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(Algebra: solve 2 × 2 linear equations) You can use Cramer’s rule to solve the following 2 × 2 system of linear equation provided that ad − be is not 0:
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- Simplify the following expressions in normal form, if one exists: (λq. q q)(λs. s s a)arrow_forward() Wride the bonlowering in mathematica expression z= Je'ry? + loe-yt b. q EKarrow_forward(Thermodynamics) The work, W, performed by a single piston in an engine can be determined by this formula: W=Fd F is the force provided by the piston in Newtons. d is the distance the piston moves in meters. a. Determine the units of W by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for work listed in Table 1.1. b. Determine the work performed by a piston that provides a force of 1000 N over a distance of 15 centimeters.arrow_forward
- (Statics) An annulus is a cylindrical rod with a hollow center, as shown in Figure 6.7. Its second moment of inertia is given by this formula: I4(r24r14) I is the second moment of inertia (m4). r2 is the outer radius (m). r1 is the inner radius (m). a. Using this formula, write a function called annulusMoment ( ) that accepts two double-precision numbers as parameters (one for the outer radius and one for the inner radius), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 5a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.arrow_forwardWrite computer codes using any programming language for one of the following methods to solve a linear equation system.1- Gaussian elimination.2- LU decomposition.3- Gauss-Seidel iterations.Execute the program for the linear equation system given below.arrow_forwardSimplify the following logical expressions:arrow_forward
- (X-3)²+(y-1)²=4arrow_forwardF= (~A xor ~B) or ~CF= ~A or ~B or ~CF= ((~A or B) and (~A or ~B)) or (C+~A) Use the functions above to create digital circuits.2- Use Boolean Algebra to simplify the following functions.F= (~A+B) (A+B)(C+A)F= ABC+ A(~B+~C)+C(A+B)F=(A+B)(A+C)(B+C)arrow_forward(Prove using Direct Proof)Theorem: Directly prove that if n is an odd integer then n^2 is also an odd integer.Proof:arrow_forward
- Q.2: Write Regular Expression for the following automation by using Kleene's Theorem (q, is the final state). 90 ga 9b qc a barrow_forwardQuestion The refractive index of Sodium Chloride is 1.54. Make a function by which user can Find the critical angle of diamond by taking Air as a rare medium (Refractive index of Air is 1). Note: (User Take different incident Angles as a Input)arrow_forwardPyhton Help, As soon as possible You and your friend sell 80 tickets to a raffle. You sold 20 more than your friend. The goal of this problem is to find how many tickets you and your friend have sold. (a) Set up the linear equation for this problem as Ax = b, where x = number of tickets your friend sold. (b) Find A-¹ (Please show your steps). (c) Use A-¹ to solve x. (d) Use python to verify that your A-¹ and solution x are correct. Write your answers for part a here, find the Matrix A from scratch. Write your answers for part b here, please calculate A-¹ manually Write your answers for part c here, x = A-¹b, please perform this calculation manually. [] import numpy as np A = np.array(...) b = np.array(...) [] x2 Fill in the blank in the code cell below for part d, please use your own Python code to replace "..." parts. If you prefer, you can write your piece of code from scratch instead (without filling in the blanks). A_inverse = . Let x₁ represent number of tickets you sold, and x2…arrow_forward
C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr