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# Basic Algebra

### Simplify Seven Trigonometric Expressions

1. [sin(x+b) + cos(x+b)]/[cos(x+b)-sin(x+b)]= 2. cos^2(x+b)-cos^2(x-b)= 3. tan x + cot 2x = 4. tan (45 + x) -tan (45 -x)= 5. tanx - cotx + cot 2x = Plus two more...

### Word Problems, Simplify, Area, LCM, Solve for X and Hypotenuse

Divide (12a squared - 25a -7 divided by (3a-7) (x cubed - 6x squared + 7x -2 divided by (x-1) A circle has a radius of 10 inches. Find the increase in area that occurs when the radius is increased by 2 in. Round to the nearest hundredth. An object is released from the top of an building 320 ft high. The initial velocity

### Derivatives and Integrals of Exponential and Logarithmic Functions (24 Problems)

1. Find the derivatives for the following functions ("^" means "to the power of", sorry I can't do double exponents on my keyboard) : a. f(X) = 100e10X b. f(X) = e(10X-5) c. f(X) = e^X3 d. f(X) = 2X2e^(1- X2) e. f(X) = 5Xe(12- 2X) f. f(X) = 100e^(X3 + X4) g. f(X) = e^(200X - X2 + X100) 2. Fi

### Functions : Graphs, Limits, Continuity, Equation of Line from Two Points, Equation of Line from Slope and a Point and Linearity (15 Problems)

1. Take the function f(X) = (X-1)/X a. What does this function equal when X = 0, X = 1, and X =2 ? b. How about when X =100, X = 1000, and X = 10,000? c. Describe in words what a graph of this function would look like. d. What would you say the limit of this function is as X approaches infinity? You can use logic or

### Equation Given Two of the Complex Conjugate Roots

The equation x^4 - 18x^3 + 121x^2 - 368x + 420=0 has complex conjugate roots (4+j2) & (4-j2). By a process of division and solving a quadratic equation, find all the roots and hence write down all the factors of : x^4

### Solve using the quadratic equation.

1) -2X^2 - 1 = 0 2) &#8730;X + 4 = 0

### Prove using Mathematical Induction

If x > 1 is a given real number, then for every integer n > or equal to 2, (1 + x)^n > 1 + nx.

### Quadratic Equation and Equilibrium Concentration

The Quadratic Equation. Consider the reaction N2O4(g) = 2 NO2(g) at 25 C in a 5.00-L container. Use the quadratic equation to determine the equilibrium concentrations of the N2O4 and NO2 if the initial amounts are 0.100 mol N2O4 and 0.00 mol NO2. The value of the equilibrium constant for the reaction is 4.63 x 10-3 at 25 C

The Quadratic Equation. Question: Consider the reaction 2 COF2(g) = CO2(g) + CF4(g) at 1000 degrees Celsius in a 5.00-L container. Use the quadratic equation to determine the equilibrium concentrations of all reactants and products if the initial amounts are 0.105 mol COF2, 0.220 mol CO2, and 0.055 mol CF4. The value

### Find roots and solve a quadratic equation given two complex conjugate roots.

The equation {see attachment} has complex conjugate roots (4+j2) & (4-j2). By a process of division and solving a quadratic equation, find all the roots and hence write down all the factors of ... {see attachment}

### Congruences : Primes, Inverse Modulo, GCD and Wilson's theorem

Please assist me with the attached congruence problems (hint: use Wilson's Theorem) a)Prove if a,b,c Z, N and gcd (c, ) = , then ac bc(mod ) if and only if a b (mod ). b) Let a Z, N, and p > 2 be a prime. Prove that a is its own inverse modulo p if and only if a 1 (mod p ). C) Let a,b Z, N .prove that ax

### Algebra Application Word Problem: Finding Ages

Adding two years to the boys age would make him a quarter of his father's age. Five years ago his father was one year less than ten times his sons age. Determine the age of the boy and his father. See the attached file.

### Metric Conversions: km^2 to mm^2

Please provide the step-by-step answer to how to come to the answer given in the practice test. Problem (also attached): 36 km² to mm² = ?

### Find the Irrational Factors of a Quadratic Equation

Find the irrational factors of 7x²-9x-2 expressing the answer to two decimal places.

### Solve: Formula Weight

Question: Determine the formula weight of K3PO4. a. 134.1 amu b. 185.1 amu c. 212.3 amu d. 173.2 amu e. 228.3 amu.

### Graphing an Inequality

Graph: 3x - 2y < 6 ....Must show graph.

### Simplify the Expression: Solve and Simplify

Solve and simplify: 26/3- 23/6 13(6t+4r)-2(10t-8r). See the attached file.

### Simplify the expressions.

Please solve the attached expressions. Please see the attached file for the fully formatted problems.

### Graphing Equalities and Inequalities

The following must be graphed on 2 seperate graphs * Graph y = -1/2x +3 * Graph 3x - 2y < 6

### Solving Algebraic Equations for a Given Variable

Solve: 6/45 = 4/x

### Solving Algebraic Equations for a Given Variable

Solve for y in the following equation (7y/8) + (1/8) = -(3/2)

I received your response to my problem the square root of 12 times the square root of 2 minus the square root of 7. I did not indicate that the square root of 2 minus the square root of 7 was in parenthesis. I am having difficulty understanding this concept, and my final exam is tomorrow.

The square root of 12 times square root of 2 minus square root of seven.

### Statistic terms

Suppose you calculate a mean of a population and you want to know how representative that mean is of a random data point in that population. In other words, is the data bunched tightly around the mean, or is it more loosely distributed over the possible range of values? An example would be high temperatures in July versus high t

### Convert Equation Into Given Form (Numerator Dependent on S)

[(Kp * s + Ki)/s] * (K * Km) / [s[(Ls+R)(Js+b) + K^2m)]] I want to get the above into the form of d / [s^3 + a s^2 + b s + c] Please give complete solution. I want the numerator dependent on s. All the other values are given other than s. I just need it into that form.

### Find the Vertex and Intercepts of a Function

See attached file 1. Write the polynomial in descending order and find the degree: x2 - x5 + 2x4 - 1 2. Subtract 3x -5 + 2x3 from 3x3 - 1 3. Multiply: (9x - 2) (x + 4) 4. Multiply (5x - 6y) (5x + 6y) 5. Simplify 6. Divide:

Questions (also attached): Graph each equation and state its domain and range. 27) g(x)= x 2 + 2 28) f(x)= x 2 - 4 32) y= 2x 2 + 3 Graph each square root and state its domain and range. __ 34) g(x) = &#8730; x - 1 _____ 36) f(x) = &#8730;x + 1

### Linear inequalities and conditions

Compare the amount of information conveyed to a collaborator when you inform her that an object is located: At a point (1,3) On a line y=x+1 Below this line, so that its coordinates satisfy y < x+1 When are you being the most specific, and when are you being the most vague? What happens as you increase the number o