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# Basic Algebra

### Stereographic Projection, Riemann Sphere and Mapping

A plane is inserted through the equator of a unit sphere. A point on the sphere is mapped onto the plane by creating a line from the point on the sphere, through the north pole, where this line hits the plane is the projection of the point. Show that circles on the sphere map to circles on the plane except when the circles run

### Propagation of Error

(See attached file for full problem description and equations) --- A 100 uL (microLiter) sample of a 7.0 millimolar protein is diluted to 500.0mL. If the error in measurement of the molarity(M) is ±0.02 mM, of the uL pipet is ±1 uL, and of the volume of the 500 mL flask is ±0.15 mL, determine how the molarity of the resul

### Borel-measurable function

Prove that the following function is Borel-measurable function. f_n(t) = { [t*2^n]*2^-n , 0 < t < n, n , t > or = to n | f_n(t) - t | < 2^-n , t < n } I want a detailed proof. I want to kn

### Sigma-Algebra, Measures, Properties of Measures

Let m be a sigma-algebra, M_1 and M_2 are measures on m. a). Is M = M_1 + M_2 a measure? b). Is M = M_1 - M_2 a measure? c). Is M = M_1M_2 a measure? Either prove or disprove by providing a counter example.

### Write the Equation of a Line Given : Two Points; Slope and a Point or A Point and a Perpendicular Line

WRITING AN EQUATION FOR THE LINE CONTAINING THE INDICATED POINTS: 1. (0,0) AND (3, 30) 2. (-4, -4) AND (-3, -3) 3. (-6, -6) AND (-3, 1) 4. (4, -8) AND (3, -6) 5. ( -1/2, 7) AND -4, 1/2) 6.(-9, 1) AND (-1/2, 1) Those are the types of problems I am having trouble in writing equations containing indicated points. How do

### Algebra: Least Common Multiple

Let n ≥ 2 and k be any positive integers. Prove that (n - 1) | (nk - 1). (We can use induction.) (Please show each step of your solution. Thank you.) --- (See attached file for full problem description)

### Reflect on the learning of radical expressions and their applications, and then consider how you might apply a radical expressions to your daily life.

Reflect on the learning of radical expressions and their applications, and then consider how you might apply a radical expressions to your daily life. Explain this application, and elaborate on what the equation might be. Does the study of these types of equations help anyone understand the application better?

### Removing Symbols and Grouping Like Terms

1. Simplify: Remove the symbols of grouping and combine like terms. 5[3(4x - 2) - 3(6 - x)] + 7 2. Subtract (18x2 - 5x + 4) from (3x2 - 3x - 8) 3. Simplify: (27a3 b6 )2/3 4. Simplify: (102x+1)(104x) 5. Simplify and express your answer with positive exponents only. #6 & 7: Perform the indicated o

### Present value of Perpetuity

FIVE YEARS AGO, AN ALUMNUS OF A SMALL UNIVERSITY DONATED \$50,000 TO ESTABLISH A PERMANENT ENDOWMENT FOR SCHOLARSHIPS. THE FIRST SCHOLARSHIPS WERE AWARDED 5 YEARS AFTER THE MONEY WAS DONATED. IF THE AMOUNT AWARDED EACH YEAR (IE:, THE INTEREST) IS \$5OOO, THE RATE OF RETURN EARNED ON THE FUND IS CLOSEST TO? A. 7.5% PER YEAR B.

### Perform Computations in Scientific Notation

(See attached file for full problem description with equations) --- 1. Perform the following computation. Write the answer in scientific notation. 2. Perform the indicated operation. Solve for x. Reduce your answer to lowest terms. 3. Perform the indicated operation. 4. Solve this equation. Solve for x. 5. S

### Instantaneous Current, Voltage and Power

The instantaneous current and voltage in an electric circuit are given by i = Icos50 pi t v = Vcos(50 pi t + pi/6) Determine an expression for the instantaneous power in the circuit, p = iv, as the sum of two cosines. If I is 3 mA and V is 5 V, calculate the maximum value of p, giving your answer in watts correct to three si

### Solving Equations (4 Problems)

Solve equation. Watch for extraneous solutions #30 6 + 7 =y-1 y-2 y-8 y-8 Solve equation and check for extraneous solutions # 35 square root oft 2t+4= square root of t-1 Solve each equation #88 square root 9x2= x+6 Solve each equation by using the quadratic formula. 3z2-8z+2=0 ---

### Rational expressions and their real-life applications

Based on the eduation and learning curve of rational expressions and their applications, consider how someone might apply rational expressions in their daily life. Explain this application, and discuss what the equation might be. Did the study of these types of equations help to understand the application better?

### Radical Expressions: Limitations of Square Roots

Discuss any difficulties you might have with grasping the concepts used in radical expressions. How would you explain square roots, cube roots, nth roots, and radicals to a student who is having difficulty understanding these concepts? What are some limitations of square root?

### Factoring a Cubic Equation

Question: Each of the three dimensions of a cube with a volume of x^3 cubic centimeters is increased by a whole number of centimeters. If the new volume is x^3 + 10x^2 + 31x + 30 cubic centimeters and the new height is x + 2 centimeters, then what are the new length and width?

### System of Differential Equations : Solve Using matrix Algebra

Using the matrix algebra technique find a general solution to x'=3x-4y, y'=4x-7y

### Mass of Planets, Gravitational Accelerations, Pendulum, Real-World Applications of Imaginary Numbers and Accuracy of Formulas

A simple pendulum, such as a rock hanging from a piece of string or the inside of a grandfather clock, consists of a mass (the rock) and a support (the piece of string). When the mass is moved a small distance away from its equilibrium point (the bottom of the arc), the mass will swing back and forth in a constant amount of tim

### Quantitative Methods : Integer Variables - Restrictions and Flexibility

Why does the use of integer variables create additional restrictions but provide additional flexibility?

### Logarithms

Write 4^2=x in logarithmic form

Simplify the radical expression : 8730;300 Solve the radical equation : 2x + 4 = 4 Simplify (fraction) : 5y/16 + 7y/16 - 3y/16 Simplify (fraction) : 5/8 15/16 +1/2 Solve (fraction) : x/6 - x/8 = 1

### Egyptian multiplication methods

Problem 1 problem 2 13* 25=325 18* 17 =306 1 25 (1*25) 1 17 2 50 (2*25) 2 34 4 100 (4*25) 4 68 8 200

### Finding a Zero of a Polynomial Function

Finding a zero of a polynomial function. I know that we the zeros by setting f(x) equal to 0 and solving the equation. The book only gives two examples--so I am pretty much stuck. The problem is: f(x)=2(x-5)(x+4)^2 This is what I have done so far-- 0=2(x-5)(x+4)^2 0=2(x-5) + (x+4)^2.

### Find zeros of a function

See the attached file.

### Need these Algebra problems explained

(See attached file for full problem description) --- ALGEBRA Please add a bit more detail to each problem as to how the answers were derived. Thanks! 1. Perform the indicated operation: (x3 - 2x2 - 4x + 3) &#61624; (x - 3) Since x3 - 2x2 - 4x + 3 = (x - 3) ( ), we have (x3 - 2x2 - 4x + 3) &#61624; (x - 3) =

### 25 Problems : Solve for Real or Imaginary Roots, Word Problems (Sum of two numbers) , Lowest Terms, Inequalities and Quadratic Equations

1. Perform the indicated operation: (x3 - 2x2 - 4x + 3) &#61624; (x - 3) 2. Find the product: (x - 2)(x + 3)(x - 4) 3. Simplify without having negative exponents: (- 3s-3t2)-2 4. Convert to scientific notation and then solve. Give answer in scientific notation: (0.0000003)4 5. Factor completely: 3a3b - 3ab3 6. Factor

### Inequalities Word Problem - Compare financing a car for 0% financing for 60 months or 2500 vs a 60 month 4 % interest rate.

I need to understand how to figure out a word problem to compare financing a car for 0% financing for 60 months or 2500 vs a 60 month 4 % interest rate. Payments at 0 % are 16.67 per 1000 and payments at 4 % are \$18.41 per \$1000 financed. Need to know how to find out the range of new car prices for which the cash back options

### Functions and Graphs

Hi--we are currently working on composite functions. I am having difficulty getting started with this problem. A company that sells radios has a yearly fixed cost of \$600,000. It costs the company \$45 to produce each radio. Each radio will sell for \$65. The company's costs and revenue are modeled by the following functio

### Find the domain, range, vertex and intercepts for quadratic functions.

Please see the attached file for the fully formatted problems.

### Separation of variables

Please show each step of your solution. When you use theorems, definitions, etc., please include in your answer. If there is anything unclear in the problem, let me know. Thank you. Solve... in the rectangle 0<x<3, 0<y<2 by separation of variables... (See attachment for full problem)

### Equations with Rational Expressions & Ratios

55. Solve the Equation: 14/(a^2 - 1) + 1/(a -1) = 3(a +1) 64. The student-teacher ratio for Washington High was reported to be 27.5 to 1. If there are 42 teachers, then how many students are there?