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Basic Algebra

Solve the Equation or Inequality

1. SOLVE (X-2)(9X+6)>0 2. SOLVE THE INEQUALITY X+43/X+3<6 3. SOLVE: SQUARED ROOT X+36-6=-X 4. 15X-SECOND POWER+2X-FIRST POWER+1=0 ANSWER: A.X=5,X=-3 B.X=5,X=1/3 C.X=-1/5,X=-1/3 D.NO SOLUTION

Quadratic Functions, Maxima, Minima, Even Function and Least Squares Regression

1. Given f(x)=16-x squared,and g(x)=4-x, find f/g (x). 2. Find the maximum or minimum value of the quadratic function f(x)-x squared+10x-19. State whether this value is a maximum or minimum. 3. Evaluate the function at at specified value of the independent variable and simplify. F(x)=/x/-2; f(4) 4. Given f(x)=2/x-6

Expression for period of pendulum

In the expression for the period of a simple pendulum, we do not take into account the mass that is hanging from the string. How is it possible that the mass does not affect the period of the pendulum? It was stated that the displacement that started the pendulum was small. What would happen if we started the pendulum with an ex

Finance : Interest and the Fisher Effect

What is the nominal interest rate (i) in Canada if the real estate of return is 2.5% and the expected rate was 4.5%. (The Fisher Effect formula should be used in this problem).

Quadratic Equations, Graphs, Rational Inequalities and Word Problems

Please see the attached file for the fully formatted problems. Includes the following Exercises: -Quadratic Functions and Their Graphs -Quadratic and Rational Inequalities; Equations, Functions and Inequalities -Quadratic Equations, Functions, and Inequalities Maximum height. If a baseball is projected upward from groun

Solve: Integral of a Polynomial

Suppose that p(z) and q(z) are polynomials with a complex coefficient with the property that deg q(z) is greater than or equal to deg p(z)+2. If C is a positively oriented simple closed contour containing all of the roots of q(z) on its interior, then prove that Integral C of p(z)/q(z) dz = 0

Upward lift

An upward force of 47 N is sufficient to lift a window. What force must be exerted along a pole that makes an angle of 27 degrees with the wall in order to give the necessary upward lift?

Important Information about Exponential and Logarithmic Functions

A. Convert to logarithmic equations. For example, the logarithmic form of "23 = 8" is "log2 8 = 3". a) 16 3/2 = 64 b) ex = 5 B. Write the logarithmic equation in exponential form. For example, the exponential form of "log5 25 = 2" is "52 = 25". a) log 3 27 = 3 b) log e 1 = 0 c) log 125 25 = 2/3 C. Use the

Use mathematical induction to prove...

See attached file for full problem description. Please provide proof along with explanation. For integers n>= 1 and for all real numbers x>=-1, use mathematical induction to prove that 1 + nx =< (1 + x)^n

Factor Group and Torsion Group

Heres my problem. Consider the group <R,+> (reals under addition) and its normal subgroups Z (integers) and Q (rationals0. (These are normal because R is abelian, of course.) (i) Find an element of Q/Z of order 350. (ii) Show that Q/Z is the torsion subgroup of R/Z. This problem is quite straightforward if you use the defini

Matrix Algebra - Definite vs. Indefinite

Let A be an nxn symmetric matrix such that det {see attachment}. We know from the matrix algebra that the associated quadratic form {see attachment}, where x = (x1,...xn), is either positive-definite, negative- definite or indefinite. Now assume the diagonal entries of A are all zero. Explain why q(x) is indefinite. (Hint:

Heat Equation : Non-Homogeneous PDE

Please see the attached file for the fully formatted problem. 2. (30 points) A thin, one-dimensional rod of heat-conducting material with length L = pi is internally and uniformly heated at a rate of alpha degrees per unit time. This means that the temperature of the rod, u(x, t), satisfies the inhomogeneous heat equation ..

Investment allocation

Matrix Algebra Investment Allocation Problem Donald Trump has some pocket change he wants to invest to make $3380. His stock broker suggested four (4) investment possibilities to accomplish this goal. The investments and their expected yields are listed in the table below. Investment Rate of Return Risk Level Magellan

Graphical Addition

Find the voltage V where V=V1+V2 using graphical addition and analytical methods, given that V1=3sin(theta+20 degrees) and V2=5sin(theta-40degrees).

5 Algebra Problems : Inequalities and Systems of Equations Word Problems

1. Solve the following equation for the variable y. 5x - 3y + 9 = 0 2.Solve the following problem by identifying a variable, writing an equation that describes the situation, and then solving the equation. Find two consecutive even integers that have a sum of 450. 3.Solve the following problem by identifying a variable,

5 Algebra Problems : Solving Equations

1.Solve the following equation 19 - 3n = - 2n 2.Solve the following equation 2(a - 4) + 4 = 5(9 - a) 3.Solve the following equation and check your answer. (1/2b)- (1/2)= 1/4b 4.Solve the following equation 0.6(x - 50) = 18 - 0.3(40 - 10x) 5.Solve the following equation for the variable x. t - 5x = 4x

Plotting Graphs of Given Functions

Refer to the graph given below and identify the graph that represents the corresponding function. Justify your answer. y = 3x y = log3x See attachment for Graph Plot the graphs of the following functions. Scan the graphs and plot them. 1. f(x)=7 2. f(x)=4 x - 3 3. f(x)=(1/5x 4. f(x)= 3 log x 5. f(x) = log x

20 Algebra Problems : Sequences, Series, Combinations and Permutations

Please see the attached file for the fully formatted problems. 1. Write the first four terms of the sequence an = 64(1/4)n , for n=0, 1, 2, 3,... a) 16, 4, 1, ¼ b) 60, 56, 52, 48 c) 64, 16, 4, 1 d) 256, 1024, 16384, 262144 2. Write the given series in expanded form without summation notation. a) -x2-x3

Quadratic Equations: Formulation of Real-Life Problems and Graph

Please see the attached file for the fully formatted problems. 1. Can a graph be used to solve any quadratic equation? Why or why not? 2. Look at the graph below and comment on the sign of D or the discriminant. From the quadratic equation based on the information provided and find its solution. 3. Formulate two word