5. Solve the following quadratic congruence using the "completing the square" method: 9x² +66x +49 = 0 (mod 79)

Q: .3 T Evaluate In In e²+j²4

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Q: For any integer a, show that a²-a+7 ends in one of the digits 3, 7, or 9.

A: For any integer a , we have to show that a2 - a + 7 ends in one of the digits 3 , 7 , or 9 . Note…

Q: Q2; find all spanning tree for the following graph

A: We know that , given a graph G = V , E , a subgraph of G that connects all vertices and it is a tree…

Q: 9- Give five examples about application of polar coordinates in real life

A: Polar coordinates have various applications namely in  Animation  Computer graphics Civil…

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A: A set is the mathematical model for a collection of different things; a set contains elements or…

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Q: Which of the following is the equation of the curve having its slope always equal to half the…

A: We want to find true option.

Q: Given the family C[0, 1] of continuous functions ƒ : [0, 1] → R, and the norm ||f|| = sup f(x)]. x=…

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Q: 1. Find the derivatives of the following function (a) y=4²+2

A: Given function y=4x2x-3xx+2xx             =4x-3+2x Differentiate y with respect to x dydx=ddx4x-3+2x…

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Q: To every eigenvaluebof a sturm liouville system there corresponds only one linearly independent…

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Q: 2. Consider the following table of a periodic function h(t). t 0 1 2 3 4 5 h 4.0 5.25 6.165 6.5…

A: We can see that at t = 0, h = 4.0, so the curve starts from the height of 4.0 units or h(0) = 4.0,…

Q: 3. Let h= f(t) be your height (in meters) above the ground while riding a Ferris wheel. The Ferris…

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Q: Let 8 = {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and 8¹ = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for…

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Q: 2. The subset [a,b) of R is neither open nor closed. Prove it and construc an illustration.

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Q: Consider the curve segments: S1: y = x² from x == to x = 3 and 52: y = √√x from x = to x = 9. Set up…

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Q: What mathematical concepts are involved in optimization?

A: Solution

Q: Find the laplace transform of cosat using the formula L{f(t)} = e-stf(t)dt. Hence find the 0 laplace…

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Q: What is the isogonal trajectories cutting at angle of 0= arctan 4 to the family of curves whose…

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Q: a) The matrix B is a 3 x 3 matrix and det (B) = 3. Give the reduced row echelon form of B. b)…

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Q: 1. Consider the polar equation (a) Complete the tables for the given values of Round to the nearest…

A: Introduction: A function's graph is the set of all points in the plane of the form(x, f(x)). The…

Q: ²e²¹ sin(3x) dx, n=8

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Q: 3 Find the laplace transform of et²+ e²t (2cos 3t). 16

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Q: 3. For the following terms from the expansion of 10 (a + b)¹⁰ state the coefficient in both „C, n r…

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Q: 5- Write two examples about symmetry tests in polar graphs

A: example about symmetry test in polar graphs are:-

Q: Use Newton-Raphson (Newton's) method to find the solution to the following within 10° x³2x²5= 0,…

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Q: Find the quotient of (2√3+2i)(-4+i) 2 (1-√3i)

A: Solution

Q: Let f(x) = x² + 2x - 1 and g(x) = 2x - 4. Find 3f(x) - 2g(x). 2x² - 2x - 14 3x² + 2x + 5 Option 1…

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Q: Using the method of Least Squares, determine the value of y when x = 3.0 ation By using the given…

A: Given, the equation          y=AeBx               and x 2.07 8.60 14.42 15.80 y 1 2 3 4…

Q: 1. (5) Find the remainder and the quotient using long division, and write your answer in quotient…

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Q: Given that the tangent and normal to a curve at point P(x, y) meet the x-axis in A and B…

A: 1st we will form a differential equation from given data and then solve it to get the curve

Q: A plumber bought some pieces of copper and plastic pipe. Each piece of copper pipe was 7 meters long…

A: We will construct a system of linear equations according the given informations and will solve the…

Q: The set X is an open set in the ambient metric space . True O False Reset Selection Rationale:

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Q: Derive a finite difference approximation to of(x,y) + f(x,y) using the points f(x, y), ƒ (x+h, y),…

A: Here we use taylor series to find this.

Q: Setup a cylindrical or triple integral using. Coordinates Spherical triple integral SSS (x² + y z )…

A: Given ∫∫∫Sx2+yzdV Where S is the solid lying below the cone z=x2+y2 above the plane z=2 and inside…

Q: Which of the following images goes in the missing part of the sequence? * ? O Option 1 Option 3 O OO…

A: Correct ans is option C   From the images shown, we can observe that there are 6 rows and 6 columns.…

Q: 1. Approximate the value of each of the following definite integrals using: i. Trapezoidal Rule ii.…

A: 1. Given integral is∫12xlnx dxn=4The value of the given definite integral is approximated using the…

Q: Find the singular values of the matrix A [102] 2 1 0 3].

A: Given that A = 102210 . We have to find the singular values of this matrix A. Note that,…

Q: Find the Laplace transform of the following: 1. 4t + 12

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Q: Use the Fundamental Matrix solution to solve the following initial-value problem: 201 020 x(0) -…

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Q: 4- Write two examples about converting an equation from rectangular form [contain x,y] to polar…

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Q: an open ball in the set X, with its radius & satisfying -d(x, a), Vx € X at the open ball Be (x)…

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Q: The cash-flow diagram is provided. a. If P = $2,000, A = $200, and 7% = 9% per year, then N= ? b. If…

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Q: olet S= [-2,2], then find M*(S)? @let E= {3}, then findl M°(E)?

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Q: Which of the following statement/s is or are correct? * i. A function is necessarily a relation. ii.…

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Q: a 12 d 8 g 4 11 2 13 b 3 h e 1 7 14 10 5 f 9

A: We can use Kruskal's algorithm to find the minimum spanning tree and the minimum spanning tree is…

Q: Evaluate ·SSV. Vx (3yi) •n do where S is the hemisphere x² + y² + z² = 16, z 20. Use the normal…

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Q: . Let u₁ = (1, -2, -1), U₂ = (2, 2,-2), and v = = (0, 0, 1). v is not in the subspace W spanned by…

A: In this question, a vector that is orthogonal to a given vector is to be determined. A non-zero…

Q: Find the inverse laplace of s2+78-8 -81 Ofe + o get - 10 9 6 e-8

A: Given Laplace function is y(s) = s+4s2+7s-8

Q: Abby C. Dee borrowed P10,620.00 from Jakey L. Em on October 30, 2020. He promised to repay it after…

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