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# Basic Algebra

### 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.

### Limits of logarithmic functions

"Prove that: the limit as x goes to infinity of (ln(x))/(x^p)=0 for any number p>0. This shows that the logarithmic function approaches infinity more slowly than any power of x."

### Isolated Singluar Point: Pole, Removable Single Point and Essential Single Point

1. In each case, write the principal part of the function at its isolated singular point and determine whether that point it a pole, a removable single point, or an essential singular point {see attachment for expressions} Please specify the terms that you use if necessary and clearly explain each step of your solution.

### Simplify the expression.

1 over x+5 -2 over x-5 +6 over x^2-25

### Simplify the Expression

X^3+y^3 over x+y divided by x^2-xy+y^2 over x^2+y^2

### 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

### Solving Inequalities: Solve for X

A) 11x-2x+13>9x-(5-6x) b) Find the solution set in interval notation: 5/w-3 ≤4/w+3. See the attached file.

### Detailed Explanation to Solve Algebraic Problem

Solve: x-1 > 1 and -x-2 <1.

See attached

### Proving the Mod

Prove that: if bd= bc (mod p) where p is a prime (and p does not divide b) , then d= c (mod p).

### 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

### Solve the rational inequality. State and graph the solution set.

1) a/(a+2)>0 2) x/(x+2)>-1 3) (x+3)/x=<-2

### 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.

### Inequalities and Quadratic Formula - 5 Math Problems

1. Solve the inequality...State the interval(s) where the inequality is valid using the symbols <, >. 3. Solve problems with the quadratic formula. 3. 4x2 - 12x - 7 = 0 (See attachment for full questions)

### 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

### Banach Space and Hamel Dimension

Suppose that &#61541; is a Banach space. Prove that the Hamel dimension of &#61541; is not Please see the attached file for the fully formatted problem.

### Sample Point Of Intersection Calculation: Quadratic With Line

Find the points of intersection algebraically of the graphs of the equations y=x^2-3x+4, and 2x-2y= -8 need to see the algebra got a bit lost as to how to get from Solve equations: Take y=x^2-3x+4 into 2x-2y=-8, we got: Here x-x^2+3x-4=-4 to here We got: x1=0,

### Slope-intercept form

Write the slope-intercept form of the equation of the line that passes though point (6,-9) and is perpendicular to the line y+3x=9

### Find the equation of the tangent plane to a surface at a given point.

Find the equation of the tangent plane to the surface at the point . Please see the attached file for the fully formatted problems.

### Solving a Quadratic Equation

When I work the problem square root of 4x^2 + 15 - 2x = 0, by using the quadratic equation, my answer is a real number because I end up with the square root of 256 which is 16. Should I square both sides 1st or how do I solve the equation?

### Find the difference quotient.

Find the difference quotient f(x+deltax)-fx)/deltax for the function f(x)=2x^2-4x-3.

### Unit multiplies converted

Use two unit mulipliers to convert 100CM2 to square millimeters

### 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) =

### 10 Algebra Problems : Solve Equations and Quadratics

Please see the attached file for the fully formatted problems. #1 Solve a2 - 9a = -14 #2 Solve 2e(e +1) = 12 #3 Solve #4 Solve #5 Solve for z #6 Solve the equation and check for extraneous solutions. #7 Solve #8 Solve by completing the square. s2 + 8s -