The figure below is the graph of a sinusoidal function C(x) with midline y = 6 and a minimum value of 1. Write a formula for C(x) involving cosine.

Q: 1. (i) Show by hand that 2 is a primitive root mod 19. (ii) Find² a complete set of primitive roots…

A: Note: According to guidelines I will answer first question only.

Q: Example 4.5 Find the convolution of the two continuous-variable f(x) = e-x² and functions g(x) = 3x²

A: We have to find the convolution of the two continuous-variable functions

Q: Question 2. The subgroup generated by S could have been defined a second way, as the set of all…

A: The subgroup generated by a set in a group , where represents the subgroup generated by and is…

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A: The orthogonal basis is the set of linearly independent vectors whose inner product is zero andthese…

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Q: The set B={[−1010],[00−11],[0002]} is a basis of the space of upper-triangular 2×2 matrices. Find…

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Q: Let P₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

A: a. We have to find the dimension of the subspace H. b. We have to check whether {4 - (9x2 + 3x), 7 -…

Q: 2. Is i=0 5 103i rational or not? Justify your answer. What about 5 103⁰ ? Justify your answer. i=0…

A: Given series is ,this is , so given series represent rational number .2nd part : Taking first 2…

Q: 10. Find the remainder of x4 + 3x + 2 after division by x + 3 in

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Q: Let x be the number with the decimal expression 0.a1 a2 a3 a4..., where an is the remainder of n…

A: Given Data:Let   be a number with the decimal expression 0...., where  is the remainder of upon…

Q: Show that (-6,0) -10,-1) independent of path: af |ss|8 dy ag əx = = (-6,0) (-10,-1) (-6,0) (-10,-1)…

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Q: 1 -x dy - y dx gives the area of the region enclosed by the simple closed curve C. ZYX Use this to…

A: We have to find out area enclosed by the curves  Noted that using Green's theorem ,for simple closed…

Q: 4. Find a rational and an irrational number between 71.8094 and 71.8095.

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Q: 2. Let ƒ(x) = x² sin(1/x) when x ‡ 0, ƒ(0) = 0. For any a ‡ 0, find ƒ'(a).

A: Since these are multiple questions according to our guidelines we can solve only first one.please…

Q: Let Pn denote the vector space of polynomials in the variable æ of degree n or less with real…

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Q: In the previous part, you developed the Method of Disks for computing the volume of solids of…

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Q: Find the parabola of the form y=ax^2+b which best fits the points (1,0), (4,4), (6,8) by minimizing…

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Q: 3. Suppose that (X, d) is a metric space which is not compact. Let {an}_1 be a sequence of distinct…

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Q: Problem 0.6 Determine whether the following series converges. (3) o(-1)" cos(+1)

A: The given series .The aim is to check the convergence of the series.

Q: Calculate M5 using a diagonalization process. =[63] has eigenvalues 5, 2. M =

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Q: Use Hudde's procedure to find the GCD of x4 - 18x³+72x² + 130x825 and x³ + 5x² - 29x - 105

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Q: A boat leaves a port traveling due east at 18 mi/hr. At the same​ time, another boat leaves the same…

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Q: 5. ( function Locate all relative maxima, relative minima, and saddle points of the following 1…

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Q: graph wn grapn ycle Cn-1 by adding an additional vertex vn (in the center of the cycle) and…

A: A wheel graph  Wn  which  is constructed from a cycle graph Cn −1​ by adding an additional central…

Q: Find the parabola of the form y=ax^2+b which best fits the points (1,0), (4,4), (6,8) by minimizing…

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Q: A matrix A= -10 -5 -1 40 37 -12] 20 20 -7 4 1 1 Find a basis for Nul A: 1 reduces to 0 0 -4 0 -4 3…

A: A matrix  reduces to .Find a basis for .

Q: Use the graph to evaluate the following expressions. (a) (fog)(1) (b) (g of)(2) (c) (go g)(0) (a)…

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Q: Consider the following line integral. fxy dx + x²y³ xy dx + x²y³ dy, C is counterclockwise around…

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Q: Find the surface area of the piecewise smooth surface that is the boundary of the region enclosed by…

A: Consider the region enclosed by the following paraboloids            and   For the intersection of…

Q: Suppose that V is finite dimensional real vector space and that ⟨⋅, ⋅⟩ is an inner product on V.…

A: Given V is a finite dimensional vector space over , say n dimensional, and is an inner product on…

Q: 3. Please prove[x"In(x)] = x¹Jn-1(x) and [x"n(x)]= -x¯¹]n+1(x) dx

A: (.) We have to prove,(.) Bessel's functions  is given by,

Q: Solve the following differential equations. Express the solution of the given initial value problem…

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Q: 2. Use the power series representation for f (x) = combined with Combining Power 1-x Series to…

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Q: Let x have an exponential density (>0) de-z p(x | 0) = { 0 0 x>0 otherwise

A: Given thatP is pdf and find the maximum likelihood estimator

Q: Rectangle areas are found by calculating height x width. The width of each rectangle equals Ax and…

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Q: झाई उडका दु

A: We need to find

Q: Problem 9. Define LZ → Z and M : Z → Z by the rules L(a)= a² and M (a) = a mod 7 Find (1) (2) (3)…

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Q: 1. For the lamina in figure #1 compute the moment of Inertia about the x-axis. The density is p(x,…

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Q: Let X = {−1,0,1} and consider the inner product on F(X) defined as follows: ⟨f, g⟩ = f (−1)g(−1) +…

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Q: You are the loan department supervisor for a bank. This installment loan is being paid off early,…

A: This installment loan is being paid off early, and it is our task to calculate the rebate fraction,…

Q: Estimate zx (0.50, 0) and zx (0, 1.0) and zy (0, 1.0) from the contour diagram for z (x, y) in the…

A: z(0.50,0) = 1z(0.75,0) = 2z(0.50,1) = 1z(0,1) = 1z(0,1.2) = 3z(0,1) = 1

Q: and let B = {1,2,3,4}. Provide examples injective surjective injective but not surjective surjective…

A: A function  is said to be injective if , for . That means every distinct element of the domain is…

Q: Find the equation of the line passing through the point (2, -7) and perpendicular to the line 3y =…

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Q: Construct a truth table for the given statement. ~p ~q

A: First recall the Truth Table for p⇔q .pqp⇔qTTTTFFFTFFFTAnd recall the Truth Table for ¬p .p¬pTFFT

Q: A1. Milk or meat production Y per day is best explained by the inputs: feed needed per day in kg,…

A: Since you have posted a multiple question according to guidelines I will solve first(i) question for…

Q: 7) A student is enrolled in four courses that require submission of projects covering different…

A: As per the question, a student faces the challenge of optimizing project choices across four…

Q: are F2 and F3 conservative?

A: As they are different questions, we have to solve the first question only. Please repost the rest to…

Q: Letf : R → R3³ be defined by f(x) = (-7x, -3x, 8x). Is f a linear transformation? a. f(x + y) = f(x)…

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Q: Use the power reducing formulas to rewrite cot23x sin 3x in terms of the first power of cosine.…

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Q: 4 A Cartesian and a polar graph of r=-2 cos (40) are given. Identify the points on the polar graph…

A: (a) We have to find Which point on the polar graph corresponds to point A on the Cartesian graph.…