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Basic Algebra

Quadratic Equation : Maximizing Profit

A movie theatre sells tickets for $8.50 each. The manager is considering raising the prices but knows that for every 50 cent the price is raised, 20 fewer people go to the movies. The equation is R= -40c to the power (exponent) of 2 + 84c describes the relationship between the cost of the tickets, c dollars, and the amount of

25 Questions - Algebra 2, College level.

(See attached file for full problem description with equations) --- 1. The diameter of the Milky Way disc is approximately 9  1020 meters. How long does it take light, traveling at 1016 m/year to travel across the diameter of the Milky Way? Time = distance/speed = 9  1020 m/1016 m/year = 9*104 years

Need help with Algebra

Page 17 & 18 10. 7 ? -- = -- 2 8 18. 5 ? -- = --- 7 98 30. 34 102 31. 70 -- 102 40. 5 12 -- . -

25 Questions - Algebra 2, College level.

(See attached file for full problem description with complete equations) --- 1. The diameter of the Milky Way disc is approximately 9  1020 meters. How long does it take light, traveling at 1016 m/year to travel across the diameter of the Milky Way? 2. Divide. 3. Multiply. Write the answer in

Group of algebra problems

Algebra problems: Page 24 55. - 0.03 - 5 56. 0.7 - (-0.3) 71. - 161 - 161 72. - 19 - 88 94. Net worth. Melanie has a $ 125,000 house with a $ 78,422 mortgage. She has $ 21,236 in a savings account and has $ 9,477 in credit card debt. She owes $ 6,131 to the credit union and figures that her

Various Quadratic Problems

See the attached file. 1. Find the axis of symmetry. y = x2 + 5x - 7 2. Solve. 5(x - 2)2 = 3 3. Solve by completing the square. x2 + 2x - 8 = 0 4. Find the x-intercepts. y = x2 + 5x + 2 5. Is the following trinomial a perfect square? Why? x2 + 18x + 81 6. The demand and supply equations for a cert

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.

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)

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 ---

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?

Radical Equations

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

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.

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) =

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