Which of the following is the orthogonal trajectories of the family of curves y = ax³ ? x³ + 3xy² = C x² + 5y² = C 5x² + y² = C 5x² + 2xy = C O A

Q: Find the minimum value of f (x,y,z) = 2x² + y² + 3z² subject to the constraint 2x - 3y - 4z = 49

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Q: Use three-point midpoint formula to evaluate the first derivative of y=tan(x) at x = O-2√/2 00…

A: Given function is y=tanx. We have to evaluate the first derivative of y=tanx at x=π4 using a value…

Q: Suppose  there exist transposition f_i , 1<=I<=t  such that

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Q: (d) A curve is defined by the parametric equations: -21 x(t)= e' cos 2t, y(t) = e²¹ sin 2t dy…

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Q: Problem 6. Let A2 = A. Prove that either A is singular or det (A) = 1.

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Q: Find the values of w,x,y and z in fraction form using a)gauss elimination, b) gauss-jordan…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Find the coordinates of the intersection points A and B, between the closed curve (x + 1)² + 4(y-1)²…

A: In this question, we can find the intersection points of the given curve. Using the equation of…

Q: 4. Is M₂ (R) a field? Justify.

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Q: y" - y' - 12 y = e^(x/3)-e^(-x/3) A) Find the complementary solution of this homogeneous equation B)…

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Q: Match each of the following with the correct statement. A. The series is absolutely convergent. C.…

A: 1. The given series is ∑n=1∞-5nnn6n To find: The given series is converges or not. Please post the…

Q: 1. Define f: R → R by f(x) = ar³ + br for a, b = R. (a) For which a, b is f injective? Prove your…

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Q: Which statement below best describes the graph? 8 6 A X +2+ -4 -6- O Domain = {-4,-3, 0, 2, 7);…

A: We want to find domain and range of given graph.

Q: 10 Mr. Kelly pays $10,140 a year for rent. His rent is a constant amount each month. Which equation…

A: Solution :  Given that  Mr.Kelly  pays $ 10,140 a year for rent

Q: Use a parametrization to express the area of the surface as a double integral. Then evaluate the…

A: The solution starts with the next step.

Q: How do you find the focus and the directrix of a Prabola?

A: We find directrix equation and focus of given parabola.

Q: find the equation of the inverse of one-to-one function  n(y) - y^2+9, y≥ 0

A: We know that x = y2 + 9 is a parabola with the vertex at (9, 0). The graph that is shown below…

Q: For each of the following equations, • find general solutions; solve the initial value problem with…

A: Solution a(1): Given system is x'=-2-1314x Let A=-2-1314 Let the eigenvalue of A is λ Then…

Q: solve the following system of equations: x'=dx/dt=7y+7e4t y'=dy/dt=5y-3e-5t x(0)=2 and y(0)=3

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Q: (b) 1 (c) e 1 123. the curves y=-e* and y=In (ax), (where a is positive) has only one point is comm…

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Q: 21 After elimination clears out column 1 below the first pivot, find the symmetric 2 by 2 matrix…

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Q: QUESTION 2 A professor design an online quiz covering six different topics. The quiz has one…

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Q: Solve the differential equation below using series methods. (-7x²+8)y'' - 2xy = 0, y(0) = 4, y'(0) =…

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Q: Find the area of the region between the curve y = 3 - x² and the line y = 1 -x from x = 0 and x = 2.…

A: We want to find area between the curves.

Q: At by first finding a fundamental matrix X(t) for x' = Ax and then using the formula e At 099 A = 90…

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Q: Four heirs (A, B, C, and D) must divide fairly an estate consisting of three items - a house, a…

A: The following steps are used for fair division by the sealed bids method. To determine the fair…

Q: Evaluate // (1+x² + y2) dV, where E is the region bounded E by the surfaces z = 6y2 - 9x², and z = 6…

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Q: 4. A 2 kg mass is attached to a spring whose constant is 6 N/m, and the entire system is submerged…

A: Note: We are entitled to solve only one question at a time and up to 3 subparts only. As the…

Q: sistance R (ohms) and the current I (amperes) by the equation P = R1². se differentials to determine…

A: In this question, the concept of the derivative is applied. Derivative A derivative can be used to…

Q: Select the FIRST correct reason why the given series converges. A. Convergent geometric series B.…

A: We will use corresponding test to check series convergent or not .  Note: maximum 3 sub part are…

Q: et ₁ Answer: = -7/11 8/11 -2/11 -2/11 = ܕܠ = -8/11 -5/11 4/11 4/11 and U3 2/11 4/11 -1/11 10/11 .…

A: Please check the answer in next step

Q: Q.1 The latent heat of vaporisation of steam r is given in the following table of different…

A: We have: T r 40 1069.1 50 1063.6 60 1058.2 70 1052.7 80 1049.3 90 1041.8 100 1036.3…

Q: Find the laplace transform of f(t) = 5t³ - 4t² +8 OF (S) = -8s³ +8s+30 OF (s) 8s³-8s+30 -88³ +88-30…

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Q: Example 7.1. The table gives the distance in nautical miles of the visible horizon for the given…

A: Here we need to find y at x = 218 ft and x = 410 ft.

Q: 5. Residue theorem (a) +²+1 Jo° ±1 dt. +4+1 Use the residue theorem to compute

A: We have given integral∫0∞t2+1t4+1 We need  to use residue theorem to compute integral.

Q: H = {n: n is a positive even integer from 1 to 50} K = {n: n is a prime number from 1 to 50} J = {n:…

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Q: Problem 2. If det a1 a2 b₁ b₂ C1 C2 a3 b3 C3) det = 1 4 a₁ b₁ c₁ calculate a2 b2 C2 4a32a2 4b3 - 2b2…

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Q: Let u(x, y) = e¹ cos y + xy. Show that u(x, y) is harmonic. Find an analytic function g(z) such that…

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Q: 8. Solve the recurrence relation an = given do = 40, a₁ = = 37. 2an-1-an-2, n ≥ 2,

A: Given recurrence relation is an = 2an-1 - an-2 , n ≥ 2 given a0 = 40, a1 = 37

Q: Observe the set Is D bounded/closed/open/compact / convex? D = {(x,y) ERIy2x²-1 and y ≤4-e"}

A: The given set is: B=x, y∈ℝ2 | y≥x2-1, y≤4-e-x The region is bounded below by the graph of y=x2-1 and…

Q: 6. Sarah prepares a side dish of peas and carrots to bring to her family potluck lunch. The recipe…

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Q: Use Golden-Section search method to find the maximum value of the function f(x) = 3x-x²-e* +5. Use…

A: Given,f(x)=3x-x2-ex-2+5xl=-2 , xu=4 , ξs=0.000005To find: Maximum value of f(x) using Golden-Section…

Q: From Rogawski 2e section 5.5, exercise 11. A particle moves in a straight line with velocity 2-1fUs.…

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Q: 2. Let a1, a2, a3,... be the sequence defined recursively as follows: a₁ = 1, a2 = 20, and for all k…

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Q: Prove that [2,5] and (3,4) have the same cardinality.

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Q: Problem 1. Show that, if v1, U2, U3 are perpendicular in R", then |||v₁ + V2 + v3||² = ||v1||² +…

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Q: Solve the following L... problem quaphically. IN CUI CIRCHEN maximize z = 4x₁ +5x₂ 4x₁ +5X₂es…

A: In this question, the concept of linear programming is applied. Linear Programming An approach to…

Q: x² whether the limit exists or not. / (x,y)→(0,0) x²+y² 3. Find lim

A: Given limit is lim(x,y)→(0,0)x2x2+y2

Q: 1 -dz, C is the circle |z1|= 2 2³ (z-2) C

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Q: Let f (x, y, z) be a function such that : (i) the function f (x, y, z) decreases most rapidly at the…

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Q: if the Positive root aso: ax²+x-1=0 it is calculated using the recurring formula X₁+1 = 1 = a (x₁)²…

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