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# Basic Algebra

### Expression is Simplified

How do I simplify and express without negative exponent? -22w^-4/2w^-2.

3x^4 * 7x^9

### Equation or expression? Please simplfy.

10x^2y^4 + 4x^4y^2 - 16x^6y^3/-2x^2y^2

### Using the Distributive Property to Find the Product

I am trying to use the distributive property to find the product of (and combine terms for) this problem: (y^2 z - 3y^4)(y^2 z + 2x^2 - y^4).

### Equation - for how many seconds is this arrow more than 86 feet high ...

1) If an arrow is shot straight upward with a velocity of 96 feet per second (ft/sec) from an altitude of 6 feet, for how many seconds is this arrow more than 86 feet high? Note If an object is given an initial velocity straight upward of "v lower case 0" feet per second from a height of "s lower case 0" feet, then its altit

A person's revenue "R" (in dollars) on the sale of "X" fruitcakes is determined by the formula R = 50x - x squared. Her cost "C" in dollars for producing "X" fruitcakes is given by the formula C = 2x + 40. For what value of "X" is the person's profit positive? (Profit = revenue - cost).

### Log Derivatives : Chain Rule

Find the first derivative of the function. 1.) y= ln x^2 2.) y= ln sq rt x^4- 4x 3.) f(x)= x^2 ln x 4.) y=ln x/x+1

### Expression as a Sum Difference or Multiplication of Logarithms

Use the properties of logarithms to write the expression as a sum difference or multiplication of logarithms 1.) ln 2/3 2.) ln xyz 3.) ln sq rt x^2 +1 4.) ln 2x/ sq rt x^2 - 1 write the expression as the logarithm of a single quantity. 5.) ln(x - 2) - ln(x+2) 6.) 3 ln x +2 ln y- 4 ln z 7.) 3[ln x+ ln(x+3

### Find the Equation of a Line Given X- and Y-Intercepts.

Find the slope intercept form of a linear equation when the line crosses the x-axis at x=2 and the y-axis at y=3.

### Power Series, Partial Sums and Radius of Convergence

Suppose that you have done some mathematical modelling. This has produced a differential equation which you have solved by assuming a power series solution. The power series you have found is the following.... (a) What is the radius of convergence of the power series? (b) Use Mathematica to plot the partial sums....

### Set Operations : Commutativity, Unity, Zero Divisors and Multiplicative Inverses

Consider the set R={0,2,4,6,8} C Z10. a) Construct addition and multiplication tables for R, using the operations in Z10. b) Is R a commutative ring? Does it have unity and, if so, which element is unity? c) Does R have zero divisors? d) Which elements of R have multiplicative inverses? Please see the attached fi

### Does the operation a*b = ab in Q give a group structure?

Modern Algebra Group theory Determine whether the following binary operation give

### Convergence of series

Please help with the following problem. This problem is from Advanced Calculus II class. It is also an introduction to real analysis. Consider the series n = 1 to infinity 1/( 1 + n^2 x) (a) For what values of x in R does the series converge absolutely? (b) On what intervals of R does it converge uniformly? (c) On wh

### Finite Extension Field and Isomorphism

Argue that every finite extenstion field of R is either R itself or is isomorphic to C. Note: R is set of all real numbers C is set of all complex numbers

### Toy Rocket Maximum Heights

A toy rocket is launched from the ground so that its distance in feet above the ground after t seconds is s(t) = -16t squared + 208t. I am trying to determine the maximum height it reaches and the number of seconds it takes to reach that height.

### Quadratic Equation: Vertex and Intercepts

Can you please help me finding the vertex and intercepts for this equation, and whether it opens up or down? y + -3x squared + 6x.

### Solving an Inequality using Interval Notation

Please help solving this inequality and using interval notation to solve it. x - 4/x + 5 > 0.

### Solve an inequality using interval notation.

How do I solve this inequality and state the solution using interval notation? y squared - 9 < 0

### Solve the inequality using interval notation and graph the solution.

I need help solving this inequality and stating the solution using interval notation and graphing it. a squared + 2a less than or greater than 15

### Finding the Vertex and Intercepts for the Quadratic Function

How do I find the vertex and intercepts for this quadratic function? y = x squared - 4x - 12.

### Solve an inequality using interval notation.

How do I solve this equation using interval notation? 3x - x squared greater than 0

### Solve the inequality.

Solve this inequality.. 4x squared - 8x greater than or equal to 0

### Exponential & Logarithmic Models : Continuously Compounding Interest

An initial deposit of \$3000 is made in a savings account for which the interest is compounded continuously. The balance will double in seven years. What is the annual interest rate for this account? Please show all work and logic in getting the answer.

### Exponential and Logarithmic Models.

Solve for x: log(3x + 7) + log(x - 2)=1 Please show all work and logic in getting the answer.

### Exponential & Logarithmic Models : Solve for X

Solve for x: 1/64=16^(8x+2)

### Maximizing and Minimizing Area

A rectangular play yard is to be constructed along the side of a house by erecting a fence on three sides, using house wall as the fourth wall. Find the demensions that produce the play yard of maximum area if 20 meters of fence is available for the project. What are the dimensions of an aluminum can that can hold 28 ounces

### Simplify the logarithm response

The population of a town will double in t= 10ln 2 / ln 67 - ln 50 Find t.

### Simplify the logarithm.

1/2[ln z + ln(z-8)]

### Simplify the Logarithm using Properties of Exponents

Use the properties of exponents to condense the expression to the logarithm of a single quantity. ln y - 51n(y+3)