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Basic Algebra

Perturbation Theory

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 - 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

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 +

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

Quadratic equation

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?

Simplify and Divide

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 - 6x


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


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.

Solve the Algebraic Equation

Please see the attached file for the fully formatted problem. Solve the algebraic equation. (x-6)^1/2 = (x+9)^1/2 - 3

Solve an expression

One eighth of the square root of 7 less than a number is 2. What is the number?