Theorem 2.9. Let n be a positive integer and write it as n = N²m, where m is square-free. If m contains no prime factors of the form 4k +3, then n is a sum of two squares.

Q: Find the curvature. k(t) = r(t) = 7ti + 5sin tj + 5 cos tk

A: Curvature of the curve

Q: Sketch the function. p(x) = 0.2(x+3)²(x-3)³

A: Sol:- Sketch the Function : First we need to find some information about graph :- Domain of…

Q: Solve the following problems. Show your solutions neatly. Use Polya’s four-step problem solving…

A: 1. Understand the problem We need to find the number of bones in each part of the body 2. Devise a…

Q: 7) Find all complex solutions to the equation below. Express your answers in both polar and…

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Q: Assuming that the function f has continuous second partial derivatives and that a and b are…

A: Here we have given that f has continuous second partial derivative and also a and b are constants.…

Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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Q: Use polar coordinates to find the volume of the given solid. Inside the sphere x² + y² + z² = 16 and…

A: We need to determine the volume of the solid that is outside the cylinder: x2+y2=1 and inside the…

Q: i) Solve the differential equation + dx +tan x tan y = cos x secy.

A: dydx+tanxtany=cosxsecy We have solve the above differential equation.

Q: what is the 22nd term  in the fibonacci sequence with the calculation

A: The nth term of fibonacci sequence is Fn=1+5n-1-5n2n5

Q: Part A is in the provided image, the two choices for the first "Select Choice" box are 12.5π or 25π.…

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Note: Show all your calculations steps. A 14-m beam is subjected to a load, the shear force follows…

A: For accuracy using: 1st preference: Simpsons 3/8 rule for four equi distance nodes. 2nd preference:…

Q: solve the problem The plot best represents which type of growth?

A:

Q: 1. Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3…

A: Given X be the number of times a certain numerical control machine will malfunction:  1, 2 or 3…

Q: Find a power series expansion for f'(x) given the expansion for f(x). (-1)k (2k+1)! f(x)=sinx=> k=0…

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Q: Let f(x, y) be a function such that The limit of f(x, y) as y → 0 along the path x = y is 1. The…

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Q: Verify Stokes Theorem for the vector field F(x, y, z) = (y-z)i + 3xy j + 5zk by evaluating the line…

A: note :  As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Convert 4-j9 to polar form √972-1.1526 Option 1 √972-1.9890 Option 3 √97 21.1526 Option 2 √9721.9890…

A:

Q: Q3 – A// If P(1,2,-1),Q(2,-1,1), R(-1,-1,2) are three point in space. 1- Find the vector…

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

Q: Solve the given system of differential equations by systematic elimination. (D²+4)x - (x(t), y(t)) =…

A:

Q: Problem #1: A rank two tensor L is given as: 7 10 3 L=L=4 -1 -2 945 (a) Calculate the symmetric (S)…

A: We are given that L=71034-1-2945 (a) We have to calculate symmetric S and skew-symmetric W parts.…

Q: –2πίαξ e (1+x²)² 50% dx = (1+2π||)e-27§|¸

A: The function is f(x)=e-2πixξ1+x22 The function has poles where 1+x2=0x2=-1x=i,-i These are poles of…

Q: Find the volume V of the described solid S. The solid S is bounded by circles that are perpendicular…

A: The given problem is to find the volume of the given solid bounded by given parabola and x-axis.…

Q: Use the figures to calculate the left and right Riemann sums for f on the given interval and the…

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Q: b. L-¹ [+1) s3-1-

A:

Q: Given the function below, is fx (x,y) (the derivalue of f with respect to x) continuous at origin?…

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Q: The data below show the number of car thefts in a city for a period of 20 days. Complete parts (a)…

A: Sol:- Stem & Leaf Plot:-

Q: Which of the following is a 4th root of -1.25-12.3? 0.9931 +j 0.8113 O 1.4454-j 0.4312 -0.5569-j…

A: The given problem is to find the fourth root of the given complex expression. Given complex…

Q: Show that the sum of the degree of all vertices in a graph is an even integer.

A: We will use the fact that edge contributes 2 to the degree in the graph.

Q: 1. Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3…

A:

Q: Compute the Inverse Laplace transform of the following signal. (s+1)² s²-s+1 2 Re{s} > 1/12

A: Given,             (s+1)2s2-s+1, Res>12

Q: (-3-15)(-1.23+/2.1)

A: The given problem is to find the principal value of the given complex number. Given complex number…

Q: Obtain Newton's interpolation polynomial in divided differences considering the data (1,2), (3,3),…

A: We have: x x0=1 x1=3 x2=4 x3=8 y y0=2 y1=3 y2=2 y3=10 We first make the divided difference…

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: The formula for wind chill C (in degrees Fahrenheit) is given by C = 35.74…

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Q: n open field is bounded by a lake with a straight shoreline. A rectangular enclosure is to be…

A: This is the problem of the Application of Calculus.

Q: 1) For the vector field F(x, y) =−x²'yi + xy²j, find the following: a) Find the 2D curl of this…

A:

Q: let The Linear Transformation given by T:P3toP2 T(ax³+bx²+cx+d)) = 3 ax²+2bx c find a basis for…

A: The given linear transform is T : P3→P2 such that Tax3+bx2+cx+d=3ax2+2bx+c To find: The basis or…

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

A:

Q: Use polar coordinates to find the volume of the given solid. Enclosed by the hyperboloid -x² - y² +…

A: Here I am using polar coordinate and substution to solve this question. In this question we have to…

Q: Based on data from Hurricane Katrina, the function defined by w(x) = -1. 19x +990 gives the wind…

A:

Q: Let A = {5, 6, 7, 8, 9}, B = {7, 8, 9, 10, 11}, and C = {6, 9, 11}. a. Find An B. b. Find AU B. c.…

A: Given: A={5,6,7,8,9} B={7,8,9,10,11} C={6,9,11}

Q: X Let X and Y be independent random variables and distributed as Uniform distribution on the…

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Q: pproximate the requ 8600 m6 X

A: Given as, Aquarium long=7m wide=1m deep=1m

Q: Determine X(S) expressed as a rational polynomial with simplified numerator and factored denominator…

A: We determine X(S) expressed as a rational polynomial with simplified numerator and factored…

Q: Justify your response thoroughly to communicate your understanding of the concepts. Suppose on an…

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Q: Determine to and the Values of sake following y PDES elliptic, parabolik, or J hyperbelic tho + X…

A: Let us consider the PDE of the form a∂2ϕ∂x2+b∂2ϕ∂x∂y+c∂2ϕ∂y2=0 Determine ∆=b2-ac The PDE is…

Q: iii) Show that the sum of the degree of all vertices in a graph is an even integer.

A:

Q: Let E be the pyramid with top vertex at (0,0,1), and base vertices at (0,0,0), (1,0,0), (0,1,0) and…

A:

Q: Determine whether y₁=et, y₂ = sin2t, y3 = cos2t make up a fundamental set of solutions by finding…

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Q: Question 19 Determine the continuity of the function f(x, y) = continuous except at (0, 0)…

A: Continuity of the function