

### Solving Equations

1/a + 1/b = 1/f for a P1V1 P2V2 ______ = ______ for P2 (note: the 2 is a tiny #2 below the P) T1 T2

### Solving Equations

How do you do these type of problems? 2.4=3(m+4) 5(1-2w)+8w=15 If 3(x+1)=7 what is the value of 3x

### Word Problems : Break-Even Points

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a \$29 one-time activation fee and charges \$0.11 cents a minute. The second plan has no activation fee and charges \$0.15 cents a minute. After how many minutes of long distance calls will the costs of the two plans be equ

### ABCD is a trapezium in which AC is parallel to BD and AC

In this question ABCD is a trapezium in which AC is parallel to BD and AC is 4/5 times the length of BD....See attached file for full problem description. Find Image of C C1 A1C1 // B1D1 A1C1 must have x-coordinate = 1 B1D1 = 1 A1C1 = 1 = Therefore, C1 = (1, )

### Solving Equations With Exponents

((-1)^2 - 2)^3 - 4.5

### Solve: The Slope of a Perpendicular Line

Consider the line x+5y = 5. Please address the following questions: What is the slope of a line perpendicular to this line? What is the slope of a line parallel to this line?

### Rainstorms

Two rainstorms occurred in one week in a certain area. The first storm lasted 15 hours, and the second storm lasted 30 hours, for a total 1650ml of rain. What was the rate of rainfall for each of the two storms if the sum of the two rates was 75ml per hour?

### Solve the recurrence

Solve the recurrence T(n) = 2T(sqrt(n)) + 1 by making change of variables. The solution should be asymptotically tight. 2. Use a recursive tree to give an asymptotically tight solution to the recurrence T(n) = T(n-a) + T(a) + cn, where n > = 1 and c > 0 are constants.

### Word problem

Two rainstorms occurred in one week in a certain area. In the first rainstorm 35ml of rain fell per hour, and in the second rainstorm 40ml of rain fell per hour. Rain fell that week for a total of 55 hours for a total rainfall of 2075ml . How long was each of the two rainstorms?

### Recursive Definitions

I want to get a better understanding of how these problems are done. For Exercises #1-3, decide whether the sequences described are subsequences of the Fibonacci sequence, that is, their members are some or all of the members, in the right order, of the Fibonacci sequence. 1. The sequence A(n), where A(n) = (n-1)2^n-2 +

### Writing Equations from Word Problems : Intersecting Lines

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a \$26 one-time activation fee and charges 14 cents a minute. The second plan has no activation fee and charges 18 cents a minute. After how many minutes of long distance calls will the costs of the two plans be equal?