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}

Linear Algebra: Matrix of Transformation

Are the following examples linear transformations from p3 to p4? If yes, compute the matrix of transformation in the standard basis of P3 {1,x,x^2} and P4 {1,x,x^2,x^3}. (a) L(p(x))=x^3*p''(x)+x^2p'(x)-x*p(x) (b) L(p(x))=x^2*p''(x)+p(x)p''(x) (c) L(p(x))=x^3*p(1)+x*p(0)

Linear Algebra: Vector Spaces

Consider R2 with the following rules of multiplications and additions: For each x=(x1,x2), y=(y1,y2): x+y=(x2+y2,x1+y1) and for any scalar alpha, alpha*x=(alpha*x1, alpha*x2) Is it a vector space, if not demonstrate which axioms fail to hold. Also, show that Pn- the space of polynomials of order less than n is a vector spac ...continues

Linear Algebra: Linear Mapping

Consider the following linear mapping from C[-pi,pi] into itself: L(f)=integral from -pi to pi of G(x),h(y),f(y)dy for any function f(x) in C[-pi,pi]. Here G(x), H(x) are given continuous functions. Find a function f such that L*f=lambda*f for some lambda and find the value of lambda. This is a generalization of the notion ...continues