Prove that there are no solutions in integers x and y to the equation 2x2 + 5y² = 14.

Q: Solve the following equation with master theorem  T(n) = 2T(n/2) + n2

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Q: Prove that there are no integer solutions (x, y, z, w) to the equation x³ +y³ 3z²+9w² +3. =

A: The given equation is x3+y3=3z2+9w2+3. We have to prove that there is no integer solution to the…

Q: b) Consider the second-order DE. y+25y = 0 rE(-00,00) Show the zero's of the solutions separate each…

A: Given differential equation is, y''+25y=0 We know that the solution to a homogenous differential…

Q: 9. Solve u = 3b – 2a + 2 , for a -

A: see below the answer

Q: Find all solutions to 2sín (20)-12=0 on the interval

A: Solve using basic of all silver tea cups graph for trigonometry quadrants .

Q: Solve the following equations in Z6 with x expressed in both standard and non-standard names: (i) xx…

A: We solve the equation and find the value of x in ℤ6.

Q: [20] Find the general solutions of 4y" – y = 8et/2 2+ et/2

A:

Q: GIVEN: (xn , yn) = (1, 3), (2, 4), (4, 7), (5, 9) Determine the best-fit quadratic curve that…

A: GIVEN: (xn, yn)=(1, 3), (2, 4), (4, 7), (5, 9) we have to determine best-fit quadratic curve that…

Q: Find all the exact solutions of 2cos^2x+2=5cos(x)

A: Consider the following equation:…

Q: would you prove that the answers to the diophantine equation y^2-x^3=0 are the pairs (n^2,n^3) for…

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Q: (d). Use the Secant method to find solutions accurate within 10-5 for et +2+2cosx-6=0 for [1,2].

A:

Q: 1. x3 – 2x2 – 5 = 0, [1,4]

A:

Q: 10. Write the sustem of lineor equations in the form Arebuand solve this motrit equat 2と, X, t Xu-9…

A: Given: 2x1  -x2 +x4 =93x2 -x3 -x4 =-9x1 +x3 -3x4 =-2x1 +x2 +2x3 =0 To find : x1x2x3x4 for system of…

Q: Consider the DE: x' -[2, x, with solutions x = and x2 = 12 a) Verify that x, and x, are solutions to…

A:

Q: Z1OS (0)-170

A: The given equation is: 2cos2θ-1=0 to find all the solutions of it.

Q: Let (xp, y,) be the solution of the following equations In 2 (2x)™² = (3y)n3 3Inx = 2lny %3D Then xo

A: Given equations are 2xln2=3yln33lnx=2lny

Q: 2. Determine all solutions in the integers of the following Diophantine equations: (a) 56x + 72y =…

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Q: B. If AC = x + 11, and AB = 24 solve for x. %3D

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Q: Verify that x and x* are solutions to x²y" – 6xy' + 12y on (0, 0), and give the general solution to…

A:

Q: If a, b, c are integer powers of 2, prove that equation a + 64 = does not have solution, otherwise…

A: Given: Let a,b,c are integer powers of 2 .

Q: 1.) Find all solutions of 34x-62y=8 with X,yZO

A:

Q: 4. The roots or solutions of x² + x + 1 = 0 are nonreal. %3D

A: We are solving the first question and for the next question post the question again and also mention…

Q: Use the previous problem to show there are infinitely many solutions. to r² = 1+ y² +².

A: As per the question we have to prove that there are infinitely many solutions to the equation : x2 =…

Q: Prove that the following equation has no natural solutions x? + x +1 = y².

A: we have to prove that given equation has no natural solution

Q: 11. Solve in the interval [0, 2n). 4sin?x + 2cos2x = 3

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Q: How many non-negative integer solutions are there to the equation x1 + x2 + x3 = 13, if we insist…

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Q: determine by inspection at least two solutions of the given first-order IV . 16. xy-  2y, y(0) …

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Q: (1- х?)у' — ху%3D 3x(1 — х?)

A:

Q: n 10x + 11y = n has

A: The equation as, ax+by=S. The smallest positive integer S is expressed as, S=(k+1)*a*b

Q: which are the solutions for 4sinxcosx=1  over the interval [0,2pie)

A:

Q: b) Consider the second-order DE. y" +25y = 0 rE (-00, 00) Show the zero’s of the solutions separate…

A: The given differential equation is y''+25y=0 If D=dydx then equation will be D2+25y=0 Now Auxilliary…

Q: 3. Use the Intermediate Value Theorem to show that there is a solution of the equation, ³-4x = 1 in…

A:

Q: 3 Find The solution of X-2x+2=0 Using reton raphsen-

A: This question can be solved using the concept of Newton Raphson method of approximation of roots.

Q: Find all integer solutions to 66X + 42Y = 258. Also find all solutions (x, y) with x, y positive…

A: Given : 66X + 42Y = 258

Q: Show that the equation 2³ + 3y3 = 923 has no solution in integers, other than x = y = z = 0.

A: Suppose that, x3+3y3=9z2 has a non-trivial solution, that is other than (0,0,0), and minimal.

Q: If a, b, c are integer powers of 2, prove that equation a³ + 64 = c does not have solution,…

A: Given,a,b,c are integers of the form 2k, k∈Na3+b4=c5

Q: 6. Show that the quadratic equation ax² + b – a = 0 (a± 0) has two distinct real roots.

A:

Q: Find the positive integers m such that t2x"+tx'+(t2-m²)x = 0 has a nontrivial solution such that x…

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Q: How many non-negative integer solutions are there of the equation: x + y + z + w = 15, such that w=5…

A: If we have an equation of the form x⩾a then the variable x can take up any value greater than or…

Q: Prove that if one root of ax? + bx + c = 0 is twice the other then 2b = 9ac

A:

Q: Let (x, y,) be the solution of the following equations In 2 (2x) = (3y)m3 3Inx: = 2Iny Then is

A: This is very complicated & lengthy problem.So I can do it in Advanced Mathematics.

Q: 3 Find the general solution of x = Ax, where A

A: we need to find all eigenvalues and eigenvectors for the coefficient matrix

Q: (b) Show that for x > 0 and k + 0 the equations In x x* = e* and 1 have the same solutions

A:

Q: 2) Find all the solutions in the interval [0, 27T) for the equation 6cos(3t) + 8 = 5

A:

Q: Prove that the equation Z = 1 has no ++ solutions in positive integers x » Y, Z.

A: Assume some value and substitute it many times taking different domains like integers, whole numbers…

Q: 3- Prove that y=x is a solution of (x³ + 2x?)y"+ 2xy'- 2y = 0 and hence find the general

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Q: Verify that yp = 3e2x is a particular solutions of y" − 6y′ + 5? = −9e2x .

A: Explanation is given below...

Q: How many non-negative integer solutions are there of the equation: x + y + z + w = 15, such that w =…

A: We need to find the number of non-negative integer solutions are there of the equation: x + y + z +…

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.