Algebra Problem of the week

There is a hallway that is infinitely long, with a series of lightbulbs that are all turned off. Someone enters and pulls the string on every light bulb, turning them all on. Another person enters, pulling the string on every other lightbulb. A third person enters, pulling the string on every third bulb. This continues indef ...continues

Complex Numbers: Solve the system of equations letting p=1/x and q=1/y.

Solve the following system of equations 4/x-9y=-1 -7x+6y=-3/2 HINT: let p=1/x and q=1/y

Systems of Equations : Substitute p and q for 1/x and 1/y

Please see the attached file for the fully formatted problems. Solve the following system of equations: 4/x - 9/y = -1 -7/x + 6/y = -3/2

Parabola and Hyperbola : Formula and Perimeter of Quadrilateral

Please see the attached file for the fully formatted problems. 1. Assume that 11 and 12 are represent two straight lines: 11 : y= ax+c 12 : y= bx+d a, b, c, and d are real constants If 11 and 12 are parallel and neither is vertical then: a) 2a = b b) ab = 1 c) a= -b d) a = b 2. If the parabola X = y^2 + ay + ...continues

Algebra: Logarithms - Solve for X, Solve for Base

Please see the attached file for the fully formatted problems. 1. The value of e ln 1+ ln 2+ ln 3 is ? 2. If logN(25) – logN(81) = 2, then N is? 3. Solve for x: log5( x) + log5(2x +13) = log5(24) 4. Find the coefficient of the fourth term in the expansion of (2x +3y)^11

Functions : Parabolas and Difference Quotient

1. Given that f(x) = x^2 – x +4 and g(x) = (sqr root x) +2 find (f o g)(x) 2. Find the equation of the parabola with focus F(12,20) and directrix y = 10 3. For f(x) = 1/ (x –2) , find and simplify the difference quotient (f(3+h) –f(3)) / h

Working with TI-82 Graphing Calculator - Can't figure out settings for problem.

6(x + 2) = 5(x + 2) Instructions are to use a graphing calculator to find the solution. Check your solution algebraically inthe original equation. I keep getting Err:stat Plot

Finding the slope of a linear equation.

FIND THE SLOPE OF THIS EQUATION: 8x-2y= -48 Is the answer 4, -4, -6 or 6? Please explain how to solve the equation step by step and how to find the slope, also.

Linear Alegbra: Span of Dimension

What is the span of the dimension of... _______________________ over P3 v1=x^2, v2=1-x^2, v3=1 _______________________ over C[0,1] v1=cosx, v2=cos2x, v3=1 ___________________________ over R3, v1=(2,2,1),v2=(-3,0,-1),v3=(-4,2,-1) ______________________________

Linear Algebra: Find a Vector in a Basis

In the standard basis of P3 (i.e. {1,x,x^2}) p(x)=3-2x+5x^2, that is, it has coordinates p=(3,-2,5). Find the coordinates of this vector (polonomial) in the basis {1-x,1+x,x^2-1}