4. a) Compute P (P (0)) and P({{0.(0}}, {0}}). Show all steps of your cal- culation. b) Calculate where A, = {n, 2n – 1,3n - 2} and B, = {n, 2 - n,n+ 4). %3D

Q: Determine one real root of 2xcos2x – (x – 2) = 0 cn the interval (2, 3)using the Regula-Falsi…

A: Given 2x(cos(2x)) - (x-2)2 = 0  Let f(x)=-(x-2)2 + 2x(cos(2x)

Q: 512x 1-x -3 - =—1 find volue of Σ(x²)"=? n=1

A: Given that the equation 512x1-x-3=-1   .

Q: ¤1 + ag – r3 = 0, -2r1 – 12 + 5r3 = 0, -#1 + 4.x3 = 0 find the Rank(A), where 1 1. -1 A = -2 -1 -1…

A:

Q: 5-solve for the unknown d (P,„P.) = /2ī d (P,P,) = 5 1. P,(x,2,3) P,(2,1,1) 2. P,(x ,x,1) P,(0,3,5)

A:

Q: A herd of 100 deer is transported to a small island, where it grows rapidly for food resources,…

A: Given that  A herd of 100 deer is transported to a small island, where it grows rapidly for food…

Q: B = {1 + x + x, x + x2, x2}. for P2. Let p(x) = 2+x + 2x?. Then [p(x)]3 : %3D %3D 2 - 1

A: Using linear combination of three polynomials

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A: given z=-8i To find the fourth root of the given complex number proceed as follows comparing the…

Q: Show that 1/2 is an eventually fixed point for

A: T22 or T12 That can be proved as it will have the 12 in the equation, for any fixed point .

Q: Without a calculator, show that 2√3-3 2√6-3√3 √6-√√2 4

A:

Q: (4 -3) Please show all working 9. -2 (1) Given that P = 2 ) and Q = ( %3| -3. 4 -3. Calculate: (i) P…

A:

Q: At a company, 20 employees are making contributions for a retirement gift. Each of the 20 employees…

A: At a company, 20 employees are making contributions for a retirement gift

Q: Let B = {1-3t +t² , 2 - 5t + 3t2, 1 + 5t2} and p (t) = 2 – 5t + 4t. Find x [p]g. %3D X1 = X2 = X3 =…

A:

Q: Find real numbers x, y and z such that (x + 4)i + (y – 5)j + (z – 1)k = 0

A: To Determine :-  The real numbers x , y and z  such that   x + 4  i +  y -5  j +  z - 1  k =0

Q: X= y = Determine x and y such that 1 x-y 3 [(4 4 4 ] + [* 1 2 1] = [(1 2x+y 0] -1 0 x 4 4 3]

A: Step 1: Step 2:

Q: 16) n = 4; 2, 1 and 3 + 3i are zeros; f(1) =78 %3D

A:

Q: List all the possible factors of: S(x) = 2x* - 3x' +2x -7x-8

A:

Q: Find S. (12z+ z²) dz, where C is the boundary of the rectangle with vertices at the points 1+ 2i, –…

A:

Q: (a) (5.18) Find the Newton's Divided Difference interpolating polynomial for the points (-h, 0), (0,…

A: (a) x                  fx                    1st order                                  2nd order…

Q: dthe She (5y-3)

A: We have to find (5y - 3)2

Q: if the Legendre polynomials P.(x) = -1 then: Find 1) ,x* P,(2) dx 2)P'(-1) A) L P.) dx = and P,(1) -…

A:

Q: Find all the values of In(4 – 4j). What is its principal value?

A:

Q: x+3 Evaluate: S dx 5-4x-x A. -V5 – 4x – x² + arcsin+ C x+2 B. -V5 – 4x – x² +arcsec+C 3 C. -V5 - 4x…

A:

Q: Write a in the form a=a+T+aNN at the given value of t without finding T and N. 4 r(t) = (41²) ₁ +…

A:

Q: (15.2): Find In(x) – In(x² – 1) +2 In(z +3) 3

A: Find 13ln(x)-lnx2-1+2lnx+3. Logarithmic properties used: alogcb=logcba logca-logcb=logcab…

Q: Q=[X1,2,3,X2- A. length(Q) B. Q(1:4) C. Q(5) ==0 D. max(Q) E. sum(Q) F. Q'

A:

Q: If gcd( m,91) = gcd(n, 91) = 1 %3D %3D

A: Given, if gcd(m, 91)=gcd(n, 91)=1,  To prove that                     91|m37-n37

Q: Starting with x0 - 1.5, yo 1.2, the values x3 and y3 obtained using the pair formulae /+-y.. Y... -x…

A:

Q: If m divides n, show that [GF(pn):GF( pm)] = n/m.

A: Given: m divides nWe need to show that GFpn:GFpm=nm

Q: The annihilator operator form for the function e + cos(2x) is:

A: The annihilator operator form for the function ex+cos(2x) .

Q: If m divides n, show that [GF(pn):GF( pm)] = n/m.

A: Given : m divides n . To prove : GFpn:GFpm=nm.

Q: Consider the quantities M = {1} and N = {x, y}. List all elements of the power sets P(M) and P(N)…

A: We are given :M = {1} So this implies that  Also, we have : N = {x, y} So, this implies that

Q: Let X be N(0, 1)and Y be N(0, 9) , with X and Y independent. Let Z 2X – 16Y, and let W = 3X3 + 4Y5…

A:

Q: Determine a and b such that p(x) = x² + ax + b satisfies p(1) = 0 and p'(1) = 9. (Give an exact…

A:

Q: Find In(x) – In(x² – 1) +2 In( +3) -

A: Our Aim is to find 13 ln (x) - ln (x2-1) +2 ln (x+3) -(i)

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A:

Q: Find a natural number n such that 7 * 1(n) : 1(n) = 180.

A:

Q: Factor the following expression: x*y² - 8x²y³ +15x*y* O A. x*y (x-3y)(x+5 y) B. Nonfactorable OC.…

A: Solve for factor

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.