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- Exercise III: Catalan numbers For n e N, denote by c, to be the number of ways to form a "mountain range" with n upstrokes (U) and n downstrokes (D) that all stay above a horizontal line. For instance: for n = 1, only UD is allowed, so c = 1; • for n = 2, only UUDD and UDUD are allowed, so c2 = 2. 1. Check that c3 = 5 by writing down or drawing all possible options. 2. Consider the power series +00 g(x) = 2 n=0 (by definition co = 1) called the generating function of the sequence (en). Justify that cn < 4" for each n, and deduce that the radius of convergence of g is at least 1/4. 3. It can be show that for r E (-1/4, 1/4), g(x) = 1+ xg(r)? and therefore 1- VI 4.x g(x) = 2.x Use this formula and the known power series of V1+ x to write the first terms of the power series expansion of g, in the form g(x) = co + c1x + c2x2 + C3x + c4x* + ·.. Show how you obtain a few terms, but you do not need to show all computations and you can use a calculator for fractions. Check that you recover co,…F3 R1 F2 R2 The wheel shown is free to rotate around a fixed axis which passes from its central point. Three strings are tied to the wheel and pulled, which results in the forces shown on the figure. The moment of inertia of the wheel is I. Data: 0.6 m, R1 = 0.3 m, F, R2 10 kg m2 F Find the angular acceleration a of the wheel along the indicated direction. 20.0 N 30.0 N, F3 10.0 N, rad/s? Check6- Write a program to read three numbers A,B,C then find whether A,B,C can form the sides of a triangle, if yes compute the parameter of the triangle, if no print the massage ( not a triangle), then determine whether A,B.C form the side of an (a)) equilateral triangle b) isosceles triangle ,c)) right angle triangle Hint: (A,B,C can form a triangle if each side is less than the sum of the other two sides)
- Hw12-Matrices äböi ).. إضافة تعليق صف Write a program to make a table of the physical properties for water in the range of temperatures from 273 to 323 K. The Density : d = 1200.92 - 1.0056 T + 0.001084 T^2 The conductivity: K= 0.34 + 9.278 * 10-4 T The Specific heat: CP = 0.015539 (T - 308.2)^2 +quadratic.py by using "sys.argv" ● Create a program, quadratic.py, that takes in three arguments that represent the a, b, and c values in the quadratic formula. The values should be to two decimal places. You do not need to account for imaginary values. Then print out both roots in the form: “The solutions are x and y” Where x and y correspond to the positive and negative roots, respectively.Python Programming TasksQuestion 3Businesses some time market their contact no as: 111-GET-SONY. This technique makes easy for the customers to remember the brand name. To do so they use the alphabets that are printed on the numbers on dial pads of Tele/Mobile phones as follows: A, B, andC = 2D, E, and F = 3 G, H, and I = 4 J, K, and L = 5 M, N, and O = 6 P, Q, R, and S = 7 T, U, and V = 8 W, X, Y, and Z = 9. However, the telecom systems needs proper numbers for dialing. Create anapplicationthatshould prompt the user to enterthe no in specified format such as XXX-XXX-XXXXand then translates the number to their numeric equivalent. Input: 111-GET-SONYOutput: 111-438-7669 Question 4Write a program imitating a website where users can signin/signup, view certain information which can only beseen by signed in users, logout or exit the application.Initially you would have asequence userswithfollowing structure:users =…
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- Create a four-function calculator for fractions by using following formulas. a) Addition: a/b + c/d = (a*d + b*c) / (b*d) b) Subtraction: a/b - c/d = (a*d - b*c) / (b*d) Note:The program should display above mentioned formulas first. The user should take the values of a, b, c, d from user. The program should then display the result of each process Addition, Subtraction, Multiplication, and Division on separate lines on screen.Q3: The volume of a circular cylinder V=Ttr?h, write a program to compute the volume if r=8m and h=15m and then create another cylinder have a size larger than the first by 20%, but having the same height as the first, how much the radius should beTutorial 3: A simple force balance on a spherical particle reaching terminal velocity in a fluid is given by; |4g(P, -p)D, V : 3C,p Where Solution by Visual Basic V Terminal velocity in m/s g: Acceleration of gravity Pp: Particle density Dp: The diameter of the spherical particle in m CD: Dimensionless drag coefficient. The drag coefficient on a spherical particle at terminal velocity varies with Reynolds number (Re) as followings: Cp=24/Re Cp=24*(1+0.14* Re^0.7)/Re Cp=0.44 Cp=0.19-80000/Re Where, Re =(D, Vi p)/u =994.6 kg/m3 µ=0.0008931×kg/m.s. Calculate the terminal velocity of spherical particle using visual basic program? for Re< 0.1 for 0.1=SEE MORE QUESTIONS
