3. Consider the following knapsack problem: x1 + 3.x2 + 6x3 + 7x4 max x1 + 2.x2 + 3.x3 + 4x4 < 11 3.1 Solve the problem for x; E {0,1}. 3.2 Solve the problem for x; E Z+ (non-negative integers: 0, 1, 2, 3,...).

Q: 2. Show that (2) (¹)+(2-1). Can you provide = an interpretation of this equality?

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A: Given query is to find the limit of the expression.

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Q: 5. SET-B Form the PDE of the following by eliminating arbitrary constants a and b from Z = (3x - a)²…

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Q: 2. K-5InX+3 find dw dr dw

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Q: 0 Find m/RTS R 7x+1 19x + 11 T 6x - 4 S

A: Given query is to find indicated angle.

Q: э) Compute P(-1< 3X < 12). p) Compute P(2 < 3X < 12).

A: Let ,  The mean of exponential distribution is ,  The probability density function of X is ,  =  0…

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A: Given, limx→03x4+9x35x4+3x3

Q: 4. Prove that x*+2x²+5 + x²+2x*+6 =0 x-1 x-7 has a solution between 1 and 7.

A: We need to solve the polynomial.

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A:

Q: 2. Maximize z = 2x₁ + x₂ subject to: x1 + x₂ ≤7 2x₁ ≤ 11 2002 ≤7 X1, X20 ₁ and 2 integers

A: The given problem is to solve the given linear programming problem for the given constraints. Given…

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Q: 4. Let h(r) = 5 x 6 20 x²3x18 Find all values of N for which h(N) = 3.

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Q: 3. Factor each of the following fully. a. f(x) = x* + 3x³ – 38x² + 24x + 64

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Q: Show that if ax2 + bx + c = 0 for all x, then a = b = c =0

A: It is given that, ax2+bx+c=0 for all x,  To prove a = b = c = 0

Q: 10. Solve 3(h – 5) – 3 =- 5(h + 5) | |

A: To solve: 3(h-5)-3=-5(h+5)

Q: 1. Given that r + px+q and 4x +q have a factor (x-r) where p,q and r are non-zero. Show that 4p…

A: topic - quadratic equations

Q: 3x²³-2x² + 3kx + 18 by x- 6 to be equal to zero, k must be equal to.

A: Use division

Q: 2- Max z =30 x, + 30 x2 X +2 x2 2 80, 3x +2x2 2 120, Simppler s.t. X, X, 20

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Q: For what a is ||ai - 3j + k||=16

A: Topic - vectors

Q: Which

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Q: 1. Given the following: 1 P5(x) = (63x5 - 70x³ + 15x), Determine P(x). A. P(x) = (231x6 - 315x4 +…

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Q: Ex:- Min Z= X-3 X2-2 X3 %3D sub to 3X1 - X2 + 2 X3<7 -2 X + 4X2 く12 -4Xi+ 3X2+8X3 slo Find anew…

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Q: 10. Suppose X-N (3.2) Find P (22}, P(X>3)

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A:

Q: 4. Is (1,5) a solution of 3x-2y S-4

A: Let's find.

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A: Basic probability

Q: 2. Find the limiting values of 3x2 + 5x-4 (i) 5x? - x +7 as x → 00

A: