Find all solutions in positive integers of the diophantine equation x^2 + 3y^2 = z^2

Q: tion 2 he equation fx) =3ex = x2 = 0 has a solution in the interval 2<x<0. With xo= -2 and x, =0,…

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Q: Use Newton's method to approximate a nonzero solution of the equation 2sin(x)=x2sin(x)=x as follows.…

A: Let us assume a function f(x)=2sin(x)-xSo, f'(x)=2cos(x)-1

Q: Solve sin(3æ)cos(5æ) os(3x)sin(5x) = - 0.25 for the smallest positive solution. Cos

A: Given : sin(3x)cos(5x) - cos(3x)sin(5x) = -0.25   Both side multiply 2. 2sin(3x)cos(5x) -…

Q: Place these trig equations into general form: 1.   y = 3/2 cos (πx - π) 2.  y = cos(2x - π) 3.  y…

A: As per our per our guidelines I am solving only first three parts plzz repost other part To place…

Q: 19. 2 sin 3x 22. 2 sin (2 21. 2 cos (2r + 1) = 1 23. 2 sin (4x - 1) = 1 %3D 24. 2 cos (4 3x 25. 2…

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Q: Solve 4sin(2x) - 2cos(x) = 0 for all solutions 0 ≤ x < 2π x =

A: 4sin2x - 2cosx = 0 , 0 ≤ x &lt; 2π

Q: GIVEN: [7 A = 2 340 -71 - 3 1 -1 4 6 010-3 -3 -5

A: Since you have asked multiple questions, we will solve the first question for you  If you want any…

Q: y" + 4y= cos²x

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Q: ind the solution in the interval from 0 ≤ θ < 2π 4cos2 x - 4sinx - 5 = 0

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Q: 1. Find all solutions of 3 sec 0-2 tan 0 = 0 if 0s0s2n . 2. Find all degree solutions for sin 20 +…

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Q: (1+i)·(10Z60°) Express your answer in rectangular form. (3–7i)+(9Z120°)`

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Which method can solve: 2y+2y'-y"=4x+5(tan x) Method of Undetermined coefficient Constant…

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Q: ind the smallest positive solution to 2sin^2(2theta)+3sin(2theta)=-1

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Q: Solve 2sin2 (θ)sin(θ) − 1 = 0 on the interval 0 ≤ θ ≤ 2π

A: The standard form of a quadratic equation is given by ax2+bx+c=0, where a, b and c are the…

Q: Find all exact solutions on [0, 2?). 2 cos2(t) − 3 cos(t) = −

A: given :

Q: Find the indicated root of the given quadratic equation by finding x3 from Newton's method. Compare…

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Q: 1) Solve 3tan(x)=√3 over the interval [0,2π)  2) Solve 2cos(x)=2 over the interval (−∞,∞) 3) Solve…

A: 1. 3tan(x) = 3 tan(x) =13 So, x = π6or x = 7π6   2. 2cos(x) = 2 cos(x) = 1 x = 2nπ, where n = 0, 1,…

Q: 6. From Descantes rule of signs, condude that the equation roots. x2n-1=0 has 2n-2 imaginany

A: x2n - 1=0 So, total number of roots are 2n.

Q: Determine the Differential equations that you could solve using Separation of Variables, Homogenous…

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Q: Derive three-dimensional heat equation in cylindrical polar coordinate system.

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Q: ((2+tan^2x)/sec^2x) -1 solve showing work

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Q: Solve sin(4x)cos(8x)−cos(4x)sin(8x)=−0.2sin(4x)cos(8x)-cos(4x)sin(8x)=-0.2 for the smallest positive…

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Q: Why are separable differential equations called "separable"? State an application of these types of…

A: Suppose we have a differential equation involving x and y as variables. Separable differential…

Q: Solve for a root/roots of the functions 2. x2 – 3 sin x + 2 In(x + 1) = 3. 5 Applying both a.…

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Q: 3) Express 4sin 2x+3 cos 2x in the form of Rcos (2x-a). Hence, solve the equation | 4sin 2x+3 cos 2x…

A: The given trigonometric expression is, 4sin2x+3cos2x=5432+42sin2x+332+42cos2x=545sin2x+35cos2x⋯⋯1…

Q: 5. Use Newton's method to find all four solutions of 4z cos(2r) - (r-2)2 = 0 in [0, 8 accurate to…

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Q: 400 inch-lbs of work is required to stretch a spring from its rest length to 10 inches beyond its…

A: Given:- 400 inch-lbs of work is required to stretch a spring from its rest length to 10 inches…

Q: The two smallest positive solutions of 2sin(x)+3cos(x)=2 are:

A: 2sinx+3cosx=2 We need to find the two smallest positive solutions for the above function.

Q: Given 0≤θ<2π , solve 4 tan ⁡θ−4=0 .

A: By using trigonometric equation formula, we solve the given trigonometric equation.

Q: f(x) = Jsinx 02x>N T >x22n

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Q: Compose a Homogenous DE problem. Prove it's HDE using homegeinity test (degree n), solve for general…

A: We know that , A function fx , y is said to be homogenous differential equation if fλx , λy = λn fx…

Q: Use the most appropriate method to solve the equation 7cos x = 4 - 2sin2 x on the interval [0, 2π).…

A: Given trigonometric equation is 7cosx=4-2sin2x   .....1

Q: Find the root of the cubic equation 4x3 + 3x2 – 8x – 2 = 0 in the domain [ 1 , 2 ] using numerical…

A: We have fx=4x3+3x2-8x-2 The initial interval is 1,2 The error tolerance is 1%=1100=0.01 So, we need…

Q: 2 sin2 4x − 2 cos 4x = 1 if 0° ≤ x < 360° Please show all steps in clear handwriting or typed.…

A: Given: 2 sin2 4x-2cos 4x=1                 0°≤x≤360°

Q: Find all exact solutions on [0, 2?). sec(x) sin(x) − 2 sin(x) = 0

A: follow 2nd step

Q: -2n de 24. Show that 2n. V2-cose

A: We have to prove given identity:

Q: Find all solutions of the equation in interval [0,2pi). 6sin^2(x) = 6+3cos(x)

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Q: 2sin2(x)-sin(x)-1=0 for all solutions 0≤x<2π.

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Q: Find all exact solutions on [0, 2?). tan(x) − 2 sin(x) tan(x) = 0

A: Note: There is an unknown symbol “?” in the question. We assume it is “pi”. To find all exact…

Q: Find the solution of the equation in the interval 0° ≤ x < 360° cos x + √3 = - cos x

A: We have to find out solution of the equation

Q: 67. 4 cos lx - 2T = 2 cos-1x

A: Given information: 4cos-1x-2π=2cos-1x

Q: Find all solutions to 2sin(θ)=√32sin(θ)=radical 3 on the interval 0≤θ<2π?

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Q: #11. Determine the exact value of csc 0 if the point (3, -7) is on the terminal side of 0 . csc e =…

A: Since you have posted multiple questions in this question i can do first question as per our company…

Q: Use Gauss's method to solve the cyclotomic equation x^6+x^5+x4+x^3+x^2+x+1=0.

A: given cyclotomic equation x6+x5+x4+x3+x2+x+1=0   ...i claim- to solve the equation using gauss's…

Q: Solve. State general solution and solutions on the interval 0≤ θ≤ 2π 4sin2(θ) + 2sin(θ) - 2 = 0

A: Our objective is to find thita .

Q: 4. Find all real solutions of 3sine 4cos0 that each of them does satisfy the given equation. = 2.…

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Q: Solve (ut)² + (Ux)² = 1

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Q: Use Gauss's method to solve the cyclotomic equation x^6+x^5+x^4+x^3+x^2+x+1=0.

A: Consider the cyclotomic equation,  x6+x5+x4+x3+x2+x+1=0 The objective is to use Gauss's method to…