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Question: prove by induction 2^2 + 4^2 + 6^2 + ... + (2n)^2 = (2n)(2n+1)(2n+2)/6 ANSWER we will use induction on n base case : n=1 we have, 2^2 = 2*3*4/6 = 4 which is true inductive hypothesis let it be true for n = k i.e.,  2^2 + 4^2 + ... + (2k)^2 =   [(2k)(2k+1)(2k+2)]/6 inductive case let n = k+1 then we have 2^2 + 4^2 + .... + (2k)^2 + (2(k+1))^2 =   [(2k)(2k+1)(2k+2)]/6 + (2k+2)^2 =(2k+2)*[(2k)(2k+1)/6 + (2k+2)] =(2k+2)*[ (4k^2+2k)/6 + (12k + 12)/6 ] =(2k+2)*[ (4k^2+14k+12)/6 ] = =(2k+2)*[(2k)(2k+1)/6 + (2k+2)] =(2k+2)*[ (4k^2+2k)/6 + (12k + 12)/6 ] =(2k+2)*[ (4k^2+14k+12)/6 ] = (2k+2)*[ (4k^2 + 8k + 6k + 12)/6 ] = (2k+2)*[ (4k(k + 2) +6(k+2))/6 ] = (2k+2)*[ (4k+6)(k+2)/6 ] =  (2k+2)*[ 2 (2k+3)(k+2)/6  ] =   (2k+2)*[  (2k+3)*2*(k+2)/6  ] =   (2k+2)*[  (2k+3)(2k+4)/6  ] = [(2*(k+1))(2*(k+1)+1)(2*(k+1)+2)]/6 replacing k+1 by m, we get replacing k+1 by m, we get [(2*m)(2*m+1)(2*m+2)]/6 this completes our proof b...

Question: Q1 a. Sketch the static characteristics of a diode. (6 marks) b. An AC voltage source V drives a transformer with centre tap second indin gs connected to two rectifiers is shown in the following diagram. The load has constant current Io. Assume that when the diode conducts the forward voltage drop is Ve d V Vmsnot. The turns ratio is N: 1:1. Sketch the current waveform through one of the diodes. (6 marks) c. Write down an equation for efficiency of a power converter in terms of output power and converter losses (2 marks) d. Given the following parameters, calculate the efficiency of the power converter. Va = 310 V ω-2π50 forward voltage drop of the diodes VF = 0.7 V Transformer turns ratio = 10: 1 : 1 load current = 10 A Assume that the transformer has no loss and converter losses come from the diodes only. Also assume the diode voltage drop does not change with current. State your assumption if there is any 6 marks) ANSWER

Chris Johanson wants a program that calculates and displays a 10%, 15%, and 20% tip on his total restaurant bill. First, create an IPO chart for this problem, and then desk-check the algorithm twice, using $35.80 and $56.78 as the total bill. After desk-checking the algorithm, list the input, processing, and output items in a chart similar to the one shown in Figure 3-23, and then enter the appropriate C++ declaration statements.   ANSWER Program to calculate tip for the total bill. #include using namespace std; int main()       //reading inputs     double cupPrice,platePrice,cupsPurchased,platesPurchased,salesTax,totalBill;     cout     cin>>cupPrice;     cout     cin>>platePrice;     cout     cin>>cupsPurchased;     cout     cin>>platesPurchased;     cout  ...

Question: Determine the mass moment of inertia of the assembly about the z axis. The density of the material is 7.85 Mg/m3. ANSWER  

Question: 7. A circular cam 200 mm in diameter rotates off centre with an eccentricity of 25 mm and operates the roller follower that is carried by the arm as shown in Fig. 23.35. ???200 mm +100mm- Spring 25 mm Fig. 23.35 The roller follower is held against the cam by means of an extension spring. Assuming that the force between the follower and the cam is approximately 250 N at the low position and 400 N at the high position. If the spring index is 7, find the diameter of wire, outside diameter of spring and the number of active coils. The maximum shear stress may be taken as 280 MPa. Use G 80 kN/mm2 ANSWER

Question: AVL & Hashing in JAVA LANGUAGE PLEASE :) Building a data structure for countries visa applications data Step 1: build a sample data file that contains countries visa applications records in the following format: Country_Nme / Country_VISA_related_data_file_name (e.g. Germany / Germany.txt ) Step 2: using the data file created in step 1, build an AVL tree of countries nodes (use country name as key). Step 3: implement the following functions on countries AVL tree:  Print out countries sorted.  Search for a specific country  Insert a new country record.  Delete a specific country record.  Calculate tree height.  Save Tree back to file. Step 4: using the Country_VISA_related_data_file_name that stored in each tree country node, load the visa data that stored in each file. The visa record data format in these files is as follow: Passport_#/Full_name/Age/Gender/ Intended_date_of_arrival/ Intended_date_of_departure (e.g. 289332/Mamoun Nawahdah/40/M/26\4\2016/2\5\2016) S...

Question: {Nt}t >= 0, Nt = 0 for t < T1, Nt = 1 for T1 <= t < T1 + T2, ... , where each Ti is exponentially distributed and {Nt}t>= 0 is a Poisson process with rate λ. Prove that Nλn/n converges to 1 in probability as n goes to infinity. Probably have to use weak law of large numbers. ANSWER

Question: 9. An influenza virus is spreading according to the function P(t) 50(2)2, where P is the number of people infected after t days. a) How many people had the virus initially? b) How many will be infected in 1 week? c) How fast will the virus be spreading at the end of 1 week? d) How long will it take until 1000 people are infected? ANSWER

Question: NOTE: Do NOT forget to check if the necessary keyways will result in excessive stress concentrations hence make your design unsafe. The shaft to be designed is part of a larger power transmission system, which is expected to operate in an environment of 35oC, for 16 hours per day and for 5 days per week. A level of 90% reliability should be considered, while the deflection of the shaft should be less than 1/500 of its length. The angular velocity of the shaft is 1500rpm and the shaft should be designed for infinite life, while all bearings if used, should be selected so that they may be replaced after at least 12,000 hours of operation. The shaft should be supported at its ends only. The design of the supports (i.e. type, size, etc) is free but you should fully justify your choice. Some additional information (e.g. length of the shaft, the location of pulleys, etc) is also shown in the given sketch. The distance between the given shaft and each one of the collaborating s...

Question: I need your help~~ Find an expression for a cubic function f iff(1) = 12 and f(-3) =f(0) = f(2) = 0. f(x) = ANSWER Find an expression for a cubic function f if f(1) =12 and f(-3) = f(0) = f(2) = 0. f(x) =   ax3   +bx2+cx+ d f(1) = 12   ==> a(1)3   +b(1)2 + 1 c + d     = 12 f(-3)= 0 ==> a(-3)3   +b(-3)2   -3   c + d    =   0 f(0) = 0   ==> 0+0+0+ d     =   0    ==>d=0 f(2) = 0   ==> a(2)3   +b(2)2   +2   c + d    =   0 Solve[{a+b+c+d==12, a*(-3)^3+b*(-3)^2-3*c+d==0, d==0, a*(2)^3+b*(2)^2+2*c+d==0 },{a,b,c,d}] a=-3, b=-3, c=18, d=0 f(x) = -3x3   -3 x2 +18x+ 0   ANSWER

Question: Show that a Johnson counter with n flip-flops produces a sequence of 2n states. List the 10 states produced with five flip-flops and the boolean terms of each of the 10 AND gate outputs. ANSWER A Johnson counter is a sunchronous ring counter with theinverted output of the last flip flop connected back to the D inputof the first flip flop. An n flip flop Jhonson counter sequence startingfrom all 0's, First clock pulse  insertsa 1 to  the left most FF Second clock pulse inserts 1 to the 1st FF and shifts 1 to thesecond FF This sequence continues until all the n flip flops are 1 ,that is at the end of n clock pulses all the FFs are HIGH.This goes thrugh n states The next clock pulse inserts a 0 to the left most and thesequence conitues until all the FFs are LOW. This goes through nstates. Thus a total of n+n = 2n different states are present in an-bit Jhonson counter With n=5, the truth table and the ouput of ht...