1. Find y as a function of t if
y'' - 3y' - 18y = 0,
y(0) = 6,
y(1) = 8.
Remark: The initial conditions involve values at two points.
2. Find y as a function of t if
3y'' + 28y = 0,
y(0) = 8,
y'(0) = 5.
Note: This particular problem can not handle complex numbers, so write your answer in terms of sines and cos

1. Use the quadratic formula to determine the x-intercepts (if any) of the following function. Then evaluate the function for several values of x, and use the resulting points to graph the function. Show your work.
F(x) = 7x^2 - 28x + 28
2. Use the discriminate to determine whether the following equations have solutions t

Please see the attached file for the fully formatted problems.
(a) FIND the Green's function for the operator with L = + w2 with u(a) = 0
dx2 u(b) = 0
and a < b, w2 a fixed constant. i.e. SOLVE Lu = ?รถ(x ? ) with the given boundary conditions.
(b) Does this Green's function exist for all values of w? If NO, what are the

Representative problems:
1. A function is continuous but its first derivative has a finite discontinuity at the origin. What is your estimate of the rolloff rate?
2. A system is characterized by a transfer function H(s) = 1 / s+5 . What is the natural response of the circuit?
3. If a function is even, then its Fourier tran

Find all real or imaginary solutions to each equation: 3v^2 + 4v - 1 = 0
Solve the equation
2y^2 - 3y - 6 = 0
(x-10)(x-2) = -20
Determine whether the parabola opens up or down: y = -1/2x^2 + 3
Find the vertex and intercepts for each parabola: g(x) = x^2 + x - 6
Find all real solutions to each equation: x^2 + x +

Assume that the proportion of commercial vehicles among users of the Humber Bridge varies randomly from day to day, with density {see attachment} over 0function, and sketch the density and distribution functions over -1

1. Write a word problem involving a quadratic function. How would you explain the steps in finding the solution to someone else? Provide a detailed example. You may use the Internet for help/ideas. Cite your source if it is not an original idea.
2. Quadratic equations, which are expressed in the form of ax2 + bx + c = 0, where