Find the smallest positive integer solution to the following system of congruence: x≡17(mod35)     ≡8(mod43) x=

Q: Solve the following congruences: (a) 3x  8 (mod 5) (b) 3x  8 (mod 12)

A:

Q: Calculate C(12,5) by hand. As C(n,r) = n!/(n-r)!r! identify n and r, and write out every number in…

A:

Q: Solve for x: 7x = 3 mod 11

A:

Q: Q2: Find the solution of 143x³ + 22x¹ + 5x² + 3x + 1 = 0 (mod 11), if any.

A:

Q: Find all solutions of the congruence x2 ≡ 29 (mod 35).

A:

Q: Find all solutions to the system of congruences: x ≡ 7 mod 12 x ≡ 37 mod 45 2x ≡ 134 mod 150

A: The given problem is to find the all solutions which satisfies the given system of linear…

Q: Find the smallest positive integer x that solves the congruence: 7x≡5 (mod52)

A: 7x≡5 (mod52)---(1)

Q: Solve the following congruence: x73 ≡ 614 (mod 1159).

A:

Q: Solve the congruence 863x ≡ 880 (mod 2151).

A: we can observe that  863 and 2151 are co primes ,  that means  863 , 2151  = 1 and  1 / ( - 880 )…

Q: Take the last four digits ABCD of your student identification number, and let AB and CD be the…

A:

Q: Solve the following system 3x + 7y ≡ 4 (mod 11) 8x + 6y ≡ 1 (mod 11) Hint: Use Cayley’s table to…

A: We are given the equations 3x + 7y ≡ 4 (mod 11) and 8x + 6y ≡ 1 (mod 11).  Our aim is to find the…

Q: Which of the following linear congruence has 2 incongruent solutions? (a) 3x = 9 (mod21) (b) 14x =…

A: to solve linear congurence , ax≡b(mod m) .........(1) the first stem is to reduce the congurence  by…

Q: SorvE THモ CONGROEモNしE 626 X Rエ mod5

A: As 5 is an odd number, by fermat's theorem, we have             x5-1 = 1 (mod 5)           => x4…

Q: Solve the following quadratic congruences: (a) 3x² + 9x + 7 = 0 (mod 13) (b) 5x² + 6x + 1 = 0 (mod…

A: According to Q&A guidelines, I can answer only one question. So I answered (a).

Q: Find the solutions of the congruence 15x2 + 19x ≡ 5 (mod 16).

A: Congruence modulo relation on integers:Let a,b∈Z and let m be a fixed positive integer. Then we say…

Q: Solve for x : 5x ≡ 7 (mod 6).

A: Here remainder is 7 and modulus is 6 we can write it as  5x-7 =6n          Where  is an positive…

Q: Find the solutions of the congruence 15x2 + 19x ≡ 5 (mod 65)

A: The given equation is: 15x2+19x≡5(mod 65)

Q: Solve the congruence x² = 79 mod91.

A: The given problem is to solve the given quadratic congruence equation. Given congruence x2=79(mod…

Q: Solve the system of congruence x ≡ 3(mod6) and x ≡ 4(mod7) using the method of back substitution.

A: System of congruence equations

Q: Find the integer that satisfies: 30x4 ≡ 12 (mod 67)

A: Given the expression is, 30x4≡12mod 67

Q: Solve the congruence: 6x ≡ 4 (mod10)

A: The congruence could be written as,

Q: ind all solutions of the linear congruence: 9x = 5 mod (14)

A:

Q: Solve the congruences: 52x + 4 = 8(mod 22) 17x = 19(mod 100) 3x = 9(mod 12)

A:

Q: Find all solutions of the congruence x2 ≡ 16 (mod 105).

A:

Q: In this problem, x = c₂ cos t + c₂ sin t is a two-parameter family of solutions of the second-order…

A:

Q: Solve the simultaneous system of congruences: 3x = 7 mod 11 5x 10 mod 15

A:

Q: tind all ins ongrnent solution the cangruence i¥ exist for 36X= 96mod 156

A:

Q: Find the smallest positive integer xx that solves the congruence: 11x≡5(mod57)

A:

Q: solve the following congruence equation:3x+58 ≡1(mod 12)

A: If ab≡bc(mod nb) then a≡c(mod n) And if ab≡bc(mod n) and if (b,n)=1 then a≡c(mod n)

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.