5.Transform this LP model into a proper standard form Minimize Z = 8x1 +2x2 +7x3 Subject to : 2x1 + 6x2 + x3 = 30 3x2 + 4x3 < 60 4x1+ x2 + 2x3 < 50 X1 + 2x2 > 20 х1, х2, х3 > 0

Q: Find the two positive integers whose sum is 16 and the sum of whose square is minimum

A:

Q: 2. Form a polynomial f(x) of least degree having real coefficients, i as a simple root, 0 as a root…

A:

Q: Evaluate the integral [/4x4 – 12x² +7 xdx (2x2 – 3)/4x4 – 12x² +7 – 2ln|2x2 /4x4 – 12x² + 7|} + c…

A: Given that, The integral is following, I = ∫4x4-12x2+7xdx We have to solve this integral.

Q: (²) BC₁crp (u² csc² 6) + K = = 9 ( 3 ) πr²u²p + K

A: Given: 29BCLcrpu2csc2θ+K=49πr2u2p+K

Q: Find the parabola y = ax2 + bx + c that best fits the four points (0,0),(1,2),(2,3),(-1,1) by the…

A: Step 1:Step 2:  Step 3: Step 4:

Q: Use the given real ZERO of the polynomial function to find the remaining real ZEROS. f (x)= 380x² +…

A:

Q: Find the counterexample to show that the following conjecture is false. (x + Y)^2 = x^2 + y^2  is…

A: We need to show that the conjecture: x+y2=x2+y2 is false using a counter example. It is known that…

Q: Exercise 21 Simplify the following: (2x - 1)(x - 3x - 1) (3x + y}(9x² - 3xy + y) 2. 1. (x+2)(x² +…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Explain Perpendicular Least Squares.

A: Introduction: The perpendicular least squares method is a special method of fitting a linear model…

Q: Let a0, a1, a2, a3, a4 be constant real numbers such thata0/5 + a1/4 + a2/3 + a3/2 + a4 = 0.Show…

A: Consider−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−f(x)=5a0​x5​+4a1​x4​+3a2​x3​+2a3​x2​+a4​x.with  input from…

Q: use to Fixed point iteration method solve FØx1= e-x Xo=0 A=4

A: Given function is fx=e−x and x0=0, n=4. We have to solve the fx=e−x by using fixed point iteration…

Q: Identify the value of a in the quadratic function 4. – 21 = –3x. O A. 4 O B. 3 O C -21 O D. -3

A: To identify the value of a in the quadratic function 4x2-21=-3x. Solution: We know that a quadratic…

Q: Find a linear funtion P(z) = a + a₁ which gives the best least squares fit for the following points:…

A: Given the points -4,0, -2, -2, 4,-9, 5, -8. Now,  x y x2 xy -4 0 16 0 -2 -2 4 4 4 -9 16 -36…

Q: Find the absolute max or min for (x+1)(x^2-4)

A:

Q: Find the gcd of (x^4+x^3+x^2+2x+3) and (x^3+4x^2+2x+3) in Z5.

A:

Q: Let u = 3 II x₂ that satisfy the equation X2 -4 CHE 3 || -5 -3 (Simplify your answers.) and w= -4 -5…

A:

Q: A test program for grade 10 can generate quadratic functions in a standard form y = ax + bx + e…

A: Given quadratic function in a standard form is y=ax2+bx+c wherein coefficients a, b and c are…

Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: Find a polynomial P(z) = a + a₂z+ª₂x² of degree 2 which gives the best least squares fit for the…

A:

Q: Suppose P is the invertible and A = PBP^-1.  Solve for B in terms of A.

A: Do an algebraic manipulation of matries by multipliation.

Q: What does is mean for two functions f(x) and g(x) to be orthogonal

A:

Q: Write the equation of the square root function that has domain 5, 00) and range -4, oo). f(x) = Vx…

A: To write the equation of the square root function that has  domain [5, ∞) and range [-4, ∞)

Q: Perform Crout's method on 2x₁5x₂ + x3 = 12 -X₁ + 3x₂x3 = -8 3x₁4x2 + 2x3 = 16

A:

Q: Construct a polynomial from the data (1,4),(3,14)(5,19),(7,21),(4,23),(11,21) and also find…

A:

Q: Factor 6b-10b'.

A: To factor 6b-10b3

Q: Why the minimal polynomial x^2 - (sqrt(2)+sqrt(-2)) splits into linear factors over K?

A: Assume K is a field that includes the square roots of both 2 and -2. The formula for the element  α=…

Q: The product of 2x³ + 3x² + 1 and 2x² + 4 in z5[x]/ is: 5x^2+ 5x +1 4x+1 O x^2+2 None

A:

Q: With f(z) = 5z² – 7z – 2, find the following: a) f(2) b) f(1) + f(0) c) f(r+h) – f(r - h)

A:

Q: Min 2こ d 2 t0125 + 3 X2 X + X 2 X, i XZ

A: Min Z =   2 x1 + 3 x2 subject to   0.5 x1 + 0.25 x2 ≤ 4     x1 + 3 x2 ≥ 36     x1 +…

Q: If x² +2y+3z? = x² + 2y² + 3z² = x² + 2y3 +3z3 =2, and x₂x3 +2y₂y3 +3z₂z3 = x3X₁ + 2y3V₁ +3Z3Z1 =…

A:

Q: Ques. Apply a change of vaviable X=Py txansforms Hhe quuardratic form 2. into a quadratic form with…

A: Consider  Rx=5x12+6x22+7x32+4x1x2-4x2x3 In matrix form: XTAX=x1x2x352026-20-27x1x2x3 Here,…

Q: 2.

A:

Q: why the minimal polynomial x^2 - (1+sqrt(2)) does not split into linear factors over K?

A: Let K be a field  . Then a polynomial f(x)∈K[x] splits into linear factors in K if K contains all…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.