Question What is the maximum flow rate of air that may occur at laminar condition in a 4 in diameter pipe at an absolute pressure of \( 30 \mathrm{psig} \) and \( 100^{\circ} \mathrm{F} \) ? If the pressure is raised to \( 60 \mathrm{psig} \), what is the maximum flow rate ? If the temperature is raised to \( 200^{\circ} \mathrm{F} \), what is the maximum flow rate? Explain the differences in answers in terms of the physical mechanisms involved. Provide answers in base \( \mathrm{SI} \) units.

(4 marks) 4. Consider the sequence (an) defined by an = cos(10/n). (a) Find the integer N >0 such that the sequence (an) is increasing when n > N. (b) Using the value of N found in (a), show that the Monotone Sequence Theorem can be applied to (ar) for all n > N; hence find the limit of (an). (c) Plot n against (ar) for some points n > N, where N is the value found in (a).

Determination of polarization for combinations of linearly polarized vectors. Three sinusoidally time-varying linearly polarized vector fields are given at a point by F V3 a, cos (271 X 10°t + 30°) F2 = a, cos (27 X 10t + 30°) V3 + a cos (27T X 10ºt – 60°) 2 2) cos Determine the polarizations of the following: (a) Fi + F2; (b) Fi + F2 + Fz; and (c) F1 – F2 + F3.

please help MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 36 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4 months, and the distribution of lifetimes is normal. (ə) If Accrotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production will the company expect to replace? (Round your answer to two decimal places.) (b) If Accrotime does not want to make refunds on more than 12% of the watches it makes, how long should the guarantee period be (to the nearest month)? months

Are the following systems (i) Linear? (ii) Causal? (iii) Time-invariant? Consider x to be the input signal and justify your answers, specifying key conditions/assumptions as needed. (a) y[n] = x[n] +1 (b) y[n] = x[-n] (c) y[n] = z[n + 1] – x[n]

I need this exercise to be implemented in MATLAB. (NotSimulink) ܕ EXAMPLE 2.1. This example illustrates the ability of the adaptive linear combi- ner, trained with the LMS algorithm, to estimate the parameters of a linear model. The input data consist of 1,000 zero-mean Gaussian random vectors with three components, that is, re R3xl; and the bias is set to zero, or B = 0. The variances of the components of r are 5, 1, and 0.5, respectively. The assumed linear model is given by b = [1,0.8, -1]. To generate the target values (desired outputs), the 1,000 input vectors are used to form a matrix X = (x ? ... $1,000), and the desired outputs are computed according to d=b'x. The covariance matrix of the vector input signals can be estimated as 1.000 C Irx= XXT 1,000 1,000 h=1 [30]. Using the LMS algorithm in Table 2.1, with a value of Ho = 0.9/Amax = 0.1936, where Imax is the largest eigenvalue of the covariance matrix Cy, and t = 200 (the search time constant), the input vectors along with the associated desired output values are presented to the linear combiner. The criter- ion used to terminate the learning process involved monitoring the square root of the MSE values every time step k. The learning process was terminated when VJ = leik) < 10-8, where elk) = dík) – W" (k)(k). The initial values of the synaptic weight vector were selected as zero-mean Gaussian random numbers with a variance of 0.25, Winitial = (-0.3043, -0.8195,0.3855)". The LMS learning process was terminated after only 204 iterations (training epochs). In other words, after the first 204 input vectors along with the associated desired output values were presented, the network converged. The final synaptic weight matrix was given as wrinat = [1.000000, 0.800000, -1.0000001", which is exactly the assumed linear model b (out to six decimal places). In fact, the L2-norm of the difference between the linear model band the final weight vector is | 5-Wfinal ||2= 1.505404 x 10-7. Figure 2.17 shows the progress of the learning rate parameter as it is adjusted according to the search-then-converge schedule. As we can see from the plot, at the beginning of training u does not change much; then toward the end of training it becomes much smaller. Figure 2.18 shows the root mean square (RMS) value of the performance measure, that is, VJ, as training of the network progresses. This exercise is similar to problems in system identification of estimating a parameter vector associated with a dynamic model of a system given only input/output data from the system, that is, parametric system identification [31]. W finai $) X():11C1, 5000) )- d=6x X(2,:) = randa (1, 1000 X(2, ) d=$3x3 3 SX1000) X(3,:) = sqrt(0.5) Condn (11000) : {{x1000) scalar coux-x***/1000 randa (N) normally distrand. numbers I rand (0) NXN uniform dist the interval (0.0, 1.0)

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 26 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4 months, and the distribution of lifetimes is normal. (a) If Accrotime guarantees a