(d) How many solutions are there to the equation x₁ + x₂ + x3 = 11, where x₁, x₂ and x3 are positive integers? Explain your answer. Note: this means the values of the variables are strictly greater than zero.
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- Answer the following and show solutions.3- Simplify the following equation: f(4, B,C,D) = E(0,3,4,6,10,11,14,15) dm(2,7,8,12) where dm is denoted for don't care.Eliminate useless variables and symbols. Afterwards, convert to Chomsky Normal Form. (Start variable S) S -> ABBC | BA A-> abB | aa B -> bB | Aa C -> Cb | aC
- (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.Simplify the following logical expressions:The number 72 is to be represented as the sum of two positive parts, such that the product of one of the parts by the cube of the other is a maximum. It is desired to find the two parts.
- design a code as expected solution in the below problemCan you answer 12 and 13?Write 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.