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Basic Algebra

Graphical Addition in Degrees

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

Graph

Refer to the graph given below and identify the graph that represents the corresponding function. Justify your answer. y = 3x y = log3x Plot the graphs of the following functions. 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 +2 See Attachment for Graph

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

Exponential and Logarithmic Functions: Real-Life Applications

1. Explain the relevance and application of exponential functions in real-life situations. 2. Explain the relevance and application of logarithmic functions in real-life situations. 3. Think of a real-life situation that can be represented by a logarithmic function, translate the situation to the function, and solve the

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

Algebra : Four Word Problems

1. A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet. 2. A business invests $10,000 in a saving account for two years. At the beginning of the second year, and additional $3500 is inve

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

Algebra: Systems of Equations - 3 Word Problems

1. Joe has a collection of nickels and dimes that is worth $5.65. If the number of dimes was doubled and the number of nickels was increased by 8, the value of the coins would be $10.45. How many dimes does he have? 2. An express train and a local train leave GraysLake at 3 P.M. and head for Chicago 50 miles away. The express

Hamilton's Equations

A system with two degrees of freedom has Hamiltonian (see attachment) ? Show that p2 and H will remain constant during the motion. ? If (see attachment), show that at other times (see attachment) ? Show that in the subsequent motion cannot reach the value (see attachment).

Exponentials, Simple and Compound Interest, Annuities, NPV and Amortization

1. Rational Functions Graph the following function when a=3 and b=2. Develop a generic expression (i.e., as a function of "a" and "b") to find the "x" and "y" intercepts for this function (see attachment) 2. Exponential Functions Once a new automobile enters the market, the manufacturers try to estimate their residual valu

Divisbility

Prove that for all odd integers n, (1^n)+(2^n)+(3^n)...+(n^n) is a proper multiple of 1+2+3+...n

Irrational roots

If a,b,c are odd integers, show that all real roots of ax^2+bx+c=0 are irrational numbers.

Laws of Logarithms

Q a) log y = 1.2x - 1 A y = 0.1(10^1.2)^x Q b) ln y = 1.2x - 1 A y = 1/e(e^1.2)^x

Algebra Topics: Radical Equation, Complete the Square etc.

See the attached file. 1. Solve the radical equation: {see attachment} 2. Find the equation of the line through the point (-2,-4) and perpendicular to the line {see attachment} 3. Complete the square, find the vertex, the axis of symmetry, all the intercepts, and graph the parabola: {see attachment} 4. ... Find the

Correspondence of Upper Hemicontinuity

Please tell me whether or not the 2 correspondences are upper hemicontinuous and PLEASE (using the definition) justify why. 1)F:[2,3]->R^2, F(r)={(x,y):abs(x)+abs(y)<=r} 2)F:R^n{0}->R^n, F(x)=B(x;||x||), the closed ball centred at x with radius ||x||. Thanks Note: abs=absolute value is the complement ||x|| is d

Algebraic continuity theorem

(Algebraic continuity theorem): Assume f:A->R and g:A->R are continuous at a point c belong to A)then f(x)/g(x) is continuous at c, if both f and g are provided that the quotient is defined, show that if g is continuous at c and g(c) not= 0 then there exists an open interval containing c on which f(x)/g(x) is always defined.

Logarithmic and trigonometric equations

Section on using the properties of algebraic, trigonometric, logarithmic and exponential functions to solve problems. 1) Solve the following equation: log5 X + log5(X-2) = log5 X 2) The half-life of a certain radioactive element is 100days. That means that after 100 days ½ of the radioactive substance wil

Chinese Remainder Theorem : Problem of Sun-Tsu

Find all solutions of the problem of Sun-Tsu. Find all integers x such that the remainder after division by 3 is equal to 2, the remainder after division by 5 is equal to 3, the remainder after division by 7 is equal to 2.

Algebraic Expression : Word Problem

Three prizes are to be distributed in a Creative Design Talent Search Contest. The value of the second prize is three-fourths the value of the first prize, and the value of the third prize is two-thirds that of the second prize. Write the total value of the three prizes as an algebraic expression.

Classify the Polynomials

Classify the 15 given polynomials as monomials, binomials, trinomials, and polynomials. Use the format given below for categorizing the polynomials. [Note: Simplify wherever possible] (Please see attachment for polynomials)

Laws of Exponents and Opposites of Poynomials

1. Using one of the laws of exponents, prove that any number raised to the power 0 is 1. 2. You are given the following polynomial: 2x7 - 4x3 + 3x. If x were replaced with its opposite in each of the terms of the given polynomial, will it result in the opposite of the polynomial? Explain why or why not and illustrate to supp