How many vertices and how many edges does Kn have? Multiple Choice It has n(n-1)/2 vertices and n edges. It has n vertices and n(n-1)/2 edges. It has n vertices and n(n+1)/2 edges. It has n(n+1)/2 vertices and in edges.

Q: True or false Ć Stochastic approximation is the same as sample average approximation.

A: To Explain : Stochastic approximation is the same as sample average approximation is it true or…

Q: a) show that the given function is 1-1 or give a counterexample. b) show that the given function is…

A: (a) Let, f(X) = f(Y) for X, Y ∈ P(N)            => N - X = N - Y           => N - (N - X) = N…

Q: (a) Give an example of a bounded sequence that diverges.

A: Since all questions are different ,so according to the guidelines I will solve first question. That…

Q: Find the lines that have four point contact x4 + 3xyz + x² − y² − z² + 2yz − 3xy - 2y + 2z = 1. - -…

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Q: G K O + + R ca B +

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Q: P3 Find the Maclaurin expansion for the following functions and indicate for which values of r it…

A: We find Maclaurin expansion of given function

Q: Prove that: ² ² ; x ²) = ↓ sin¯' x + 1 + + ((a) 2 ³₁ ( ² ² ² i (b) 2 -x tan X

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Q: Investigate whether the series ∞∑n=1n3/(ln3)n converges or diverges.

A: Ratio tes: test for Series converge or diverges

Q: i=1 ow, assume that the series 1 an with nonnegative terms an> 0 is a convergent series. Use ✓n= e…

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Q: FIND THE GENERAL SOLUTION OF THE GIVEN SYSTEM : dx dt = 2х-у dy dt = X

A: Use the given equation.

Q: Compute the "best fit" plane containing the following points: (4,0,-2) (2, 1, -3) (-3, 1, 4) (-2.9,…

A: To find the best fit plane that for the points 4,0,-2,2,1,-3,-3,1,4,-2.9,0.9,4.1 To find the normal…

Q: The figure F, shown below, is a square-based pyramid with edges all of equal length. The location of…

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Q: Find the general solution of Euler's differential equation, x²y" — 4xy' + 6y = 0, - y = y(x).

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Q: Consider the two power series Σ f(x) = x + n=0 (3x)2n+1 (2n + 1)! 8 (x + 1)" g(x) = Σ 3 n ln(n) n=2…

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Q: Based on the above, find the general solution of the following differential equation y""-y" - 2y' =…

A: This is method of undetermined coefficients

Q: FIND THE INTERVAL AND RADIUS OF CONVERGENCE FOR THE GIVEN Enso ६०. (-1)7 qn 2n+1 x 2n

A: The given problem is to find the radius of convergence and interval of convergence for the given…

Q: Find the equation of osculating plane at any point 't' on the hell- : Y = @ sin t x.= @ Cost,

A: We will find binomial vector from given parametric equation as binomial vector is perpendicular to…

Q: As the equation is exact, there is a function f such that. = M(x, y) and = N(x, y). af ax af ду To…

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Q: student council consists of 8 students, with 5 women and 3 men. e. In how many ways can a committee…

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Q: F = -3xyi +10yj+k is the velocitiy field of a fluid flowing through a region in space. Find the flow…

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Q: Show that the length of the curve x = 2a sin [sin ^²)]», t+t | - 2 », y = 2at², z = 4at is 4 √2 a…

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Q: Find the average temperature on that part of the plane2x + 2y + z = 4 over the square 0 ≤ x ≤ 1, 0 ≤…

A: The given function of temperature is, Tx,y,z=e2x+y+z-3. The surface is z=4-2x-2y over 0≤x≤1,0≤y≤1 To…

Q: Consider the system: |x₁x3 + x₂x² = 0 |x₁x³+x²x² = 0 1. Can we solve for x3 and x4 as functions of ₁…

A: Implicit function theorem for system of equations:  Consider a system of equations:…

Q: a raindrop falls, it evaporates while retaining its spherical shape. If we make the further…

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Q: 1. Consider a function : DR where DCR is measurable. Show that the following are equivalent: (i) is…

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Q: Determine whether the set {0.0-0} is linearly dependent or linearly independent. Justify your answer…

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Q: 80% of the voters favor Ms. Stein. If 450 voters are chosen at random, what is the expected number…

A: We shall use the formula for expectation of a random variable following binomial distribution: E[X]…

Q: Use (a) the Trapezoidal Rule integral 1to 4    sqrt x cos x dx                 with n= 8

A: The trapezoidal rule is the technique used to find the approximation of the integral by dividing the…

Q: 1). Calculate the Taylor polynomials T2(x) and T3(x) centered at x = a for the given function and…

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Q: Show that the following series are convergent and find their sums: 1 a) 1ײ×3 +2×3×4 + ... +…

A: (a).

Q: Find the equation of osculating plane at any point 't' on the helix x = a cost, y = a sin t. z = ct

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Q: To obtain some idea of the possible dangers of small errors in the initial conditions, such as those…

A: We can solve the given differential equations.

Q: Consider the following parametric curve. Answer parts a and b. t+7√₁y=t-7√₁t=1 x=t+ b. Make a sketch…

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Q: Flux across the boundary of an annulus Find the outward flux of the vector field F = ⟨xy2, x2y⟩…

A: Given: F=xy2, x2y,  R=x, y| 1≤x2+y2≤4=r, θ | 1≤r≤2, 0≤θ≤2π To find: Outward flux of a vector.

Q: Tuberculosis (TB) is one of the top 10 causes of death worldwide. According to the World Health…

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Q: The book club has 15 members, 7 distinct romulans and 8 distinct klingons. In how many ways can a…

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Q: Approximate volume (rounded to the tenths place): ft3

A: Kindly refer to Step 2 for the solution.

Q: Let fE C(R) such that f is an infinitesimal of order 3 with respect to x-3, as x→ 3. It's true that…

A: Given that f∈ C4R. Then any function f(x) can be expand by using Taylor series as f(x) = f(3) + f'3…

Q: We have written the given differential equation in the form M(x, y) dx + N(x, y) dy=0 where M and N…

A: Given a differential equation Mx, ydx+Nx,ydy=0. Here Mx, y=y-8xex-6x2 and Nx, y. To find the partial…

Q: Let a and c be nonzero real numbers and consider the differential equation ay" + y + cy=0 Color the…

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Q: 5. A pitcher contains 4 cups of juice. The pitcher is filled to 15 of the capacity. How many cups of…

A: This is a problem of counting.

Q: Identify the type of frieze pattern illustrated in each of the following design. Frieze Pattern…

A: The first frieze group F1 contains only translation symmetries Hop The  fifth frieze group F5…

Q: Show that the osculating plane at P has three point contact in general (contact of second order)…

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Q: b) Σ=1sec*x

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Q: Consider the following matrix: A The following vectors are linearly independent eigenvectors of A:…

A: The given problem is to find invertible matrix P and diagonal matrix D for the given eigen vectors…

Q: With a present value of $150,000, what is the size of the withdrawals that can be made at the end of…

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Q: (c) Study the convergence of the following series Is it absolutely convergent? Σ n=1 (-1) n+1 2n +…

A: Leibniz's test for alternating series: An alternating series converges if it is monotonically…

Q: Find the 2nd order linear differential equation whose fundamental set of solutions is {y₁(x) =…

A: y1x=cosbx, y2x=sinbx

Q: Prove that if p and q are distinct odd primes

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Q: Q1- 1 = √² x² √a² — x² dx 0

A: I=∫0ax4a2-x2dx