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Basic Algebra

Steady-State Error

Consider the following system in Fig.1 (see attached file). Determine K so that the steady state error for unit step input is zero.

Quadratic Equations: Discriminants and Imaginary (Complex) Numbers

When using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. (When the discriminate is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. ) Explain what the value

Cobb-Douglass

1. Let Y=L^&#945;K^1-&#945;, 0<&#945;<1; let y=lnY, l=lnL, k=lnK. a.Show that this production function is linear in its natural logarithms. b.Show that the instantaneous percentage change in out put is the weighted sum of the instantaneous change in L and K, with weights &#945; and (1-&#945;) 2. Suppose that the production

Integral Calculus : Inverse function of limited quadratic equation.

F(x) = 2x^2 - 8x, where x = or > 2 Even though I know that this particular quadratic equation does have an inverse since the domain is limited, I don't know how to figure out the formula for the inverse for a quadratic equation. I don't know how to solve for x, since there are two different x's. Thank you!

Calculate the discriminant

5. For a quadratic equation of the form, ax2 + bx + c = 0, how do you calculate the discriminant? What information about the equation can we learn by calculating the discriminant?

Solve equation for Rt

When three resistors of resistance values R1, R2, and R3 are placed in a parallel pattern within an electrical circuit (see diagram attached), the total resistance, RT, is computed from the formula: 1/RT = 1/R1 + 1/R2 + 1/R3. a. Rewrite the resistance formula by solving for RT and simplifying (i.e. RT = ...) b.

Liner Algebra / Linear Operators

See attached document. Please use only elementary theorems about linear operators, transformations, and definitions of invertibility.

Routh Stability Criterion

Consider the following characteristic equations: (a) s^3 + 2s^2 + s +2 = 0 (b) s^5 + 2s^4 + 24s^3 + 48s^2 - 25s - 50 = 0 Using Routh stability criterion, determine whether the above systems are stable or unstable.

Algebra

The questions relate to graphing of different simple functions. See attached file for full problem description.

Simple Factoring

I'm trying to factor the expression: 3a^2 - 13ab - 10b^2 But, I just don't know how. Thanks

Quadratic Equations : Completing the Square

1) Find the perfect square trinomial whose first two terms are given: w^2 - 5w 2) Solve by completing the square: 2m^2 - m - 15 = 0 3) Solve by using the quadratic formula: -x^2 - 3x + 5 = 0

Please explain in detail

Solve the following: secx = -5 find sin 2x find cos 2x tan 2x if tan x = 1/2 find sin x/2 cos x/2

Sudoku Puzzles

Please give the missing digit : it is a three by three puzzles, the first row has a 9and 7 ,but missing a first number, the second row has a 4, missing the first and third number and the last row is empty. the second thre by three square has a 3 in the first row,second row is empty, and third row has a 7 in the first box and