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# Algebra

### Conic sections

1. When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. 2. Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 +

### Geometric Sequences Word Problems : Pennies on a Checkerboard

A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter's life. Mr. Brown insisted on givin

### Geometric Sequences

Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,...to find the following: a)What is r, the ratio between 2 consecutive terms? b)Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals. c)Using the formula for the

### Geometric Sequences

Use the geometric sequence of numbers 1, 2, 4, 8,...to find the following: a) What is r, the ratio between 2 consecutive terms? b) Using the formula for the nth term of a geometric sequence, what is the 24th term? c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?

### Describing Arithmetic Sequences

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? b) Using the formula for the nth term of an arithmetic sequence, what is the 101st term? c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms? d

### Solve the following equations

The square root of x^3=8 i know the answer but confused on how to show how i go it. please show steps to the following answer x-1=3 = >x=4 3 square root of x^2=4 anwer is: =>x=2

I need to evaluate the functions for the values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of x. f(x) = 3x + 2 f(x) = x^2 + 5x + 6 f(x) = x^3 + 3x^2 + 2x + 1 f(x) = e^x f(x) = log x

### Graph, degree of polynomial

1. Graph 3x+2y=6. Where do the points cross and how is the pair figured out? 2. Give the degree of 4x. 3. Solve the linear inequality by graphing. 3x + 4y <= 12 x + 3y <= 6 x >= 0, y >= 0 4. The demand and supply equations for a certain item are given by D = -5p + 40 S = -p^2 + 30p - 8 Find the eq

### Time Value

1)You would like to take a cruise in six years. The cruise currently costs \$4,250. You expect the price to increase by 4% annually. You can earn 5% on your savings. How much do you need to save at the end of each month so you will be able to afford your cruise in six years? 2)You invest \$250 in your savings account at the en

### Time Value of Money

How would I go about answering this problem? A work template is attached. Donna and Sherman Terrel are preparing a budget for 2003. Donna is a systems analyst with an airplane manufacturer, and Sherman is working on a master's degree in educational psychology. The Terrels do not have any children or other dependents. Donna e

### Find QR Decomposition to Solve a Least Squares Solution

How will you calculate a decomposition where is rotator, and is and use it to calculate the least square solution? And also deduce the norm of the residual. Please see the attached file for the fully formatted problems.

### Geometric and Arithmetic Sequences

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) Using

### Geometric Sequence : Ratio of Terms and Geometric Sums of First n Terms

Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27... to find the following: a) What is r, the ratio between 2 consecutive terms? b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? c) Using the formula for the sum of the first n terms of a geometric ser

### Common ratio of geometric series

Use the geometric sequence of numbers 1, 3, 9, 27, ... to find the following: a) What is r, the ratio between 2 consecutive terms? b) Using the formula for the nth term of a geometric sequence, what is the 10th term? c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?

### Sequences and Series : Difference between Terms and Sums of First n Terms

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) Using

### 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? Include the following in the answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadratic, ration

### Series and Functions: Real Life Examples of Arithmetic and Geometric Series; Relationship of Series to Functions

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

### Cauchy Sequences

Consider the real number iteration scheme x_n+1 = f(x_n) for n = 1, 2, ... with x_1 given. In addition, suppose there is a number 0 < p < 1 st lf(x) - f(y)l < = plx-yl for all x,y. a) Show lx_n+1 - x_nl < = p^n-1lx_2 - x_1l for all n. b) From this, conclude {x_n}_n is Cauchy.

### Proof: Sequences and Supremum

Suppose that the sequences {a_n}_n is bounded above and lim(b_n) exists. a) Prove that for all e>0 there is an N st that for all n>=N sup{a_k:k>=n} + b_n <=sup{a_k + b_k: k>=n} + e. b) Use this to conclude limsup(a_n) + lim (b_n) <= limsup (a_n+b_n) (all limits are n ---> infinit

### Proofs : Bounded Sequences

Suppose the sequences {a_n}_n and {b_n}_n are both bounded above. a) Prove that for all n in the naturals sup{a_k + b_k: k>/=n} is less than or equals sup{a_k:k>/=n} + sup{b_k:k>/=n} b) Use this to conclude: limsup (a_n + b_n) is less than or equals limsup(a_n) + limsup(b_n) (all limits are n--> infinity)

### For the equation x - 2(sqrt of x) = 0 perform the following:

For the equation x - 2(sqrt of x) = 0 perform the following: Solve for all values of x that satifies the equation Graph the functions y = x and y = 2(sqrt of x) on the same graph. Show the intersection of these two graphs. Please show your work to help me with the more difficult equations on my assignment. Thanks

### Initial and Future Value

You have decided to purchase some shares of stock for \$1000. After five years, the value of your purchase has grown to \$2000. a. Write a formula for the relationship between the future value of an investment and the initial investment amount. Use variables instead of actual quantities in your formula. Note what each variable

### What is critical path for this project? How long will it take to complete the project? Please draw a CPM network diagram for this project.

You are in the process of selecting and awarding a major contract as quickly as possible. Management has approved simultaneous advertisements in CBD (Commerce and Business Daily), over the internet and Global media (contract journals). Here are the activities for this project, constraints of each activity and the duration for ea

### Average Annual Return on Investment Formula

The average annual return for an investment is given by the formula r= (s/p)^1/n -1 where p is the initial investment and s is the amount it is worth after n years. The top mutual fund for 1997 in the 3-year category was Fidelity Select-Energy Services, in which and investment of \$10,000 grew to \$31,895.06 from 1994 to 1997

### Problem Set

11. Assume the total number of dollars (in billions) on entertainment in the United States from 1990 to 2000 can be approximated by the model S = 148 + 6.7t + 0.58t2. where t = 0 represents the year 1990. During which year was \$215 billion the amount spent on entertainment? (5 points) 12. Solve 3x2 - 10x = 8 by factoring

### Find the constant term in the expansion (1/(2x^3) + x)^20.

Find the constant term in the expansion of (1/(2x^3) + x)^20. [The constant term is the summand which does not involve any power of x. For example the constant term in 3x^2&#8722; 4x + 23 +9x^10 + 5/(3x^6) is 23.] [Note on notation: 2^3 means '2 to the power of 3', so 2^3 = 8] [The pdf file contains the question in pr

### Transaction between Achmet and Ali

13. Achmed and Ali were camel - drivers but one day they decided to quit their job. they wanted to become shepherds. They went to the market and sold all their camels. The amount of money (dinars) they received for each camel was the same as the total amount of camels they owned. With that money they bought as many sheep as

### select the best model.

(See attached file for full problem description) --- 1. The following gives the price in dollars of a round trip ticket from Phoenix to Portland, and the corresponding profit, in millions of dollars, for each price. For the data below, select the best model. Price (dollars) 200 250 300 350 400 450 3.09 3.51

### Theory of Computation : Non-deterministic finite state automaton

Give a non-deterministic finite state automaton that recognizes the language L subset {0,1}* that consists of all words w such that some appearance of two 0's in w is separated by an even number of 1's. (For example: the words 0010010110, 001101 are in the language but the words 0101110, 001001 are not.) (As a note, this i

### Writing Equations from Word Problems : Time and Distance, Two Moving Objects

At 2:00 p.m. bike A is 4km north of point C and traveling south as 16km/h. At the same time, bike B is 2 km east of C and traveling east at 12km/h. a. Show that t hours after 2:00 p.m. the distance between the bikes is: square root (400t^2 - 80t + 20) b. At what time is the distance between the bikes the le