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Basic Algebra

Nilradicals and Prime Ideals

Assume R is commutative ring. Prove that the following are equivalent: a) R has exactly 1 prime ideal b) Every element of R is either nilpotent or a unit. c) R/N(R) is a field Here N(R) denotes the nilradical of R. The set of nilpotent elements form an ideal called the nilradical of R

Revenues Using Logarithms

Equation - R=12log10Days In 10 days revenue = $12 million how long will it take to reach $36m Answer is 1,000 days but I cannot figure out how this happened. I tried 36=12log10days 36/12 = log10days 3 = log10days 3 = days Incorrect

Coefficients of Quadratic Equations

Quadratic Equations Write three quadratic equations, with a, b, and c (coefficients of x2, x, and the constant) as: 1. Integers 2. Rational numbers 3. Irrational numbers See attached file for full problem description.

Solving Equations

(m-7)^2 = 25 (w+4)^2=16 √x^2 + 3x +6 =4 √x - √x-1 = 1 1+ √x+7 = √2x + 7

Simplifying Radicals

Simplify each radical expression. Assume all variables represent positive real numbers. Here are six problems. √48 √20n^25 4√32m^11 Find the domain of each radical expression. Use interval notation 4√-5x-1 Simplify the expressions involving rational exponents. Assume all variables re

Tangent Lines and Logarithmic / Exponential Functions

Tangent Line and Logarithmic/Exponential Functions This project is going to consider the relationship between a point (a, b) on the natural logarithmic and exponential functions and its relationship to the intercept of the tangent line to the respective functions at the point (a, b). Hint: Recall the distance between two

Fermat and Wilson's Theorem

1. If and are distinct primes prove that for any integer a, Use Fermat's theorem 2. Show that if and are both primes, then 4[ (mod Use Wilson's theorem. 3. Let be an odd prime. Prove that if g is primitive root modulo and (mod is not Use the binomial expansion See attached file for full

Solve: Simplifying Expressions

Simplify the following. Make sure to show all the steps involved. Expression: (3t^2 - 8t +3) + (-5t^2 + 4) - (t^2 + 5t - 3)

Algebra Word Problems

The payment sugar beet growers receive is based on the sucrose content of their delivered beets. A sample is taken from each load of beets and the sugar content in the beets is determined by polarimetry of the beet extract. In a typical situation 50 grams of pulverized beet tissue is homogenized with 360 mL of dilute aluminum

Simplifying Radicals

Raising each side to a power to eliminate radicals. See attached file for full problem description.

Simplifying Expressions

Find the LCD for the rational expression, and convert to an equivalent rational expression with the LCD as the denominator. See attached file for full problem description.

Greatest Common Factors (GCF) Word Problem

Happy Hector and Party Paul are each having a catered party at Fun Factory. Hector's party is in the hall and Paul's party is on the Patio. The catering manager of Fun Factory explained the rules to Hector and Paul. Both Hector's party in the Hall and Paul's party on the Patio must have the same size table, that is, for example,

Solving equations

I am trying to figure the steps with this problem since there is a negative adjacent the square root x-3-radical sign x-1=0 also x + 7/x=8 Need to know the next steps

Solving Inequalities Word Problems

How do you solve the inequality (x + 1)(x - 6) < 0, and express the solution using interval notation. If an object is shot upward with an initial velocity of 240 feet per second so that its height s (in feet) above the ground after t seconds is given by s = -16t2 + 240t. For what values of t will the object be at least 416 f