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Basic Algebra

Logarithm Simplification

Write the following in terms of simpler forms: 3^(p*log_3(q)) (Here a^b denotes "a to the power b" and log_b denotes "logarithm in base b".)

Exponentials: simplifying and solving equations

(In this problem, the notation b^x stands for "b to the power x"; for example, b^2 stands for "b squared".) (A) Simplify the expression: 10^(3x-1)10^(4-x). (B) Solve the following equation for x: 5^(3x)=5^(4x-2). (C) Solve the following equation for x: (1-x)^5=(2x-1)^5.

Algebraic Properties 8b

Given the algebra <S;f,g,a>, where f and g are unary operations and a is a constant of S, suppose that f(f(x)) = g(x) and g(g(x)) = x for all x &#949; S. Show that f(f(f(f(x)))) = x for all x &#949; S.

Crytic math questions

Cryptic Math p Q R S T U V W X 1. Each letter stands for one of the numbers 1 - 9. 2. S + Q = V and S is smaller than Q. 3. P = R + U. 4. In one of the diagonals, all 3 numbers are perfect squares. 5. In one of the two diagonals, (P, T, X or R, T, V) the 3 numbers are in ascending orde

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

Exponential and Logarithmic Functions and Compound Interest

1. Graph: f(x)=e cubic x 2. Are the following functions inverses of each other? Yes or no a. F(x)=x-1/3 b. G(x)=3x-1 3. Solve for x: ln(7x-1)=6 4. Identify the graph of the function: f(x)=2-4^x 5. Solve for x: in x = 3+in(x-1) 6. The half-life of carbon 14 is 5730 years. F

QUADRATIC INEQUALITIES

SOLVE FOR 'X' 9X^2 - 12X - 12 > 0 QUESTION :- SOLVE FOR X 1. 9X^2 &#8211; 12X &#8211; 12 >0 SOLUTION: The above given inequality is an quadratic which has two factors 9x^2 &#8211; 12x-12 > 0 = 9x^2 &#8211;18x + 16x &#8211;12 > 0 = 9x(x-2) + 6(x-2) > 0 = (x &#8211; 2) (9x + 6)>0 which implies the p

Polynomial/rational function

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) =

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