If 4 sin ¹xcos ¹x 4 COS X + 5 7 Find sin² 2x 5 + 1 12 cos² 2x 7 = ?

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Q: Let p be a prime.a. Show that the number of reducible polynomials over Zp of theform x2 + ax + b is…

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Q: ¹ (5) Use the Integral Test to show that the series 1 converges.

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A: Given, (1) z=-0.21-i (2) e8+3πie-9+πi/2 (3) z=-5+5i

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Q: [2 For 10.1 to 10.3: Let A = 1 LO 121 31 0 -1 and B =[ -21 [1 ¹0 2 -1 3 10.1 If the product exists,…

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Q: (a) Using a trig identity, write x(t) = 3 cos (7t) + 2 sin(7t) using only one cosine function. x(t)…

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Q: Prove that if f(z) and f(Z) are analytic in a domain I, then I is a constant function.

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Q: show that Hantı (0) = 0

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Q: Express these senoids as fasores: a) v = -7 cos(2t + 40°) V b) i = 4 sen(101 + 10°) A

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Q: For Exercises 9 and 10, find all x in R4 that are mapped into the zero vector by the transformation…

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Q: How many of the following expressions can be simplified further? 3x²y - 2xy² + xy + 5x² x² - 4xy+3y²…

A: Given: Expressions :            3x2y-2xy2+xy+5x2 x2-4xy+3y2+6x2+7y 2x2y-5x2+7y-13We need to check…

Q: Let f(x) = √5 + 8x|. Then for x < -5, f'(x) The left-hand derivative of f(x) at x = The right-hand…

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Q: Solve the following inhomogeneous heat problem (k = 1): ди d'u Ət Ə.r2 for 0 < x < z with initial…

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Q: 21.1.1 21.1.2 Starting with the ODE, integrate twice and derive the Volterra integral equation…

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Q: 6. Find formulas for X, Y and Z in terms A, B and C. You may assume that the matrices are compatible…

A: Given ABC0I0XY=0IZ0Block multiplicationAI+BXBYCI0=0IZ0We can writeAI+BX=0BY=ICI=Z

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Q: If f(x) is a function of x, what is the derivative of f(sin(x))? f'(x) cos(f(x)) f'(x) cos(f'(x))…

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Q: π Let R be the region in the first quadrant bounded by the curve y = sec (6x) and the line y =…

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Q: Find the general solution to this exact equation: ( y^2 (t+1) + y ) + (2ty+1) dy/dt = 0

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Q: 2.3-3 Use mathematical induction to show that when n is an exact power of 2, the solu- tion of the…

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Q: Create a 2D diagram of level curves for the surface given below. Find the level curve when k = 0.…

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Q: 17. Fill in a synthetic division chart below and answer the following questions. What is the…

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Q: 3. [Multiple questions in one item] Consider the column vector x = 02 3.1. If the product exists,…

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Q: Use Euler's method with step size 0.5 to compute the approximate y-values Y1, Y2, Y3, and y4 of the…

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Q: Let A = 314⁰ 3 2 NO CON 1 -3 OOTO (a) M12 and C12 (b) M23 and C23 0 0 6 2 -1 -4 7 0 0 0 Find the…

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Q: 1. (a) Define: invertible linear transformation. (b) T: (1₁,7₂)→ (62₁ - 82₂,-57₁ +7₂) is a linear…

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Q: 9) Solve the set of equations by finding the inverse of the coefficient matrix: x - 2y = 5 y = 15 3x…

A: 9. Given the set of equations                     x-2y=5, 3x+y=15.

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Q: (b) Prove the following generalization of the Distributive law for logical expressions. For any…

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Q: alflife of 5760 year

A: Given  T1/2=5760 years we know that T1/2=ln2 /K

Q: Find the extreme values of f(x, y) = subject to the constraint 4x² + y² = 1.

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Q: 1.19 Assume that h: R² R³ is determined by this action. (1) - (9). 2 Using the standard bases, find…

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Q: A matrix A has a LU factorization if A = LU where L is a lower triangular matrix (a matrix with…

A: L=100-110201  U=43-50-22002LU=100-110201 43-50-22002     =43-5-4-5786-8     =A

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Q: Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. -3-1…

A: Given, y'→=32-5-3y→