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Basic Algebra

Please explain in detail

1. A swimming pool is twice as long as it is wide. It took 1,224 square feet of material to covar a 6-foot wide deck around the pool. How wide is the pool? 2. The height reached by a ball thrown vertically upward is directly proportional to the square of tis intial velocity. If a ball reaches a height of 46m when it i

College Algebra

1. Which of the following numbers are examples of integers? -7, -9/3, -1.0, -3/8, 0, 2.2, 5, 6.66666 2. Multiply and simplify your answer as much as possible: (4f - 3)(7f + 1) [to express (f)(f) use f^2] 3. If n is a negative number, what is the absolute value of n? 4. Factor: 25p^2 -

Uncountable Basis

It can be shown that R (the set of all real numbers) is an infinite-dimensional vector space over Q (field of rationals). Is it true that any basis (by basis I mean algebraic basis or Hamel basis) of R over Q has to be uncountable ?

Z-Modules and Modules Associated with Representations

1)I understand what a standard R-module (ring-module) is, but I have heard talk of modules associated with representations. Could someone please give me some idea of what these are? 2) I am trying to find all modules over Z-the Integers; so far, I have only come up with additive groups. How can I find all others?

What is the advantage of using exponents rather than radicals?

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. What is an example of an equation easier to solve as a rational exponent rather than as a radical sign.

Polynomial Functions : Positive Degree

The questions are asking for solving h(x) of positive degree. --- 1A) Let F be a field and let e(x), f(x), g(x) and h(x) be polynomials in F[x] with h(x) of positive degree. Prove that if e(x) = gcd(g(x),h(x)) and e(x) divides f(x), then there is a polynomial j(x)  F[x] such that g(x)j(x)  f(x) (mod h(x)).

Finding the Discriminant in a Quadratic Equation

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. What I need to do is figure out how to create three unique equations where the discriminant is positive, zero, or negative. For each case, please explain what t

Algebra and complex numbers

Can you please show me how to calculate the following with showing full workings? (See attached file for full problem description) --- 1, X = p/q (1 + 1n r) Evaluate r when x = 0.34, p = 1.08 and q = 1.84 X = p/q (1 + 1n r) = qx/p = 1 + 1n r 2, Z1 = 5-j4 Z2 = 4+j7 Z3 = -6-j7 Z4 = j2

Exponential and Logarithmic Function Graphs

Referring to the graph below (which is attached), identify the graph that represents the corresponding function. I need to justify my answer. y = 2^x y = log2x (where the 2 is lower case below log, not above)then; x Also, I need to plot the graphs of the following functions and show them. f(x)=6^x f(x)=3^x - 2 f(x)


In the game of odd man wins, three people toss coins. The game continues until someone has an outcome different from the other two. The individual with the different outcome wins. Let X equal the number of games needed before a decision is reached. Prove by induction that the density function of X is (see attached).

Literal Equations

I am having a hard time solving literal equations. I know the process is the same as you would solve any linear equation, but I still am having trouble grasping the whole concept. Is there any way of making this easier to learn?


(See attached file for full problem description) --- 1. Graph the system x^2 + y^2&#8804;16 y&#8804;4-x^2 2. Graph the solution { y<1/4x Bracket covers both entries but I don't know how to make it bigger. y&#8805; -2x+3 3. Show the graph of the systems of inequalities? 16x^2+64y


1a. (2 x 10^3)(4 x 10^5)= 1b. (3.5 x 10^5)(2 x 10^9)= 1c. 8 x 10^11)(2.5 x 10^3)=


1a. 5^2 x 5^4= 1b. (6p^5)(8p^4)=


1a. (2 x 10)(4 x10)= 1b. (3.5 x 10)(2 x 10)= 1c. 200(5 x 10)(1 x 10)=

Sturm-Liouville Problems : Eigenvalues, Eigenfunctions and Square Norm

Please help with the following problems. 1. Find the eigenvalues and eigenfunctions of the boundary- value problem y''+lambay = 0 , y(0) = 0 , y(pi/4) = 0 ( n = pi) 2. Find the eigenvalues and eigenfunctions of the boundary- value problem y''+(lamba+1) y = 0 , y'(0) = 0 , y'(1) = 0 3. Find the square norm

Quadratic Model: Completing the Square to Solve a Maximum Profit Question

Steve owns a bakery. He has hired a consultant to analyze his business operations, and the consultant has told him that his profits from the sale of pies is given by the following function: P(x) = 120x - x2 where P(x) is the profit and x refers to the number of pies baked. (a) How many units of pies should Steve bake in ord

Complex Numbers: Power Series and Radius of Convergence

For the following complex functions f, find their power series expansions cantered at z=i, i.e., . Find the radius of convergence for each of these power series. (see attached) what are the radii of convergence of these series?

Ellipses and Parabolas

1. Find the equation of the parabola with vertex at the origin, that passes through the point (-6,4) and opens upward. X=1/9y^2 Y=-1/9x^2 X=-1/9y^2 Y=1/9x^2 2. Find the equation for the parabola with the given vertex that passes through the given point: vertex: (-5,5) point: (-3,17) y=3/16(x-5)^2+5 y=11/

Applications of Logarithmic Equations : Earthquakes and the Richter Scale

The intentisty level of an earthquake is based on the Richter scale. Using logarithms, the Richter scale measures an earthquake relative to (as a ratio of) the weaket possible tremor. Research how earthquakes are measured. What is the formula for measuring earthquakes? ? Why is a 7.0 earthquake ten times stronger than

Limits and Exponential Population Growth

5. Find the limit of the following functions. Justify your answer using algebra or explain via a sketch how the graphing calculator is used to get the answer. If the limit does not exist, write D.N.E. and justify (explain) why the limit does not exist. a. b. 6. The population of Wichita, Kansas

Simplify : Sqrt{(x+c)^2+y^2}+SR{(x-c)^2+y^2}=2a

The answer is: (x^2-c^2)x^2+a^2y^2=a^2(a^2-c^2) I know it can be reduced further, but this is the answer my teacher wants. I don't have a math font so: SR=SquareRoot and 6^2=6 squared or 6x6=36 Thank you for your help!

Solving Equations and Transposing Variables

1, Given that s = 1.59t(1 - 3v), obtain the value of v when s = 3.52 and t = 21.56 2, If x = p/q (1 + 1n r), evaluate r when x = 0.34, p = 1.08 and q = 1.84 3, Solve log(2x + 3) = log (4x) + 2 for x