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Basic Algebra

Derivatives of Logarithms and L'Hopital's Rule

Apply laws of logarithms to simplify the function. Then find its derivative. ?(x) = ln ^/¯ (9-x2)/(4+x2) Find limx→3 2x^4-3x^3-81/x^5-10x^3+27 Apply L'Hopital's rule as many times as necessary, verifying your results after each application

Microeconomics - Competitive Screening

The utility of each individual is u(w) = 80w − w^2, where 0 ≤ w ≤ 40 is wealth. The initial wealth is $40. The individuals may suffer a loss of $30. There are two types of individuals. Either an individual has low risk of loss, in which case the probability of loss is 1/5 , or high risk, in which case the pr

Quadratic Equations

A. Solve the quadratic equation (x-15)^2 = 28 B. The vertex of y = x^2 + 4x + 5 is: C. Find the value of c such that... is a perfect square. D. Solve the equation for x by using the quadratic formula ....

Solve for z: Quadratic Equations

Please answer the following question: Solve this quadratic equations and show all steps: (z+7)^2 - 45 = 0, where z is a real number.

Solving Equations Question

Solve x^2 = 75 where x is a real number. Simplify your answer as much as possible. (If there is more than one solution separate by commas.)

Simultaneous equations

1. xy = 8 X^2 + y^2 - 3xy + 4 = 0 2. x^2 - x - y - 2 = 0 x^2 + 2x - 4y + 1 = 0 Thank you

Radical Equations

Please complete the following attatchment. Make sure to show all work please. Thanks in advance!

Graphing, Applications and History of Log Functions

I am having a little trouble when it comes to Logarithms, trying to research about the history of them prior to 1614 & John Napier's contributions to their development may not be that bad but graphing is different. How do I interpret natural logs, common logs & graph them? Example: 10^x, log(x), e^x & In(x) for -5<x<5 The

Simplify

Please type the solution..(no handwriting please) 1.) Simplify 2x*2 - 18y^2 divided by 3y -x 2.)Perform the task (y^2 - 2y + 1 divided by y^2 - 1) multiplied by (2y^2 + y - 1 divided by 5y - 5) 3.)Perform the task (8x - 5)/(3x - 1) + (4x + 1)/(3x -1) 4.)Perform the task 4/(x^2 - x - 6) - 4/(x^2 - 4) 5.) Perform th

Polynomials

How do you solve these? 1) Find all numbers that are undefined for the expression, x^2 - 3x -54 divided by x^2 - 10x + 24 2) Simplify x^2 - 4x - 32 divided by x^2 - 64 3) Perform the indicated operation (x^2 + 16)/ (x^2 - 16) divided by (x + 4)/(x^2 + 2x - 8) 4) Simplify 1/x + 1/y di

Real-Life Models of Logarithmic Functions.

Many different kinds of data can be modeled or measured easily using exponential and logarithmic functions. For example, consider ideal gases: Pressure versus volume give a curved plot, but a log graph of pressure versus volume provides a linear plot that is easier to interpret. Log plots are also used in the study of the rates

Factoring

8) 9x^3 - x 9) 16x^2 - 40x + 25 10) 2y^3 - 16 11) x^4 + 125x 12) 9x^5 - 18x^4 13) z^4 - 16 14) x^3 - 27 15) Solve: 25x^2 - 64 = 0

Factoring

1) 12x^3 + 16x^2 - 400x 2) x^3 + 3x^2 + 2x + 6 3) x^2 - 3x + 2 4) 3x^2 + 6x - 24 5) 4x^2 + 4x -15 6) 8x^2 + 8x - 6 7) 12y^3 + 28y^2 + 8y

Exponential and Logarithmic Functions

Please see the attached file for the fully formatted problems. 1. Convert the following equations into logarithmic form: a. 9 = 4x b. 3 = 6y c. 5 = 7y d. X = 9y 2. Convert the following equations into exponential form: a. X = log3 6 b. -5 = log3 y c. X = log4 y d. 1000 = log5 Z

Simplifying and Factoring Expressions

1. Simplify. 2. Write in descending-exponent form, and give the degree. x5 + 9x7 - 1 3. Find the value of the polynomial 6x - 1 when x = 3 and when x = -3. 4. Simplify. Write your answer with only positive exponents. m2m-10 5. Subtract 2x - 3x2 + 5x3 from 5x3 + 4x - x2. 6. Multiply. 3x

Write each fraction in simplest form.

Please complete the following 15 equations and make sure to show ALL WORK! Thanks in advance! Please complete the following and make sure to show ALL WORK! Section 5.1 Write each fraction in simplest form. 18. 24. 36. 50. Geometry. The volume of the box is represented by . Find the polynomial that represents the ar

Factoring

1) Factor 16x^2 - 25 2) Factor 15x^6 - 9x^5 + 12x^4 + 9x^3 3) Factor 8x^3 + 64 4) Factor x^2y^2 + 11x^2y + 24x^2 5) Factor 3x^2 - 18x - 48

Factoring Polynomials

Factoring the Difference or Sum of Two Cubes A. Factor each polynomial completely, given that the binomial following it is a factor of the polynomial. B. Factor each polynomial completely. C. Factor each polynomial completely, if prime say so. D. Factor each polynomial completely, if prime say so. E. Decreasing cube. Eac

Simplifying Expressions

Please give detailed explanation. Please see attached file for full problem description. Simplify. cos ( &#61552;/2 - x) (csc x - sin x)

Simplify trig expression

Please give detailed explanation. Please see attached file for full problem description. Simplify sin2x( 1 + cot2 x) A). sin2x - tan2x B).

Factoring Polynomials

57 Factor each polynomial. If the polynomial is prime, say so. 67 Factor each polynomial. 105 Factor each polynomial completely. If prime say so. 109 Use factoring to solve problem. Area of a sail. A triangular sail has an area of sq. meters and a height of x + 3 meters. Find the lengt