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# Basic Algebra

### Binomial Theorem for Euler's Formula

(a)Express e-½iθ-e½iθ in trigonometric form, and show that (1-eiθ)2 = -4eiθsin2 ½θ. (b) For a positive integer n, series C and S are given by where is binomial coefficient. By considering the expansion of (1-y)2n show that C = (-4)n cos nθsin2n (½θ) , and find a similar expression for S.

### Algebra and velocity

When a ball is thrown up into the air, it makes the shape of a parabola. The equation S= -16t^2 + v*t + k gives the height of the ball at any time, t in seconds, where â??vâ? is the initial velocity (speed) in ft/sec and â??kâ? is the initial height in feet (as if you were on top of a tower or building). Make up a sc

### Assessment of integer roots

Note the polynomial form P(x) = x2 - a. And, note that the two linear factors ( x + a ) ( x - a ), when multiplied together, yield ( x + a ) ( x - a ) = x2 - a. Consequently, we note that an equation of the form x2 - a= 0 can be factored as ( x + a ) ( x - a ) = 0, giving the two zeros of our equation x = a, -

### Phone company charges are assessed.

A phone company charges a different rate for a local call than a long distance call. A local call costs \$0.15 per minute and a long distance call costs \$0.45 per minute. Last month a customer made 320 minutes of calls. If the total cost of the calls was \$99.00, how many minutes of each type of call did the customer make? See

### Determine the factorability of a trinomial.

How would you use this procedure (factoring a quadratic expression with leading coefficient a = 1) to determine if a given polynomial is prime, that is, determine that it cannot be factored into a product of two linear polynomials

### Algebra: Equations for Height of Buildings

The height of a building is 1411 ft. How long would it take an object to fall to the ground from the top? Use the formula s=16t^2, where s is the distance, in feet, traveled by an object falling freely from rest in t seconds.

### Algebra Problems

Part 1: find a record-breaking temperature (in degrees Celsius) for a town or city in a country other than the United States. Include the name of the town and country along with the temperature, and what record was broken. Give the formula for converting degrees Celsius to degrees Fahrenheit. Using the formula, show how to conve

### Rate per hour

2 mechanics worked on a car. the 1st mechanic worked for 10 hours. the second mechanic worked 15. the total they charged was \$1525. What was the rate charged per mechanic if their total rates combined = \$130?

### Alternate ways to solve a problem

Read the problem below. Then, describe two or more alternate ways to solve this problem. A farmer sends his daughter and son out into the barnyard to count the number of chickens and pigs. When they return the son says that he counted 200 legs and the daughter says she counted 70 heads. How many pigs and chickens does the f

### Pythagorean theorem is utilized.

1.The formula r=2sqrt(5L) can be used to approximate the speed r, in miles per hour, of a car that has left skid marks of length L, in feet. How far will a car skid at 30mph? 2.What does it mean to refer to a 20 inch TV set or a 25 inch TV set? Such units refer to the diagonal of the screen. A 25 inch TV set also has a wid

### Evaluating as Linear Equations or Not Linear Equations

1. Determine which of the following are linear equations and which are not linear equations. State the reason for your answer. (a) x + y = 1000 (b) 3xy + 2y + 15z - 20 = 0 (c) 2xy + 4yz = 8 (d) 2x + 3y 4z = 6.

### Algebra: Equations

1. How can you determine whether a system has no solution by graphing? 2. Solve by graphing: y=x-3 y=-x+1 3. Solve by the substitution method. Determine whether the equations are independent, dependent, or inconsistent. 3y-x=0 x-4y=-2 4. Ticket sales. Tickets for a concert were sold to adults for \$3 and

### Assessing the Area of a Rectangle

1. A rectangular box with volume 7 cubic metres has a square base with side length x metres. Express the surface area S of the box as a function of x. S=_______ 2. The diameter of a spherical balloon is 8 cm. Air is pumped into the balloon to increase its diameter by x cm. Express the increase in volume of air inside the

### How fast does each bicyclist travel?

1. Kathy bicycles 5 km/h faster than Javier. In the same time it takes Javier to bicycle 57 km, Kathy can bicycle 72 km. How fast does each bicyclist travel? 2. The office jet printer can copy Lisa's dissertation in 8 min. The laser jet printer can copy the same document in 10 min. If the two machines work together, how

### Unit Price for Product Sale

DQ 3.1 - Unit Price Find a product for sale that comes packaged in different sizes. Compute the unit price (e.g. dollars per ounce, dollars per foot, dollars per megabyte, etc.) for two of the available sizes. Which is the better bargain? Write an equation describing the relationship between price, P, size S, and unit pric

### Algebra

1. Graph y=x-1 List at least five points on the line 2. Graph 2x+y=6 Find the x and y intercepts. 3. Find the slope of the line through (1/3, 2) (-1/3, 1) 4. Graph the line through (2,3) with slope 1/2 . 5. Write an equation for the line in the following graph. Use slope and intercept form if possible. (

### Need Assistance with Algebra

Show all work, and use Equation Editor or MathType to format all equations. 2.1-56 Solve 2.2-36 Solve 2.3-86 Solve 2.4-30 Solve for x. 2.4-84 Finding the list price. Find the list price if there is a 12% discount and the sale price is \$4400. 2.5-20 Write an algebraic expression for two numbers that d

### Additional and Multiplication Principles Solving

I need help with the problems in the attached document. Please provide step-by-step instructions so that I can check my problems to make sure I did them correctly. 1. Solve x - 3 = -7 2. Solve x - 5 = 25 3. Using the addition principle solve 15 = n - 2. Be sure to check. 4. Solve using the multiplication principle. Be sur

### Investment: portfolio fraction

Helen has 1/5 of her portfolio in US stocks, 1/8 of her portfolio in European stocks, and 1/10 of her portfolio in Japanese stocks. The remainder is invested in municipal bonds. What fraction of her portfolio is invested in municipal bonds? Please show work in reach the solution. Thanks.

### Give an example of a logarithmic equation that can not be solved and explain why it can not be solved.

1. Solve for x in the following equations. a. log-base-3(x - 5) + log-base-3(x + 3) = 2 b. log-base-7(x) + log-base-7(x - 1) = log-base-7(2x) 2. Show that the following statement is true. Please refer to the attachment for the statement. 3. A quantity of oxygen gas had 16.32g of the radioactive isotope oxygen-19 i

### Steps to Solve Linear Equations

Discuss the following: I. Given a 1-variable linear equation 10z-4=86. Explain the techniques, and show the steps used for solving this equation. Check if the solution is correct. II. Using the same 1-variable linear equation in I above, change the linear equation to a linear inequality (Use either < or >). Explain the tec

### Are the two zeros of this equation integers, rational numbers, or irrational numbers?

DQ 6: How would you express the zeros of the equation x2 - 2 = 0 ? Are the two zeros of this equation integers, rational numbers, or irrational numbers? DQ 7: Note the cubic equation x3 - 6x2 + 11x - 6 = 0. I will claim that x = 1 constitutes a root of that equation ( replace x by 1 in the equation to verify ).

### Burnside's Formula

There are 70 = C(8,4) ways to color the edges of an octagon, with four black and four white. The group D8 operates on this set of 70, and the orbits represent equivalent colorings. Count the number of equivalence classes. D8 is the dihedral group associated with an octagon. Please refer to the attachment for more details.

### Females who Live with Non-relatives

The table below shows where people over 65 in the US live. A total of 23% of elderly men live either alone or with relatives. The sum of double the percent of men who live alone and triple the percent who live with relatives exceeds the percent of US women over 65 who live with their spouse by 13%. What percent of elderly men

### Revenue per available seat mile (RevPASM)

Alaska Airlines had passenger revenues of \$2.644 billion with a total of 24.22 billion available seat miles. Their reported load factor (average capacity usage) was 77.3% and RevPASM was 10.9 cents. With all other factors remaining constant, what would you project for RevPASM if Alaska Airlines could successfully increase the

### Ordered Pair Solution and Graphing

Chalkboard Activity Please pick 5 questions from the list below. Solve those 5 problems, showing your work, and submit them to your Individual Forum. ________________________________________ Problem Set 1 (choose one) 1. Decide if the ordered pair (-3,5) is a solution to 9x + 7y = 8 and 8x-9y = -69 2. Decide if the

### Algebra: Word Problem

Suppose wheat and sugar are two basic ingredients necessary to bake two items: a loaf of bread and a muffin. A baker has 25 pounds of wheat and 5 pounds of sugar. To bake each loaf of bread, the baker needs to use 1.3 pounds of wheat and 0.5 pounds of sugar. a. Set up the inequalities representing the baker's possible cho

### Math: Linear Inequalities

1.What is the situation when two linear inequalities have no solution? 2.What are the conditions when the solution of a system of linear inequalities will be in the first quadrant? 3.Why is it true that at x-intercept, the value of y is 0, and at y-intercept, the value of x is 0?

### Two Rational Expressions

#1) Subtract these two rational expressions: 2/(3x-1) - 1/(x+1) #2) Solve for x (find the values of x) in the following equation: 2/(3x-1) - 1/(x+1) = 0 Hint: Use the answer of problem #1 (simplified expression).

### Abstract Algebra: Odd Prime

** Please see the attached file for the complete problem description ** Need help with attached problems Let p an odd prime, show that either p == 1 mod 4 or p == 3 mod 4. Show that no prime of the form 4n + 3 can be written as a2 + b2 for some integers a and b. Show that 17 is not prime in J[i], by finding a factorizati