Question April's car was worth $9,000 at the beginning of 2000 and the value of the car decreased exponentially, decreasing by 21% each year. a. Write a function f that determines the value of April's car (in dollars) in terms of the number of years t since the beginning of 2000. f(t) 9000(1-21/100) Preview b. How many years after the beginning of 2000 was April's car worth $6,000? * years Preview c. How many years after the beginning of 2000 was April's car worth $2,400? * years Preview Submit

please solve and show work step by step EXTENSIONS For the following exercises, prove or disprove the identity, 34. 1 + cos x 1 - cos(-x) -2 cotxesc 35. cse' (1 + sin x) = cotx 36. sec'(x) - tan X2+2 tanx tanx 2+2 cotx -2 sin' * - cos 2x 37. tan x sin(-x) - cos' x 38. secl - x) tan x + cotx sin(-x) secx 39. + sin COS X COSX 1 + sin(-x)

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)

2.(a) Explain why a vessel laden to the same draught on differentvoyages may have different natural rolling periods. (5)(b) Explain the term synchronous rolling, describingthe dangers associated with it. (6)(c) State the actions to be taken by the ship's officer when itbecomes apparent that the vessel is experiencing synchronousrolling. (5)

​​​​​​​please answer the top and bottom question as I'm almost out of credit. Thank you! Compound A can undergo direct photochemical conversion with light at 400 nm to compound B with a quantum efficiency of 0.004. The concentration of compound A used in the experiment resulted in an absorbance of 0.2 at 400 nm. If the experiment was carried out over 10 minutes with a constant light flux to the sample bottle of 100 umol photons s-1then calculate the total amount (in moles) of compound B that was formed during the experiment. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). B I y S Paragraph Arial 10pt A TK 品色 0 Q 6 S V > < ... - mi < ABC lil X2 X2 Q The - +] T 19 D > Х I! AH 由 +H EXE 图 +: 2 <> Ť {:} o ? Ra КУ + Р O WORDS POWERED BY TINY QUESTION 2 points Save Answer What chemical form of Mercury was responsible for the death of Professor Karen Wetterhahn in 1997?

Polarization of sum of two linearly polarized vector fields. Two sinusoidally time-varying, linearly polarized vector fields are given at a point by F1 = (Cax + Ca, + az) cos 27T X 10t F2 = (Cax + ay 2a,) sin 27T X 10Ⓡt where C is a constant. (a) Determine the polarization of the vector Fi + F2 for C = 2. (b) Find the value(s) of C for which the tip of the vector F1 + F2 traces a circle with time.

Answer the question below: Draft a Risk management investigation project proposal for an underground Mining company of your choice. (100 marks)