For the equation, 9x² +8/3xy+y²-8=0, complete the following questions. a. Rewrite the equation in a rotated x'y'-system without an x'y'-term. Use the appropriate rotation formulas. b. Express the equation involving x' and y' in the standard form of a conic section. c. Use the rotated system to graph the system. www.

Q: Explain why you think the series Σα 1 n-1 converges to a finite number or n+1 diverges. If the…

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Q: 1. Let f(x) = x³ sin(3x) cos(3x). a. Find the Maclaurin Expansion of f. b. What is f(¹00) (0)?

A: Maclaurain Series expansion of trigonometric functions.

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Q: 4) Determine the equation for the shortest arc that passes through the point (0, 0) and (1, 0) and…

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Q: What is the minimum number of students required in a discrete mathematics class to be sure that at…

A: We solve the given problem in next step.

Q: 3.27.2. Let X be a metric space with metric d; let ACX be nonempty. (a) Show that d(x, A) = 0 iff x…

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Q: (1, Find a vector orthogonal to both (3, 2, 0) and to (0, 2, -1) of the form

A: The given question is related with vector space. We have to find a vector orthogonal to both 3 , 2 ,…

Q: sin z Prove that lim Cosz - = 1 and lim = 0. Z→0 Z Z→0 Z Hint: use the definition of the derivative,…

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Q: lim x-0 sin² (2x) + tan (2x²) x²

A: We want to calculate the limit limx→0sin2(2x) + tan(2x2)x2

Q: Example 10.28. Solve the differential equations dz dy = 1 + x2, dx -xy for x = 0.3, dx using fourth…

A: Here, We need to use the fourth-order Runge-Kuta method to solve give differential equations.

Q: V. Given: 2. Find f'(2), if it exists. el3r-61-2, f(x)=[2x - 5], √x²-9, if x ≤ 2 if 2 3

A: Given that  fx=e3x-6-2,if x≤22x-5,if 2<x≤3x2-9if x>3

Q: Answer the following problems using the specified method up to four (4) iterations only. Round off…

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Q: Let R and S in the figure above be defined as follows: R is the region in the first and second…

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Q: Exercise 15.2.20. For each of the following multiplication tables defined on the set G = {a,b,c,d}…

A: A set G forms a group if for any elements m,n,p∈G we have: Binary operation holds, that is, m∘n∈G…

Q: Determine the dimension of and a basis for the solution space of the homogeneous linear system. 3x₁…

A: The solution is given as

Q: Integrate the following functioner f(x,y) = (x-1) over the given region R: y=x and y=x²

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Q: Find A where R is the region R outside the circle r=2 and inside r= y sin o

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Q: II. Given: sinh r − 1 if x 2 x-2 Determine if f is continuous or discontinuous at x = 0 and at x =…

A: Jump discontinue of the function

Q: ind the function(x), such that f'(x)= In (3x) X ƒ(1)-1. "

A: Function of a variable x

Q: Which of the following images goes in the missing part of the sequence? * lol ? Oo O O Option 1…

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Q: Solve the differential equation: (D² + 1)y = tan x

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Q: IV. Find Do not simplify your answers. dx 1. cos x + =xcoshy - 2y, where x > 0 cot ¹(x³) sec³ x 2. y…

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Q: Let G=(V, E) be a graph such that • V| ≥ 3, G has exactly 2 leaves, and in G all the non-leaf…

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Q: Example 10.13. Using Euler's modified method, obtain a solution of the equation dyldx = x + √√y, Eth…

A: The given differential equation is: dydx=x+|y|. here f(x,y)=x+|y|       x(0)=1, 0≤x≤0.6, h=0.2. To…

Q: Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an…

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Q: 14. Let (a, b) = 1 and 2 = y for some integers x and y. Then prove that there exists an integer n…

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Q: P(5,2,-1), Q(1,-3,-2), T(4,1,5) forms a triangle. find the vector projection of Rqp perpendicular…

A: Given P(5,2,-1), Q(1,-3,-2), T(4,1,5) forms a triangle. Then the vector…

Q: | Example 10.1. Using Picard's process of successive approximations, obtain a solution upto the…

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Q: 1. Use forward and backward difference approximations of O(h) and a centered difference…

A: given function fx=sinx1+cosx claim- find the  first derivative using forward , backward and centered…

Q: Q2) Which of the following series is converge or diverge 00 Σ{1} ,0.7777777777777 n=1 . Σ n=1 ΕΙΝ 27

A:

Q: -13 2 6 1 The matrix I 09 4 3 3 2-8-1 -2 3 2 10 The Augmented matrix is as follows: -13 2 6 1 -7 09…

A: Given: -13w+2x+6y+z=-7  0w+9x+4y+3z=4  3w+2x-8y-z=-5  -2w+3x+2y+10z=0 To solve the system of…

Q: 4/3 5² = 2² -3 (2²) *² y' x

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Q: [MO31] Find the Fourier series of,

A: Given,           f(x)=0-2<x<-1-x-1<x<11   1<x<2

Q: 1. Suppose n is an integer. Find all values of n such that 6n + 3 is divisible by 5. If there are…

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Q: Q1): The concentration of salt is given as a function of time by: dx -= 37.5-3.5x at the initial…

A: We have dxdt=37.5-3.5x At t=0, x=50 g/L So, t0,x0=0,50 Given step size is h=1 Euler's method is:…

Q: Example 10.21. Given y' : x(x² + y²) ex, y(0) = 1, find y at x = 0.1, 0.2 and 0.3 by Taylor's series…

A: Here, we need to use Taylor's series method and Milne's method.

Q: Given, dr = b(cosedr+rsinėdė);r(π) = 1. Find (1) 1 1+b O 1+b 2 1 1+b O b -(1-b) 1+b

A: We have to find the value of rπ2

Q: Write the following English sentences in symbolic form- 1. Birds fly if and only if sky is clear.…

A: We have to write the given sentences in symbolic form.

Q: Q3): A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a…

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Q: Consider the function f that satisfies the following: . f is continuous everywhere except at x = -2,…

A: Given is information about the function f(x).   To Sketch the graph of f(x), label all intercept…

Q: Q3): A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a…

A: Given: x y 2.00 7.2 4.25 7.1 5.25 6.0 7.81 5.0 9.20 3.5 10.60 5.0   To find the…

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not 2. lim (√x²-x-√x² + x)

A: limx→-∞x2-x-x2+x

Q: Solve the following linear programming problem using graphical method: Minimize: Z = 60x + 30y…

A: The given linear programming problem is                                         Minimize:…

Q: H-w.4 Find the volumes for the following solids whose heights are defined by Z(x,y) and bases are…

A: Volume bounded by xy-plane

Q: Write  basic steps of developing a LP MODEL?

A: The steps for developing a LP model are as follows 1.First define the variables  2. Write the…

Q: Which one is a normal vector to the line which is perpendicular to the 8x - 3y = 9. OA (8,-3) OB.…

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Q: f(z) = cos(C * z)

A: Here we use the property of the analytic function.

Q: QI): The concentration of salt is given as a function of time by: 37.5-3.5x dt at the initial time…

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Q: Q2) Which of the following series is converge or diverge ∞ Σ ,0.7777777777777 n2 n=1 F Σ n=1 27

A: To find which of the given series is convergent :-

Q: 1. Let k € N. Determine all values of a such that Sink converges. an R

A: Suppose k∈ℕ and consider the series: ∑n=0∞nkanTo find: All values of a such that ∑n=0∞nkan…