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Basic Algebra

Function/algebra

1.SOLVE A=1/2H(b1+b2) for b2 2. write 3-square root-36 in standard form Linear Functions 3.Find the slope of the line passing through the points (-2, 4) and (-3, 5). a.1 b.-1 c.-9/5 d.-5/9 Zeros of Polynomial Functions 4.Find the zeros of P(x) = (

Mass and radius of three of the nine solar planets

I need the mass and radius of three of the nine planets in our solar system. Be sure that the masses are expressed in kilograms and the radii are expressed in meters. I chose Pluto, Venus, and Mars. Using your data, calculate the gravitational acceleration on each of the three planets you selected. The masses should be measure

QUADRATIC INEQUALITIES

SOLVE FOR 'X' 9X^2 - 12X - 12 > 0 QUESTION :- SOLVE FOR X 1. 9X^2 -12X -12 >0 SOLUTION: The above given inequality is an quadratic which has two factors 9x^2 -12x-12 > 0 = 9x^2 –18x + 16x –12 > 0 = 9x(x-2) + 6(x-2) > 0 = (x -2) (9x + 6)>0 which implies the product of (x -2) & (9x + 6

Polynomial Rational Function Zeros Calculation

1.LIST THE ZERO OF THE CUBIC FUNCTION AND TELL WHICH, IF ANY, ARE DOUBLE OR TRIPLE ZEROS y = x squared (x-1) 2. USE THE RATIONAL ZERO THEOREM TO FIND ALL POSSIBLE RATIONAL ZEROS OF THE POLYNOMIAL: g(x) = -3x cubic -8x squared +x+ 14 3.USE SYNTHETIC DIVISION TO FIND UPPER AND LOWER BOUNDS OF THE REAL ZEROS OF f. f(x) =

Quadratic Equation, Maximum, Minimum and Types of Lines

1. Which set of ordered pairs(x,y) represents y as a function of x? Answer A. (2,-8),(1,6),(1,2),(6,1) B. 2,-8,1,6 C. (2,-8),(-8,2),(6,6) D.(2,-8),(-8,1),(2,6) 2. Evaluate the function at the specified value of the independent variable and simplify f(x)=3x squared-square root2x Answers a. 22.757 b. 24.551

Quadratic Functions, Maxima, Minima, Even Function

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

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

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

Finding slope and intercept of a line, and solving equations

1. Find the slope and intercept for the line 2y-x-4=0 2. Find the slope and intercept for the line 6/9y+2/3x-5=0 3. For the line y= 3x-3 find a line parallel to it that passes through the point (-1,0) 4. For the line y= 2x+2 find a line parallel to it that passes through the points (2,0) (4,4) 5. For the set of p

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

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

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.

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

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