Question Solved1 Answer Practice Exercise 2.3 only. Thankyou Sample Problem 2.3 N W A particle is being acted upon by the following forces: F, = 4.0 N, east; F2 = 6.0 N, northeast; and F3 = 8.0 N, south. R₂ = F + F2 Find the resultant using the parallelogram method. You may add the E forces according to the grouping (F +F_)+F, . Rx = (F. + Fz) + F Solution: As shown in the figure, R, =F+F, while R2 =R, +F;. The resultant vector in the figure has nine scale units corresponding to F-scale: HIN 9 N. Using a protractor, the angle that the resultant makes with the S horizontal axis is 25°. Thus, the resultant is 9 N, 25° south of east. Chapter 2 Working with Directions 33 Practice Exercise 2.3 scale: tinct Using the same forces in Sample Problem 2.3, find F, +(F, +F). Compare your answer with the resultant obtained in Sample Problem 2.3. Polygon Method The polygon method is otherwise known as the tip-to-tail method. This method is more convenient than the parallelogram method when more than two vectors are to be added graphically. The following are the steps to be followed using the polygon method.

A series of wave fronts in a wave tank travel toward an opening in a barrier. To increase the amount of visible diffraction, one could a. increase the wave's amplitude b. decrease the wave's frequency c. increase the width of the opening in the barrier d. decrease the distance between the source of the waves and the barrier e. use a shorter wavelength 16. A series of wave fronts in a wave tank travel toward an opening in a barrier. To increase the amount of visible diffraction, one could a. increase the wave's amplitude b. decrease the wave's frequency c. increase the width of the opening in the barrier d. decrease the distance between the source of the waves and the barrier e. use a shorter wavelength 16. 17. When two wave sources are in-phase, and the wave from one source has to travel one- half wavelength further from the wave from the other source, there will be a. destructive interference b. constructive interference c. alternating constructive and destructive interference d. simultaneous constructive nor destructive interference e. no interaction

Please show your work for the answer step by step so I can understand, thanks. The two aluminum rods AB and BC have diameters of 25 and 20 mm, respectively. Determine the largest vertical force P that can be supported. The failure stress for the aluminum is fail = 400 MPa. Use F.S. = 2. P B

7. A pump receives 8 kg/s of water at 220 kPa and 110 degree C and discharges it a 1100 R$a. Compute for the power required in lalowatts.

What is the value of the equilibrium constant (K) for the following neutralization reaction: H3O+ + OH- 2H2O Remember: if you want to express an answer in scientific notation, use the letter "E". For example "4.32 x 104" should be entered as "4.32E4". Answer: Check

Partial Differential Equations Please provide the solution with steps. Thanks!   Consider a thin tube of length \( L \), oriented along the \( \mathrm{x} \)-axis. The tube is sealed at both ends. A finite amount of dye molecules is injected just inside this tube near one of its ends. You should assume that the concentration of dye molecules \( c(x, t) \) obeys the 1D diffusion equation given by \[ \frac{\partial c}{\partial t}=D \frac{\partial^{2} c}{\partial x^{2}} \] (a) Consider Fick's law and show that the following are appropriate boundary conditions \[ \left.\frac{\partial c}{\partial x}\right|_{x=0}=\left.0 \quad \frac{\partial c}{\partial x}\right|_{x=L}=0 . \] (b) If the local injection of dye at position \( x_{0} \) (close to origin end of tube at \( \mathrm{x}=0 \) ) and \( t=0 \) can be described by \( \alpha \delta\left(x-x_{0}\right) \), determine the value of \( \alpha \) in terms of the total number of molecules \( N \). (c) Use the separation of variables method, to show that the a solution to the diffusion equation for a tube of length \( L \) can be written as \[ c(x, t)=A_{0} x+B_{0}+\sum_{n=1}^{\infty}\left(A_{n} \cos \frac{n \pi x}{L}+B_{n} \sin \frac{n \pi x}{L}\right) e^{-D\left(\frac{n \pi}{L}\right)^{2} t} . \] (d) Now consider the boundary conditions noted in a) together with the initial dye injection constraints, and use these to determine the coefficients and thus the solution for \( c(x, t) \).

QUESTION 10 Asset A has an expected return of 15% and a standard deviation of 9%. The risk-free rate is 3%. What is the reward-to-variability ratio?