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Basic Algebra

10 Algebra Problems : Solve Equations and Quadratics

Please see the attached file for the fully formatted problems. #1 Solve a2 - 9a = -14 #2 Solve 2e(e +1) = 12 #3 Solve #4 Solve #5 Solve for z #6 Solve the equation and check for extraneous solutions. #7 Solve #8 Solve by completing the square. s2 + 8s -

Solve for a

Solve for a 54 4√a-4 = 3 4√a + 2

Logarithm Proofs

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.

Algebraic Simplification

The expression (a²b³c-²/a³)/(c/a) simplifies to ( b/c )³. Justify that this statement is true.

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)

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