Question A 12-ft-tall fence runs parallel to a wall of a house at a distance of 24 ft. Find the length of the shortest ladder that extends from the ground to the house without touching the fence. Assume the vertical wall of the house and the horizontal ground have infinite extent. The length of the shortest ladder is ft. (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest thousandth as needed.)

Use the graph of f and f" to find the critical points and inflection points of f, the intervals on which f is increasing and decreasing, and the intervals of concavity. Then, graph f assuming f(0) = 0. Find the critical points. The critical points are x=1,3. (Use a comma to separate answers as needed.) Find the inflection points. The inflection points occur at x = 2. (Use a comma to separate answers as needed.) Find the intervals on which fis increasing and decreasing. f is increasing on (0,1).(3.4) (Type your answer in interval notation. Use a comma to separate answers as needed.) Click to select vour answeris)

Consider the four waveforms shown in Figure P-8.3. 1. Determine the dimensionality of the waveforms and a set of basis functions. 2. Use the basis functions to represent the four waveforms by vectors s1, s2, s3, s4 3. Determine the minimum distance between any pair of vectors.  

3. Consider the signals represented in the figure below. Find an orthonormal set of basis functions using Gram-Schmidt method. a. Determine the dimensionality of the waveforms and a set of basis functions. b. Use the basis functions to represent the four waveforms by vectors c. Determine the minimum distance between any pair of vectors. j (f) sale) 5. App 0 T 2T 3 0 T 3

An electron in a long, organic molecule used in a dye laser behaves approximately like a particle in a box with width 4.10 nm What is the wavelength of the photon emitted when the electron undergoes a transition from the first excited level to the ground level? Submit My Answers Give Up Part B What is the wavelength of the photon emitted when the electron undergoes a transition from the second excited level to the first excited level? λ= In Submit My Answers Give Up

2. x = X In each of Problems 1 through 4: G a. Draw a direction field and sketch a few trajectories. b. Express the general solution of the given system of equations in terms of real-valued functions. c. Describe the behavior of the solutions as t →. ( -3) = 65 -3)* Ox=(-5-2) 3. x' = х 1 1. x-(-1). 1-1 '= 4.) x' = = X X

solve parts b and c only Problems a In each of Problems 1 through 4: G a. Draw a direction field and sketch a few trajectories. b. Express the general solution of the given system of equations in terms of real-valued functions. c. Describe the behavior of the solutions as t → . -- -4 1. x = *= (1 -1) х -