b) fx)3 6х4 + 7x? — 8х+ 9 Туре of polynomial Degree Sign of leading End behaviours Domain сoefficient

Q: b such that the surf 4x2y + z3 = 4 cut -1 ?). %3D

A:

Q: Consider 2x° – 3y? = 8 -

A: SolutionStep I :  2x3 - 3y2 = 8Now, 2x3-3y2=8⇒2x3-8 = 3y2ddx2x3-8 = ddx3y26x2 =…

Q: is a solution of 2x-6x2+7x-33D0. 2 Prove that x 1-

A:

Q: Use the IVT to prove that r-5x2 + 2x = -1 has a solution. %3D

A:

Q: 7 If ZA = ZB, find mZA. (2x + 5) (50 - 4x) A B.

A:

Q: Q4. Let flW=( Gué-4u-7) (4ax4 -8x#+15) Find tle regueetad closiuadtiul (10)

A: Given,

Q: Use the elimination method to find all soluti { % 4x - Зу 3-24 -7x + 6y = { By = 45

A: Given,             The system of equations are                4x-3y=-24                -7x+6y=45

Q: Show that x2 + 3x + 2 has four zeros in Z6.

A:

Q: Write a general polynomial q(z) of degree n with coefficients that are bo, b,, b2, ..b,. What are…

A:

Q: 9. If mZSPR = (4x - 7)° and MZSQR = (2x + 3) °, find MZSPR.

A: Given that:   ∠SPR=(4x-7)°∠SQR=(2x+3)°

Q: Differentiate the following by using product rule. (9x2-2)(3x+1) (3x+10)(6x2-7x)

A:

Q: Formulate that the Lagrange interpolation polynomial that passes through points (0, 3), (1,4) and…

A: To show that the Lagrange interpolation polynomial that passes through points (0,-3),(1,4),(2,15) is…

Q: Give a counterexample to show that (AB)-1 =/ A-1B-1 in general.

A:

Q: Find the polynomials connecting the points (0,1), (1,3), and (2,13) ​​by quadratic interpolation.

A:

Q: 1. Use polynomial fitting to find a closed form for 5, 8, 13, 20, 29, ...

A: Given , Sequence = 5,8,13,20,29,.....   To find: Closed form of sequence i.e. formula for nth term .

Q: Find the total ancd neguon between x-axis and the gruph of y==X2 - 3X, -7sx52

A:

Q: verify that 6A = 3(2A)

A: Here given  Thus

Q: (b) Show that factorial polynomial corresponding to P,- k³ – 4k* + 2k³ – k² + k + 10 is P, = k(5) +…

A: Given: The given polynomials is Pk=k5-4k4+2k3-k2+k+10, To prove Pk=k5+11k4-k3-9k2-k1+10

Q: Show that r3 + 3x² – 8 is irreducible over Q.

A: Here Q is a field and f(x)= x³+3x²-8 is of degree 3. Then by ROOT TEST we can say that f is…

Q: Part 1 of 2 Classify the polynomial as a monomial -8x+ 16 Choose the correct type of polynomial…

A: As this polynomial is having three terms.

Q: prove using the IVT. 2x + 3x = 4x has a solution.

A:

Q: Does (Z11 , + , .) have subfields? In this case which subfields.

A:

Q: Show that x2 + 3x + 2 has four zeros in Z6

A:

Q: Does S = {x² + 1,x² – 1, 2x – 1} span P2?

A: we know dimension of P2 is 3 so any set which span P2 must have at least 3 elements. here given set…

Q: Show that the polynomial x5 - 6x + 3 over Q is not solvable byradicals.

A:

Q: et) of a ball thrown by a child is 1 -x² + 6x + 3 14 -

A:

Q: Express as a polynomial. (2u +3)(u - 4) ( 4u+u ) 2

A: Given: y=22u+3u-44u+u For expressing given expression as a polynomial, we simplify given expression…

Q: attained by the func x 2) in the interva

A:

Q: In ARST, mZR = (5x – 11)°, mZS = (3x – 3)°, and mZT = (3x + 18)°. Find mZR.

A: We know that, Sum of all interior angle of a triangle is 180°. For a triangle △ABC, we have…

Q: -In ADOG, mZD = 4x, mz0 = (3x + 10), (2x + 17). Find mz0. %3D and the mzG =

A:

Q: Show that 1 -2 = R³. span 3 1

A: In R^3 if three vectors are linearly independent then they span the whole space R^3.

Q: Find the equatians of the haranntal and vertical Reymptotes for the functien 2x -7x- 30 (x) - 20-

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Are u able to do polynomial fitting without any mathematical tool? Why?

A: Polynomial fitting manually: a: Polynomial coefficient k: degree of polynomial N: no. of points to…

Q: Express as a polynomial. (3u - 1)(u + 2) + 7u(u + 1)

A: Given expression: 3u-1u+2+7uu+1

Q: Determine the upper bound on the error in the approximation – 16x5 + 256x° if |x| < 0.2 - 1+16x4

A: Given:x1+16x4 ≈x-16x5 + 256x9

Q: find a quadratic polynomials whose zeores are  (i) 3,4 (ii) 2,1

A: So here we are going to use the formula for quadratic equation when zeroes are given. So I'm…

Q: 4. a. Prove that 8s + 13 L-1 (s² + 4s – 5) 5(7et +9e-5t) by using completing the square method.

A: Since there are two questions posted, we will answer the first question 4.a). If you want the…

Q: If f1x2 = 2x3 + Ax2 + 4x - 5 and f122 = 5, what is thevalue of A?

A: The given function is: f(x)=2x3+Ax2+4x-5

Q: 5lim V3+x-J3 8→0

A:

Q: 1. Which polynomial has 31, -31, and 3 (with multiplicity 2) as its roots? A -3x' +9x + 27 Bx -6x'…

A:

Q: what is the multiplicity of -1 in x^4-2x^3-3x^2+4x+4

A:

Q: verify that 5A = 3A + 2A

A: Given that A=341127. Compute 3A+2A as follows.

Q: Use Giramer Rule to Find ,z -2x + 33-Z = 1 メ+29-2-4 -2x -+7 = -3

A:

Q: (2) Determinek such kx - 4x+- =0 that has real and different solutions.

A:

Q: 10. Determine the upper bound on the error in the approximation = x - 16x5 + 256x° if |x| < 0.2…

A: We need to find upper bound on the error.

Q: 2a] aS a product Of irreducible polynomials.

A:

Q: In ARST, mZR = (6x + 10)°, mZS = (2x + 5)°, and mZT = (3x – 11)°. Find mZR. -

A: The sum of three angles of a triangle is equal to 180°. Equate the sum of the given three angles to…

Q: Consider a quadratic polynomial with a negativ main coefficient and a negative discriminant. Which…

A: Consider a quadratic polynomial with a negative main coefficient and a negative discriminant. Which…

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.