Let What is the rank of AT A? Answer: A 3 0 0 0 0 0 5 11 −4 0 3 6 5 2 0 0 3 6 2 0 0 0 8 0 0 00 0 0

Q: Use Laplace transform to solve the partial differential equation: o²y_by -+xt where y(x,0) = 0,…

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Q: Let X be a limit point compact metrizable space. (a) Show that there exists no continuous,…

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Q: Q2/ Find ow/or if w = (x+y+z)³, x=r-s, y = cos(rs), z = sin(r + s) at the point (r, s) = (0,1)

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Q: Consider the function. + 10 f(x) = Determine the intervals on which f is increasing, decreasing,…

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Q: (b) Find the Fourier-sine transform (assume k ≥0) for 1 f(x) = x + x³

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Q: When playing Yahtzee, you roll five regular 6-sided dice. How many different outcomes are possible…

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Q: a non-planar graph that is not homeomorphic to K5or K3,3.

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Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: a) In the graph given in question each vertex has a degree of 4, hence from the Eulerian Graph…

Q: Let f(x, y, z) = g (x² + y² + z²) where 2 9 is some nonnegative function of one variable such that…

A: If S is a surface given by parametric form r→ u,v =x u,vi^+y u,vj^+zu,vk^…

Q: What is the value of k such that the lines 3x + 6ky-7 and 9kx + 8y=15 will have the same positive…

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Q: y" - 5y'=x-2, when x = 0, y = 0, y = 2

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Q: Using separation of variables find a one parameter family of s dy 8x² + 3 -2x e dx xy tions of the…

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Q: Use Laplace transform to solve the partial differential equation: dy dy +xt where y(x,0)= 0,…

A: Solution

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: A connected graph G is said to be Eulerian if the graph G has a Euler circuit. A graph has an Euler…

Q: SD a strongly connected graph? D: W

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Q: Can the graph G be orientable? G:

A: Yes the graph is orientable.

Q: b, be complex numbers and N a positive natural number such N¬I i2knx N = απ Τ n = 0 to N - 1 k=0

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Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: (a) Consider the given graph, Eulerian Graph theorem: it states that an Eulerian trail exists in a…

Q: Are the following deterministic or stochastic? Stock market Patient’s EKG, EEG, blood pressure or…

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Q: A transportation engineering study requires that you determine the number of cars that pass through…

A: Solution: Part(a)       Number of cars between 7.30 - 7.45 : In 4 min: 18 cars, So, In 15 min: 67.5…

Q: Use cylindrical coordinates to evaluate the following triple integrals toutube √²-² (x² + y²) dzdy…

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Q: ) Solve by using Laplace transform the partial differential equation ay-9 0² =0 dy(x,0) y(0,t)= 0,…

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Q: Given z = cos (2) + i sin (2241), where n is a po

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Q: ) Solve by using Laplace transform the partial differential equation 8²y 2², =9. dt² Ox² y(0,t) = 0,…

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Q: f(x) = 3.1.³ et 1. Using the laws of Calculus, provide the expression for f'(x)- which will be our…

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Q: calculate the volume of G where G is bounded by 2= x² + y²₁ ²²+ y² = 4, 200 SS f d v

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Q: A and B are two events such that P(A) = 0.4 and P(An B) = 0.2 Then P(An B) is equal to O 0.8 O 0.6…

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Q: Show that if 4, and A, are two events, then P(A₂)+P(A₂)−1≤P(44₂).

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Q: Find what value of c does f&dx = 1? с Answer:

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Q: If 11z¹ +10iz⁹ +10 iz-11 = 0, find the possible values of [z].

A: The given question is related with complex analysis. Given the equation 11z10 + 10iz9 + 10iz - 11 =…

Q: Q4) Solve the boundary value problem y - 3y + 2y = 0 with y'(1) = 1, y(3) = 2e¹-e² h = 0.5

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Q: 1. E is a triangle with vertices (1,0,0), (0, 3,0) and (0, 0, 2), with 8(x, y, z)=xz+1.

A: Note: As per our guidelines we are supposed to answer only one question and the rest can be…

Q: Sketch the curve r = 8+8cos € in polar coordinates.

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Q: Question 9 Using Trapezoidal method rounding off, no spaces) Blank 1 Add your answer 3 Points ₁x³dx…

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Q: Minimize C=3L-4K subject to 120=3K⁰.7L0.3. Find L*, K*, A*, C*. Now, Use Bordered Hessian to verify.

A: z =xy subject to x + 2y = 2lagrange function:L =U(x,y) +λ (M-p1x-p2y)

Q: Consider the curve defined by the equation y = 5x + 1x. Set up an integral that represents the…

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Q: For X and Y normed linear spaces, let {T} be a sequence in L(X, Y) such that Tn →T in L(X, Y) and…

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Q: Use Taylor series method to compute x(0.2) and given that d²x dx de -4x=0,x(0)=1,-(0)=2 dt² dt dr…

A: Taylor series of f(x) at x=0, is given by fx=f0+xf'0+x22!f''0+x33!f'''0+x44!f''''0+.....

Q: For a data set of size 10, the highest order of a polynomial that could be fitted using Least…

A: Inbtroduction: The least square approach involves minimising the sum of the squares of the points'…

Q: How many permutations of {1, 2, 3, 4, 5, 6, 7, 8) leave exactly 1 element fixed?

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Q: Consider functions f: {1, 2, 3, 4, 5, 6, 7} → {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. a. How many of…

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Q: prove that every subset of negligible. set is negligible.

A: I have used definition of negligible set.

Q: Use separation of variables method to solve: ди ổn ôn + =u where u(0, y) = 0 and ду Əx² du(x,0) ду =…

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Q: 2. g(t)= t², -8 + 3t, ((t-6)² + 2 cos (²-²). 0 2

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Q: (ylny-exy)dx + ( + xlny) dy = 0

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Q: 10 A graph of f(x) is shown above. Using the geometry of the graph, evaluate the definite integrals.…

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Q: Find the rate of change of the function fin the direction of PA. Also find the maximum value of that…

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Q: Mrs. Pack wants to teach her children responsibility and how to work while helping them earn money…

A: We can use calculus to maximize area  For relative maximum or minimum To maximize or minimize  a…

Q: uppose you 17 one-dollar bills to give out as prizes to your top o discrete math students. How many…

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Q: How many 7-letter words contain exactly 2 vowels? (For example, an 8-letter word with 5 vowels is…

A: To find the number of words contain exactly two vowels :-