Share
Explore BrainMass

# Basic Algebra

### It is an explanation of a theorem in radius of convergence of power series. &#8734; &#8734; Theorem:- &#8721; anzn is a power series and &#8721; nanzn - 1 is the power series obtained n=0 n=0 by differentiating the first series term by term. Then the derived series has the same radius of convergence as the original series.

Complex Variable Radius of Convergence of the Power Series

### Radius of Convergence of the Power Series

Complex Variable Radius of Convergence of the Power Series

### Fourier Sine Series Solution - Wave Equation, Interval and Boundary Conditions

Please see attachment for complete questions (for the below "..." indicates equation to be found in attachment). Thanks! (a) Write down the Fourier (sine) series solution u(x,t) of the wave equation ... on the interval ... satisfying the boundary conditions ... and the initial conditions ... (b) Use the identity ... to sh

### Area (Basic Algebraic Manipulation)

The three remaining blocks of land in a new estate have a total area of 2029m2. The second block is 45m2 more than the first block and the third block is 65m2 less than the first block. What is the area of the first block?

### Residues, Singularities and Conjugate Points

Please try to use the example method. 1. F(s) = (2s^3)/((s^4) - 4) Please see attachment for proper format.

### Independent and Dependent Variables

In a typical algebraic expression, there are two variables: an independent variable and a dependent variable. The independent variable is the number or the value that can change. The dependent variable's value depends on the value of the independent variable. For example, in the following formula, X=Y*5 Y is the independent

### Passing a Competency Test

I am trying to study for a competency test, but I only had intermediate algebra in college 19 years ago! I am looking for web resources and any other material that you can provide that can help me prepare for this test. Thank you.

### Find an infinite set of numbers n for which some player

Players 1, 2, 3, ..., n are seated around a table and each has a single penny. Player 1 passes a penny to Player 2, who then passes two pennies to Player 3. Player 3 then passes one penny to Player 4, who passes two pennies to Player 5, and so on, players alternately passing one penny or two to the next player who still has some

### Residue Systems: Modulo

5. If m = 11, then a reduced residue system modulo m is 1,2,3,4,5,6,7,8,9,10. Exhibit the pairing of each of the preceding numbers with its inverse modulo m (like Chinese remainder theorem). 7. What is the remainder when 41^5 is divided by 3? When 473^38 is divided by 5? 8. Prove that if p is a prime congruent to 1 modulo

### Green's Theorem (Divergence)

? Let D a domain on the plane bounded by a curve C. by applying Green's theorem (in divergence form) to a conservative vector field with potential f, defined on d, show that before attempting this question, recall what is a conservative vector field, as well as the definition of the laplacian . ? Use the divergen

### College Algebra I

1.)The following formula can be used to convert from degrees Fahrenheit, F, to degrees Celsius, C: C= 5/9*(F -32) Gold is liquid for Celsius temperatures C such that 1063 degrees <= C < 2660 degrees. Find a comparable inequality for Fahrenheit temperatures. 2.) The following mathematical model: w = 125 (6400/6400 + x)^2

### Modern algebra

I am stuck with this question. If phi : F -> R is a nonzero homomorphism from a field F to a ring R, show that phi is one-to-one (Hint: recall that for a ring homomorphism, phi is one-to-one if and only if Ker(phi)={0}. ) Can you help with this? Many thanks in advance

### Inequality Interval Functions

10 algebra problems - work must be shown so I can understand how to compute. Examples of questions: --> Solve: x2 - 8x + 20 = 5 --> Solve by quadratic formula: -3x2 - 2x + 5 = 0 --> The crop yield in bushels for a field of tomatoes is 10x2 - 80x + 200 where x is number of pound of fertilizer used. a) How many pounds

### Probability of Quadratic Questions and Real Roots

Please use words to describe the solution process: What is the probability that the quadratic equation ax^2 + 2bx + c = 0 has real roots? Note: you must first make sense of the question. What distribution are you putting on the variables a, b and c? Pick one that makes sense and isn't too hard to deal with.

### Gradient of Temperature in a Nebula

Suppose that distances are measured in light-years and that the temperature T of a gaseous nebula is inversely proportional to the distance from a fixed point, which we take to be the origin (0,0,0). Suppose that the temperature 1 light-year from the origin is 200 degrees Celsius. Find the gradient of T at (x,y,z). f = __

### Cachy's Inequality

Let f be an entire function such that |f(z)|&#8804;A|z| for all z, where A is a fixed positive number. Sow that f(z) = az where a is a complex constant. Please see the attached file for the fully formatted problem.

### Financial Math

Please explain to me where the .5675 in the following formula came from: v_0 = .5675(110-E) This is from the solution to problem 6, lecture 6. I don't understand where .5675 came from, but I understand the solution. I'ved attached lectures 5, 6, and the solution to lecture 6. The formula for a state price vector i

### Solving Rational Expressions

I'm having a difficult time figuring out some of these! For some reason the -1 in this problem is throwing me off - I think! Here's what I came up with last time, I keep getting a different answer each time I work it. 3/(y+5) -1 = (4-y)/(2y+10) 3/(y+5)-1 = (4-y)/2(y+5) y is not equal to -5 LCD is 2(y+5) 2(y+5)*3/(y+5) =

### Cauchy-Riemann Equations in Polar Form

Please see the attached file for the fully formatted problems. 8. Let a function f (z) = u + i v be differentiable at a nonzero point z0 = r0 e(i&#952;0). Use the expressions for ux and vx found in Exercise 7, together with the polar form (6) of Cauchy-Riemann equations, to rewrite the expression f &#900;(z0) = ux + i vx

### Simplify using Synthetic Division

(3x3 -4x + 5)/(x+4)

### Synthetic Division

See attachment: SIMPLIFY USING SYNTHETIC DIVISION

See attachment.

See attachment.

### Exponential and Logarithmic Functions : Capacitance

If a capacitor with a capacitance of 0.000005 farads is wired in a circuit with a total resistance of 5000 ohms (the standard unit of electrical resistance), how long must the capacitor be wired to a source voltage to reach 50% of its maximum charge? (The Hint was: Begin by expressing q as 0.5Q)

### Inequalities, Graphs and Maximizing Profit

Please see the attached file for the fully formatted problems. Solve each inequality state the solution set using interval notation and graph the solution. Solve rational inequality state and graph the solution set. A chain store manager has been told by the main office that daily profit P is related to the number of

### Algebraic Properties 8b

Given the algebra <S;f,g,a>, where f and g are unary operations and a is a constant of S, suppose that f(f(x)) = g(x) and g(g(x)) = x for all x &#949; S. Show that f(f(f(f(x)))) = x for all x &#949; S.

### Crytic math questions

Cryptic Math p Q R S T U V W X 1. Each letter stands for one of the numbers 1 - 9. 2. S + Q = V and S is smaller than Q. 3. P = R + U. 4. In one of the diagonals, all 3 numbers are perfect squares. 5. In one of the two diagonals, (P, T, X or R, T, V) the 3 numbers are in ascending orde

### Quadratic Equations (Solve by Factoring and Square Root)

Quadratic Equations: Please show how arrived at answer. Thank you. 1.) Solve quadratic equation by factoring. Solve: 2y^2 - 3y - 2 = 0 2) Solve quadratic equation by taking square root. Solve: (2 x + 2)^2 = 64

### Question about Quadratic Equations: Completing the Square

Solve quadratic equation by completing the square. 4x^2 + 8x + 1 = 0

### Removing the Demonimator by Multiplying Both Sides By LCD

When we solve a rational equation, why is it OK to remove the denominator by multiplying both sides by the LCD? Why can you not remove the denominator when simplifying a rational expression? Provide examples to support your discussion. 2. What are extraneous solutions of an equation? Why do they sometimes occur when we solve