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

Q: 13. Compute 41023 (mod 11). a. 14. Prove that for any integer n, n31 = n(mod7).

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Q: KeyConcept Law of Cosines In AABC, if sides with lengths a, b, and care opposite angles with…

A: Consider the given triangle △ABC. Here, a=9, b=7 and c=12. We have to find the angle A, B and C.…

Q: 3.8 The integral √2²¹³ x³e¯x² dx is approximated by Simpson's 3/8 rule with 9 intervals. Let f(x) =…

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Q: nath A = 30, B = 20, C = 11, D = 22. 3. Discuss how to evaluate Z enclosing the origin. dz, where C…

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Q: For this math A = 30, B = 20, C = 11, D = 22. 8 Evaluate the real integral (x ² + A -8 cos(B*x) 2 2…

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Q: For this math A = 30, B = 20, C = 11, D = 22. | 4. Given the function f(Z) = Z/ (C² – Z²), C as…

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Q: Consider the plane region to the right. Using Simpson's 1/3 rule (2 intervals), Estimate the area of…

A: Make a table as follows x 0 1.2 2.4 f(x) 1.5 1.8 1.5 Area using Simpson's rule is given by…

Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 4 using a value…

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

Q: Consider the following matrix: 3 4 0 8 0 7 0 4 A=0 2 0 3 0201 3 4 0 10 0 70 6, (a) Find a basis for…

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Q: h 1/27 (5 fn+1 +8fn - fn-1) Xn+1 = Xn + Discuss its local truncation error O(hP+1)

A: “Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: How many meters of cloth 5.2 metre wide will be required to make a conical tent, the radius of whose…

A: Solution

Q: 9. Using integration by parts, Then k is? (a) - 1.5136 [*²x³ cos(x²) dx = k − [*³x sin(x²) dx -…

A: Given integral is ∫02x3cosx2dx

Q: 5. (a) Evaluate the polynomial y=2²-82² +12z-0.45 at z 2.378. Use 4-digit arithmetic with chopping.…

A: Given,y=x3-8x2+12x-0.45 and y=x-8x+12x-0.45To find: Value of given polynomials with chopping and…

Q: Example 7.30. Using Hermita's intropolation, find the value of f(- 0.5) from the following data: : 1…

A: Given data is x -1 0 1 f(x) 1 1 3 f'(x) -5 1 7 Using Hermite's interpolation, the value of…

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

A: The given linear programming problem is                                         Minimize:…

Q: 1.5⁹ Explain why the two graphs in Fig. 1.23 are not isomorphic. Figure 1.23

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

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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: Determine the values of r for which the given differential equation has solutions of the form y = t"…

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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: cos

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Q: The function f (z) = |z|+1 O True O False is analytic

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Q: Solve using MUC. y" +4y=3sin2x 3+3+5+ y = C₁ cos2x+ C₂sin2x - -Xcos2x 4 y=C₁ cos2x + C₂sin2x +…

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Q: sec42x -dx tan 2x 1 1 12 tan 62x Find 1 1 A 16 tan 82x ⓇB (cor -=— 1+3csc²2x 12 cot82x) (4sec 22x-1)…

A: Evaluation of the indefinite integral by using substitution method

Q: (a) Let Pn(R) denote the vector space of polynomials of degree at most n, where addition is the…

A: Given :  T : P3(ℝ) → P2(ℝ)  defined by                  T(p(x)) = 3p''(x)-2p'(x) To find :  (a) We…

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: Q2): A polluted lake has an initial concentration of a bacteria of (1*107 part/m³), while the…

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Q: I. Evaluate the following limits. Using L'H 1+ 3/ 1. lim x-1 2x²+x-1

A: The given expression is limx→-11+1x32x2+x-1 limx→-1x3+1x32x2+x-1 use the formula a3+b3=a+ba2+b2-ab…

Q: f(x,y) 3 - x² + 2x - y²

A: We have given functionf(x,y)=3-x2+2x-y2. We need to find the domain of given function, sketch the…

Q: se provide correct answer for b

A: Given,                   f(x, y, z)=xy2zconstraint to                  x2+y2+z2=64

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: lowing vector in the span{V₁, V₂, V3}? 8,9) me vector is in the span. me vector is not in the span.

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Q: [MO22] Express as a single power series form: 00 (3n+2)an-1(x + 2)n+3 - Σ(5n - 2) an(x + 2)n-1 n=-1…

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Q: A continuous P&I= {ac Find V-V. 6CX-X2) C D F x has the pdf UCXCI F(x) other

A: Given PDF is P(X) = 6(x-x2),0<X<10,otherwise

Q: Use variation of parameters to solve the given system sin 2t x² = (2-1)x - (₂002)¹ X' (4 + Je4t cos…

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Q: 4/3 5² = 2² -3 (2²) *² y' x

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Q: 6. If a series Eu, converges to the sum u then so does any series obtained from Eu, by rouping the…

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Q: a. 2 uxx = Иxy - 4uy azu J2u azu ди b. + +4 +3+u = 0 ?х у дуг ?х ?x2 ди c. k = 2 ,k < 0 ду 02u ?хг

A: Classification of the Partial Differential equations

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

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Q: e²x+lnx² sin x² dx = 2x +Se²x cos x² dx

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Q: In 3 Using 4-node Gaussian integration in approximating ³ x ex dx, which f(x) in the formula has…

A: Given: Let us consider the given, ∫1ln 3x ex dx and determine the approximation using 4-node…

Q: Example 7.22. Find the distance moved by a particle and its acceleration at the end of 4 seconds, if…

A: Legranges interpolation

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.

Q: Solve the following PDE:

A: (a). Given,                 yuxy+u=0                                       ...(1)

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: Find the exact ५००/२ Solution for y₁= 2-27

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Q: 2. Specify on which intervals is f increasing/decreasing and where the graph of f is concave…

A: Given is information about the function f(x), f'(x) and f''(x) Then, to specify the intervals where…

Q: Find the solution of the equation P №²₂ a²z อ + cos y ax² ay ² which tends to zero as x→∞ and has…

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Q: a)Consider the following data: 3 is a quadratic residue for 23 and 37. 3 is a quadratic nonresidue…

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Q: Find the divergence and curl for the following vector fields. Describe the characteristics of the…

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