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# Basic Algebra

### How to get a million by spelling a word whose letters' product=1000000

If we assign number values to letters in the following way: A = 26, B = 25, C = 24 and so on until Y = 2 and Z =1, spell a word such that the product of its letters is as close to a million as possible. Explain how you went about solving this problem.

### Algebraic Equations : Reciprocal Equations

As provided by E. Galua theory the general algebraic equations for a polynomial of fourth order ax^4 + bx^3 + cx^2 + dx + f=0 (*) is the maximum order type of algebraic equations the solution to which one can write down in radical expressions. Among all the equations of fourth

### Algebra: Word Problem - Relative Velocity

A mo-ped can travel 60 miles in 2 hours less time than a bicycle can travel 50 miles. The mo-ped is traveling at a rate of 10 miles per hour faster than the bicycle. 1. How fast in mph is each traveling? 2. How long will it take each to travel their respective distance?

### Algebra : Puzzle Problems

Please see the attached file for the fully formatted problems. 1) Have you ever seen the written form of the Sanskrit language? If so, you probably are amazed at how different this ancient language from India looks from ours. Some English words, however, are based on Sanskrit. For example, cup comes from the Sanskrit work kup

### Miner and Bickford's Fuse : How to get a Fuse of Specific Length

You are a miner and you have three pieces of Bickford's fuse of equal length. You need only 3/4 of one of them. You have no ruler or other measurement device with you. You cannot also bend the fuses as they are old and can be broken at any point while being bent. You only can ignite them from any end and extinguish at any moment

### Algebra : Remainders

What is the remainder when the product of one hundred 5's is divided by 7? Please be detailed in your response.

### Algebra : Word Problem - Remainders

A large purse is full of coins. If you count them by 13's, 23's, or 31's, there will be one left over. If you count them by 73's there will be none left over. How many coins are there in the purse? Please be detailed in your response.

### Exponential Equations : Word Problem

The population of the green deer in 1999 was 17000. In 2003 there were only 15000. Write an exponential equation to express the poulation decrease p(t) in terms of t years.

### Word Problem - How many Cookies?

Dad made cookies. Dad ate 1 cookie. Dave ate 1/2 dozen cookies. Kate ate 1/2 of what Dave ate. Henry & Julie each ate 1/3 of what was left. Then Jake ate 1/2 of what was left. Mom ate 1 cookie. There was 1 cookie left. How many cookies were baked?

### Perturbation Theory Equation

Find the real roots of the equation x^5 + ex-1=0 approximately to O(e^2) usind perturbation theory. Compare the accuracy of the perturbative solution for e=0.001, 0.1, and 1

### Perturbation Theory Equation

Find the real root of the equation x^5 + ex - 1= 0 approximately to O(^2) using perturbation theory.

### Algebra : Word Problem - Sums and Products

During the census, a man told the census-taker that he had three children. When asked their ages he replied, " The product of their ages is 72. The sum of their ages is my house number." The census taker turned around and ran outside to look at the house number displayed over the door. He then re-entered the house and said, "

### Algebra: Word Problem - System of Equations

Three people play a game in which one person loses and two people win each game. The one who loses must double the amount of money that each of the other players has at that time. The three players agree to play three games. At the end of the three games, each player has lost one game and each has \$8. What was the original st

### Algebra Word Problem: Relative Speed

A column of soldiers 25 miles long marches 25 miles a day. One morning, just as the day's march began, a messenger started at the rear of the column with a message for the man at the front of the column. During the day he marched forward, delivered the message to the first man in the column and returned to his position just as

### Algebra : Word problem - Time and Distance

Two swimmers start at opposite ends of a pool 89 feet long. One person swims at the rate of 19 feet per minute and the other swims at a rate of 53 feet per minute. How many times will they meet in 33 minutes? Plese try to give a detailed response as my answer is not as important as the thought processes that I must understa

### Area of Rectangle under a Parabola and Sectors in an Arc

Proving the area of a shaded rectangle under a parabola and then differentiating the expression. Minimizing the perimeter of sectors in an arc. Please see the attached file for the fully formatted problems.

### Find a solution in the form of a power series for an ODE

Please see the attached file for the fully formatted problems. Find a solution in the form of a power series for the equation y" - 2*x*y' = 0 (ie find 2 linearly independent solutions y1(x) and y2(x)). After doing that, note that the equation can also be solved directly by integration: y"/y' = 2x ln(y') = x^2 +

### Inequality Proof Function Provided

Prove that (1+x)^n>=1+nx, where n>=1, x>=0

### Semitones and Notes from a String

If a string of length 10cm plays a note G when plucked, by how much, to the nearest centimeter, must the string be shortened to play the note B, four semitones above this G? Chose the one correct option. Options A. 6cm B. 11cm C. 16cm D. 21cm E. 25cm F. 30cm G. 33cm H. 50cm

This question concerns the quadratic equation 9x^2 - 42x+49=0 Choose the three true statements about the solution(s) of this equation Options. A. The equation has no solutions B. The equation has one solution. C. The equation has two solutions D. x= 0 is a solution of the equation E. x= 2.333 is a solution of th

### Picking a Correct Method

How would I determine which method to use for simplifying a particular complex rational expression?

### Polynomial division and multiplication

PART ONE: Simplify the following: (-3w^2 n)(2n^2)^4 A) -6w^2 n^7 B) -48w^2 n^7 C) -48w^2 n^9 D) 48w^2 n^7 PART TWO: Perform the following divisions: (32x^6 y^4 - 24x^2 y^9 + 4x^2 y) / (4x^2 y) A) 8x^4 y^3 - 6y^8 + 1 B) 8x^3 y^4 - 6y^8 + 1 C) 8x^3 y^2 - 6xy^7 + 1 D) 8x^4 y^3 - 6xy^8 +

### Polynomial Division Performed

PART ONE: solve: (32x^6 - 24x^2 y^9 + 4x^2 y) / (4x^2 y) A) 8x^4 y^3 - 6y^8 + 1 B) 8x^3 y^4 - 6y^8 + 1 C) 8x^3 y^2 - 6xy^7 + 1 D) 8x^4 y^3 - 6xy^8 + 1 PART TWO: solve: (15m^3 + 26m^2 - 11m - 6) / (5m-3) A) 3m^2 + 26/5 times m - 5 and 1/5 B) 3m^2 + 2m- 2 C) 3m^2 + 7m - 2 D) 3m^2 + 26m

### Polynomial Division and Square Roots

PART ONE: solve: (3n^5 w)^2 /(n^3 w)^0 A) 0 B) 9n^7w C) 6n^4w D) 9n^10w^2 PART TWO: solve: 9c^7 w^-4 (-d^2)/(15c^3 w^6 (-d)^2) A) 3c^4d^2/5w^10 B) 3c^4/5w^2 C) 3c^4/5w^10 D) -3c^4/5w^10 PART THREE: solve: 5m^-3 /6^-1 m^-2 A) -5m/6 B) 30/m C) 30m D) -5/6m PART

### Solving equation using natural logarithm

4e^2x = 53 My problem reads: 4e to the 2x power equals 53. When I plug my solution back in to check, I find that it is incorrect. Please send me step-by-step explanation because I do not understand the concept and my textbook has no examples for guidance.

### Proving an inequality function

Prove the inequality. (1+x)^3 >= 1+3x for x>=0

### Logarithm Equation: Solve for x

Find a solution for the following equation logx + log(x-3)-1=0

### Solving for a variable in a logarithmic equation.

Solve for w. log (3w-1) + log w = 1

### Quadratic Function: Vertex, Symmetry and Maximum/Minimum Value

For each quadratic function find: a. the vertex b. the line of symmetry c. the maximum or minimum value Then graph the function. Please show your work. y = -4x^2 - 7x + 2 Please see the attached file for the fully formatted problems.