-1 0 12 0 1 0. -3 -1 12 1 -3 -3 Ans. -1, ;-5, ; 3, -1 -4 1 1 -4 -1 1 3. ..

Q: Q2 The following graph shows the position function r(t) of a mass attached to a spring. Note that…

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Q: Q5. Solve the following classification problem with the perceptron rule. Apply each input vector in…

A: Solution: We start by calculating the perception's output a for the first input vector p1 Using the…

Q: A planet P in the xy-plane orbits a star S counterclockwise in a circle with radius 10 units,…

A: To find parametric equations for the x- and y- coordinates of the planet P at time t.

Q: Let d be a metric on X. The distance between an element p E X and a nonempt; subset AC X is defined…

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Q: If o is a k-cycle then the order of o is k. On the otherhand, if 7 is a product of disjoint cycles…

A: a) since this is a four cycle , then order is 4  b) order is lcm(3,4) = 12 c) order is lcm(4,2,3)…

Q: A smooth vector-valued function R(t) satisfies Ř(1) = (-3,7, 9), '(1) = (0,5, 6) and R"(1) = (4, 1,…

A: Introduction: In three-dimensional space, cross product is a binary operation on two vectors. It…

Q: Question 4 Suppose that for a certain product, the market price P = P(Q) can be written as a…

A: Given: P=500-QQ0=80 To find: a) P0 b) Strictly increasing Q0 c) dCSdQ0>0

Q: Let G = (a) be an infinite cyclic group. Define f: (Z, +)G by f(n) = a" %3D Prove this map is an…

A: The given infinite cyclic group is G=a. The function f:ℤ, +→G is defined as follows: fn=an Prove…

Q: 1. Which of the following functions are in the Hilbert space with indicated interval? (a) f(z) = e*,…

A: (a) f(x) = eiπx          -1≤x≤1f(x) interval [-1,1]  is finite and singeled valued. f(x)2 = finiteso…

Q: 030: Define nilpotent element. Are 1 and 3 nilpotent elements of Z11?

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Q: For each positive number n, let P(n)be the formula 1 1 (1+;)(1+ (1+– = n + 1. .. (a) Write P(1). Is…

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Q: Let Fib (n) be the nth term of the Fibonacci Sequence, with Fib (1) = 1, Fib (2) = 1 and Fib (3) =…

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Q: Problem 3. Which of the following nonempty subsets of the vector space Mnxn are subspaces? (a) The…

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Q: (2) Assume that we have a Cobb-Douglas production function for a certain industry: Q = CL°K®, where…

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Q: findinequality if 121 =1 then isl8-31Eu.

A: Introduction: The triangle inequality asserts that the sum of the lengths of any two sides of a…

Q: if it was fcx) = Sin 3X,9(x)=COS4X EC where the internal multiplication is ove katati ID =S fcx) gx)…

A: f and g are perpendicular when , <f,g> = 0

Q: Q5:(A) Let R=(Z12 ,+12, -12 ). Find a) Maximal ideals of R b) Is (Z12, +12) a simple group? c) Is…

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Q: Q4: (A) Prove or disprove each of the following 1. Every prime ideal is maximal. 3. The cancellation…

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Q: Qs: (A) Let R be a ring with identity. Define g: Z→ Z by g(x) = x. 1, Vx E Z. Is ga homorphism?…

A: We show that the given map is a homomorphism using the definitions. The detailed solution is…

Q: E Define maximal ideal, prime ideal.

A: Introduction: An ideal of a ring is a specific subset of its components in ring theory, a field of…

Q: Qi: (A) Let R =(Z12+12-12). 1. Find all maximal ideals of R. 2. Evaluate char. (R). 3. Is R a field?…

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Q: Answer the following questions.   A. Complete the square to show that f(x) can be rearranged in…

A: Introduction: A function is an expression, rule, or law in mathematics that defines a relationship…

Q: Q1/ Use the simplex method to Solve the following problem? Max Z = 8x1 + 10 x2 +7 x3 Subject to: x1…

A: The given linear programming problem is…

Q: Let T : P2 → P2 be the linear transformation such that T(1) = 4+ 2x + x², T(x) = 3x, T(x²) = 1+2x +…

A: The matrix is diagonalizable if and only if the algebraic and geometric multiplicity of each…

Q: 1 tan x Evaluate lim ( -)*. 1 tan x Evaluate lim x>0

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Q: Let G be a group and a e G such that o(a) = n < oo. Show that a = a' if and only if k =l mod n. %3D

A: Let G be a group and a∈G such that Oa=n&lt;∞. Show that ak=al if and only if k≡l mod n. If k=l the…

Q: 3 Let I be an ideal of the ring R and define the set ann (1) ={rERIra=o, VaE Prove that ann (I)…

A: We have to show that  ann(I) is left as well as right ideal of R

Q: (1) Suppose that y is a function of r satisfying the equation 5x + 10y + 3.ry+ 5y + 6x 0. Use the…

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Q: (c) What is the real part of ein/4?

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Q: Ql: what's the relation between prime and semiprime ideals.

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Q: To find two real numbers whose sum is 23 and whose product is maximum, we should find the maximum…

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Q: A formula of order 4 for approximating the first derivative of a function f gives: f'(0) = 1.0982…

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Q: Use a software program or graphing utility to solve the system of linear equations. (If there is no…

A: We will use a gauss Jordan elimination software  to compute the solution of given system of…

Q: Qs: Define the Boolean ring and prove that every Boolean ring is commutative. Is the converse true?…

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Q: Q5) Solve the equation with y (0,1) = y (1,1) = 0 y (x,0) =sin x 0,0sxSI 8 and ôy (x,0) (r=1, h= 0.1…

A: The given P.D.E is                           ∂2y∂x2=∂2y∂t2  with y0,t=y1,t=0      yx,0=18sinπx…

Q: Q2 The following graph shows the position function r(t) of a mass attached to a spring. Note that…

A: The time interval between two waves is known as a Period whereas a function that repeats its values…

Q: Let u = 10i + 2j, v=i+j, and w = i-j. Find scalars a and b such that u = av + bw. a = b =

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Q: Determine the maximum curvature for the graph of f(x) = 7 In (2x). The maximum curvature is at x=

A: We are given function f(x)=7ln(2x) of the graph Formula for curvature is κ(x)=|f′′(x)(1+(f′(x))2)32|…

Q: [8]. Consider the series (-1)" – n+4 n(n + 3) * Is this series conditionally convergent, absolutely…

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Q: B. Illustrate the following sets above in Venn 1. A' 2. BUE 3. FnD

A: Ac =U\A ,where U is universal set. Since the Universal set is not given, Ac can not compute by…

Q: 15. (i) Let A, B be 2 x 2 matrices over R and vectors x, y in R2 such that Ax = y, By = x, x"y = 0…

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Q: cos t- sint i+ cos t- sint) sint+ cost) i+ cost- sint j, N = 1 j. and K= For the space curve below,…

A: To find- For the space curve below, T = cost - sint2i + sint + cost2j, N = -cost - sint2i + cost -…

Q: Q3/ Optimize the function Z = x + x ? Subject to: x1 + x2 4 x1, x2, 2 0 Using Lagrange multipliers.

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Q: 2. Show that p q is congruent to (p - 4)A .

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Q: Determine which congruence method can be used to prove that the given triangles are congruent. AA.

A: INTRODUCTION: Triangle congruence: Two triangles are said to be congruent if their three…

Q: The following table shows the number of candidates who scored 0, 1, . . . , 10 marks for a…

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Q: MATCHING LIST Question 11 Complete the following proof by matching the correct statement with the…

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Q: Suppose r is a primitive root mod a prime p such that p = 3 mod 4. Prove ord,(-r) =

A: Given: p≡3mod 4 To find: ordpp-g=p-12

Q: Q4. A salesman has to visit the cities A, B,C,D and E which forms a Hamiltonian circuit. Solve the…

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Q: B. Solve as indicated. 1. Find the geometric mean of 28 and 112. 2. Find the geometric mean of 7 and…

A: 1)  Let a= 28 and b= 112 Then the geometric mean of a and b is √( 28×112) =  56