If A, Band C are three points on the hyperbola yx = c^2 such that AB subtends a right angle at C, then prove that AB is parallel to normal of hyperbola at point .C

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Q: Solve the given initial-value problem. d²x dt² + 4x = -2 sin(2t) + 3 cos(2t), x(0) = -1, x'(0) =

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Q: Determine the inverse Laplace transform of the function below. 1

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Q: Let a, b and w be constants, with w‡0. (a) Show that the Euler-Lagrange equation for the functional…

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Q: Learning Target C1 Core: I can use the additive and multiplicative principles and the Principle of…

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Q: Let f(z) be an analytic function defined on the complex plane, where z=x+iy and ii is the imaginary…

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Q: 21. y" - 4y' + 3y = 0; y(0) = 7, y'(0) = 1

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

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Q: 4. Solve the equation: 2x³ 3x2 - 11x+6=0 3x² - 11x +6 given that -2 is a zero of f(x) = 2x³ - 3x²

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Q: Graph the system of inequalities. Tell whether the system is bounded or unbounded and list each…

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Q: 4. Given differential equation y" + y = csc (t) a. Find the complimentary solution y, that solves…

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Q: Use the graph to evaluate the following expressions. (a) (fog)(1) (b) (gof)(0) (c) (go g)(0) (a)…

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Q: Map at least 5 key points and then sketch a graph of f(x) = −3 cos ; (2x + 1). Show your work…

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Q: 1. Solve the congruence x² + 1 = 0 mod 13³.

A: According to the given data, find the solution:

Q: Max Z = 120X1 + 125X2 + 145X3 12X1 + 24X2 + 5X3 = 45 8X1 + 5X2 + 2X2 >= 36 5X1 + 6X2 + 12X3 = 0…

A: Max Note: The second constrain given is , writing it as

Q: 5. Consider the system in state variable form x = AX + Bu y = Cx + Du with A = [ ] B = [¹₁] C = [1…

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Q: 4. Find the smallest positive odd integer n such that o(n) 7680 n 12121 You should do this by a…

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Q: Consider the following transportation problem: D₁ D2 D₁ D₁ Supplies 14 22 36 0 W₁ 10 W₂ 18 19 25 1…

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Q: Consider the functions C: R → R and S: R → R defined by 00 Σ Σ n=0 n=0 Define a constant to be 2x…

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Q: Which of the following subsets of R³×3 are subspaces of R³×³? A. The 3 x 3 matrices of rank 2 B. The…

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Q: 2. Let S be a set, and ~R a relation on S. Suppose ~R is symmetric and transitive. Show that if for…

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Q: Consider the functions C: R → R and S: R → R defined by 00 C(x) = Σ n=0 2n (-1)" x ² (2n)! Use the…

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Q: 3. Suppose that n is an odd positive integer and write o(n) a b n with gcd(a, b) = 1. Show that the…

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Q: Suppose that f: R² R² is a function such that f (1,2)= the linear approximation. (Use syntax like…

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Q: 1. Show that 2! 4! 6! (2n)! ≥ ((n + 1)!)" for ne z+. . ...

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Q: [1-12] 2 1

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

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Q: For the series below calculate the sum of the first 3 terms, S3, and find a bound for the error.…

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Q: Use Use the E-S definition of limit to establish the lim X+5 X->-12x+3=4

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Q: In Z10, express the following sums and products as [r], where 0 < r < 10. (a) [15]+ [24] (b) [15].…

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Q: 1. Let f be a differentiable function everywhere and let p be a constant. Define a function g by…

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT 10. Determine the cross product axb, if: a=…

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Q: Solve the Lucas sequence L_n = L(n-1) + L(n-2), n ≥ 3; L_1 = 1, L_2 = 3.

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Q: 4.8.) Find the SVD of the matrix A= 322 23-2

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Q: Identify the function that matches the graph except at x = 2. -54-3-2 T a) f(x)= O 29 1 -2 ↑ TY 1 2…

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Q: Suppose you ask a friend to randomly choose an integer between 1 and 10, inclusive.What is the…

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Q: Which function is always positive? 3 O a) ♬(x) = 2x²+4 Ob) f(x)- 1 O c) x)- (x-4)² +4 d) B and C

A: We have to check which Function is always positive