Use the intercept form to find the general form of the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is X += 1, a 0, b = 0. b a Point on line: (-7, 3) x-intercept: (d, 0), d# 0 y-intercept: (0, d), d = 0

Q: Q2: Iteration three of the root equation x³-x-1=0 belonging in the interval (1,2) using bisection…

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Q: Suppose that G = (a), a e, and a³ = e. Construct a Cayley table for the group (G,.).

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Q: If f & R[a, b], then f is not continuous on [a, b]. If each fn is differentiable on [a, b] and fn ⇒…

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Q: (z-4)² y² 2²- 3x² = 1. Let S be the quadric surface with equation 4 3 1. Give an equation of the…

A: We know that the traces of a quadric surface are the curves representing the intersection of the…

Q: Given A = ผล 120 -2 0 2 2 -4 01 3 and b = 31 If Ax = b, compute the solution of x.

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Q: e costu(t) e-¹ u(t) Option 3 Option 4 *What is inverse Laplace for 1 (s + 1)² + 1 y (s) = te¹ u(t)…

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Q: Prove that if lim x(t) = X and lim y(t) = Y, then lim(x(t), y(t)) = (X, Y). t-a t-a t-a

A: Now, xt, yt=∫cdxtytdt Given: limt→axt=X   , limt→ayt=Y

Q: Find the Fourier transform of ƒ (t) = 2 for -T≤t≤0 2 for 0 ≤ t ≤T

A: We have to solve given problems:

Q: 7. The value of the term in the 10th row, 7th position of Pascal's Triangle is: a. 0 b. 120 C. 70 d.…

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Q: Let f(x, y, z) = In(4xy) z² + sin(xy² + ye²). Find fxyz?

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Q: a) Solve the following LP using Simplex Method. Max z = 1500x₁ + 2000x₂ + 2400x3 Subject to 3x₁ + x₂…

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Q: * What is inverse Laplace for 1 (s + 1)² + 1 y (s) =

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Q: 15. Find the nth term of the arithmetic sequence 2, 5, 8, 11, 14

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Q: (a) Use the given information to write a system of linear equations for x, y, and z. (b) Convert…

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Q: . Find the equation of the tangent line corresponding to x = 1. (Hint: What y value does this point…

A: Given the equation x2-y3=0 To find the equation of the tangent line at x=1

Q: Q5) e-st dt = b) 0 Q6) If you know that the radius of convergent of the series method for the ODE…

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Q: Let M(R) denote the set of all mappings from R to R. For mappings f,g: R → R, define pointwise…

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Q: The critical points of the function f defined by f(x, y) = 21³ +³ +31² - 12r - 3y - 4 are (-2,-1),…

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Q: 9. The Z-score that is associated with a confidence level of 95% is: a. 2.575 b. 1.645 C. 2.01 d.…

A: We have to find the correct choice.

Q: (a) in degrees. x) in radians

A: Given as, e=10 sin 314t

Q: A) function is defined by f(x) = {²1₂ ² if x20 if x<0 Evaluate f(0), f(1)and f(2) and sketch the…

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Q: 3 s² + 1 6 s² + 1 Option 4 O * The Laplace transform of the x(t) is x (t) = 3 sint 3 s²+2 6 s² +2…

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Q: Let R be the region enclosed by the curves y = x³ and y = 2x². If we revolve R about the line y =…

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Q: 15. (a) (i) Find the Z-transforms of cos and 'n(n+1) no A (ii) Using convolution theorem, evaluation…

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Q: (c) Suppose that G = (a), a e, and a5 = e. Construct a Cayley table for the group (G,.). CIG [11

A: We shall answer first question only as you have asked more than one different question. For others…

Q: Ge + c₂0 c) y(x) = c₂e²x + c₂e² Q11) L(y") = a) s² L(y(x)) + sy(0) - y'(0) c) s² L(y(x))-sy(0)-y'(0)…

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Q: 12. 13. 14. 15. 16. Find the gradient of the line joining the points A[5, -7) and B- 3,01 Find the…

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Q: Question 6. Given integers a, b, c, d € Z, and m, n € N. (a) Suppose that a = b (mod n), and that m…

A: Part (1) Now, a≡b mod n ⇔n/b-a ⇔b-a=nk              for some constant k Also, m/n ⇒n=cm…

Q: Example: Test the following series converges. a. { In ( n + 12 ) n+2 M=1 or not

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Q: Evaluate the integral ₁2-1=1 Sindz.

A: This question is related to contour integration from complex analysis.

Q: Suppose the control problem is The Hamiltonian function will be given by Maximize √ (y + 4u)dt…

A: As per the question we are given a optimal control problem, where we have to find the Hamiltonian…

Q: d) y(x) = ce +C₂e + Cze c) y(x) = c₂e²x + c₂e* Q3) Evaluate £ (e-2t sin4t): 4 s+2 5+2 d) a) s²+85+20…

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Q: An airplane is travelling at 620 km/h on a heading of 305°. The wind of 80 km/h is flowing from a…

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Q: (c) Prove that G/N is Abelian iff aba-¹b-¹ N a,b G. 2

A: We have to prove the given theorem.

Q: Q9: If f (x)=, then the divided differences F [a, b] and F [a, b, c] are 1 a 1-b 1 с 1 D) be A) -…

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Q: Q₁) Find Jz dz 1. along the contour integral c from 1+i directly to 3+i3? 2. along line from 1+i…

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Q: Given the complex numbers z, = 2 + j3,zz = -1 - j2, and zs = 4 + j4 find; ZZ2 m(高) (5)+(6 (六)(五)+ Z2…

A: We have to simplify given complex expression.

Q: 14x10 1. The velocity of a rocket is given by v(t) = 2000 In -9.8t,0≤t≤30 where 14×10¹ - 2100t v is…

A: Since you have asked multiple questions,we will solve the first question for you. If you want  2nd…

Q: Find the upper triangular matrix of 6 15 55 A = 15 60 225 55 225 979

A: Consider the given matrix, A=61555156022555225979 here we need to find upper triangular matrix of…

Q: Directions: Complete the proof. Fill in the blank with the letter of the correct answer. A. SP TP C.…

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Q: The cost function is C(x) = 5x + 21 and price-demand function is p(x) = 25−4x • Find the profit…

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Q: Use simple fixed-point iteration to locate the root of f(X) = 2sin(√x) - x

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Q: 3x + 2y + 7z = 4 2x + 3y + z = 5 3x + 4y + z = 7

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Q: Let C be the parametric curve with parametric equations [x=t(t² + 1)-¹/2 te [-3,3] y = 2t - 2…

A: The slope of the tangent to the curve: y=f(x) at x=a is f'(a). If a line is horizontal, then the…

Q: +2y" -y'-2y = 0, is: Q10) The general solution of y" a) y(x) = c₂e²x + ₂x + c₂e* c) y(x) = c₂e²x +…

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Q: Show that the differential equation x²y³ + x(1 + y²)y' = 0 is not exact, but becomes exact when…

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Q: 4. Does the Taylor series expansion of f(x) = (1 + 3x)24 about a = 1 have only a finite number of…

A: Solution

Q: If fn ‡ ƒ on [a, b], then lim ſå ƒn ‡ ſå f. If 0 ≤ an ≤ bn for all n E N, and an converges, then bn…

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Q: Use Euler's method to find approximate values of the solution of the given initial value problem at…

A: Let us start solving the problem step by step using euler method

Q: Q3: state whether the following statement are True or False : 6. In Euclidean space R the ball B(0;…

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