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    Basic Algebra

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    Logarithm Proofs Components

    Verify log(z1/z2) = log z1 - log z2 by a) using the fact that arg(z1/z2) = arg z1 - arg z2 b) showing that log(1/z) = -log z... Please see the attached file for the fully formatted problems.

    Complex Logarithms

    Please see the attached file for full problem description. --- 3. Show that (a) Log (1 + i)2 = 2 Log (1 + i) (b) Log (-1 + i)2 ≠ 2 Log (-1 + i).

    Cauchy-Riemann Equations in Polar Form

    Please see the attached file for the fully formatted problems. 8. Let a function f (z) = u + i v be differentiable at a nonzero point z0 = r0 e(iθ0). Use the expressions for ux and vx found in Exercise 7, together with the polar form (6) of Cauchy-Riemann equations, to rewrite the expression f ΄(z0) = ux + i vx

    Exponential and Logarithmic Functions : Capacitance

    If a capacitor with a capacitance of 0.000005 farads is wired in a circuit with a total resistance of 5000 ohms (the standard unit of electrical resistance), how long must the capacitor be wired to a source voltage to reach 50% of its maximum charge? (The Hint was: Begin by expressing q as 0.5Q)

    Prove Bonferroni's Inequality

    21. If P(E) = 0.9 and P(F) = 0.8, show that P(EF) ≥ 0.7. In general, prove Bonferroni's inequality, namely, P(EF) ≥ P(E) + P(F) - 1.

    Inequalities, Graphs and Maximizing Profit

    Please see the attached file for the fully formatted problems. Solve each inequality state the solution set using interval notation and graph the solution. Solve rational inequality state and graph the solution set. A chain store manager has been told by the main office that daily profit P is related to the number of

    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

    Removing the Demonimator by Multiplying Both Sides By LCD

    When we solve a rational equation, why is it OK to remove the denominator by multiplying both sides by the LCD? Why can you not remove the denominator when simplifying a rational expression? Provide examples to support your discussion. 2. What are extraneous solutions of an equation? Why do they sometimes occur when we solve

    Quadratic equation standard form

    Consider the quadratic equation m(x)=0.20x^2-1.6x-1. Write the equation in standard form m(x)=a(x-h)^2+k, then find each of the following (to four decimal places): (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range

    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) = (

    Exponential and Logarithmic Functions

    1. Solve for x: ln(7x-1)=6 Answer: a.57.4898 b.403.572 c.403.286 d.57.7755 2. Solve for x: ln x = 3+ln(x-1) answer: a.3.95257 b.0.952574 c.1.0524 d.5.0524 3. The half-life of carbon-14 is 5730 years. Find the percent of a sample present after 5370 years. Answer: a.101.25% b.

    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