1. Suppose that d is the square of an odd integer (hence d² is also odd). Explain why there is a Pythagorean triple of the form (k, d, k + 1) such that k2 + d² = . [Hint: Expand the right hand side.] (k+1)'. %3D

Q: Suppose A is 1x4, B is 2x5, C is 4x2, and D is 3x1, then the dimensions of E= DACB are: О 3х1 3x5 O…

A: size of matrix  option B is correct answer

Q: 20. What is the value of the 4th term of the expansion of (y + 2z)°? 16y"z 448y 23 25628

A:

Q: 11. If a = y2 and b = y, and -1sys3, then what is the largest possible difference between a and b?…

A: Please refer the attached image for complete solution.

Q: 6.8. Suppose the cubic spline s E S3(N3) is such that s(x) = 0 for x E [xo, x1] and for xe[x2, x3].…

A: Given: The cubic spline s∈S3Ω3 sx=0 for x∈x0,x1 and for x∈x2,x3   To show: sx=0 for x∈x1,x2 (a.) by…

Q: Consider a, = V4n² + 3n – 2n for n > 1. %3D -

A: Introduction: The sequence is a set of functions with the set of natural numbers as the domain of…

Q: If g(4) = 3 and gʻ(x) > –6.5 for all x E [4,6], what is the smallest possible value of g(6)?

A:

Q: Since D is a square whose vertices have coordinates (0,0), (0,1), (1,0) and (1,1), which of the…

A: Please refer to the image below

Q: Given a clamped cubic spline interpolation: S(x) = (3(x-1) + 2(x-1)²-(x - 1)³ (4+4(x-2)(x-2)² +…

A: Sol

Q: For which values of a, b, and m does x + a = b have a solution in Zm?

A:

Q: The order of the element 3 in Z24 is

A: Given: Z24 Formula Used: The order of an element k in Zn is given by Ok=nhcfk,n

Q: If Pn is the sum of a G.P. upto n terms (n > 3) such that (1 – r) dP, aPn-1+ bPn, where r is the…

A: Introduction :

Q: n is increasing, and those on w 3x + 5.

A: Introduction: The input values of a function f(x) where f(x) has minimum or maximum values are…

Q: 6.13 Show that t: = B,/[s//E=, (x;- %3D VI- r in (6.20). |

A:

Q: (7) 13. Find two positive numbers, z and y, such that their product is 500, and z +3y is as small as…

A: Topic: calculus

Q: Find a number in [0, 1] such that the difference of one third the number from its cube is minimized.…

A: Let the number be x. Let f(x)= x³-x/3 So, f'(x)= 3x²-1/3

Q: Fund the Picard Iterates Yo- for the following enitial Value Problem assume that ylo) = 2

A:

Q: Prove that L ={(1Z*)"10" | n e N}is not regular.

A: The given language: Then, the above language can be rewritten as, To prove that L is not regular.…

Q: (8.20 ds: Find the tayLor seri's expen sian of In Cxri) about XozO

A:

Q: 12) If the following is a cubic spline over [0, 2] -2x3 + 2x2 + ax + 1 , 0 <x< 1 S(x) ={7(x – 1)3 –…

A:

Q: 3 In ADU DDL =9mm. Z/=6mmand //=N". Find FD. 3

A: By using the cosine rule we can can find the third side of triangle if we have given the two sides…

Q: @31 Find the nverse of the functions 1) fex) = 2x-1 2メ+) 2) fa)

A: The given functions are a fx=2x-1bfx=e2x+1We need to find the inverse of the above functions.

Q: 3. Find the constants bo, co, a1, b1, C₁ so that So(x)=1+ box + cox² + x³, S(x) = { S₁(x) = a₁ - 2x…

A:

Q: 2. Prove that, for all k E N, 2 can be written as the sum of two squares.

A:

Q: A cubic spline S is defined by: So(x) = 3(x – 2) + (x – 2)² – 4(x – 2)ª 32 if 25x53 S(x) s,(+) =…

A: true

Q: Give a clear and detailed solution of the intergral of e^-ct/m 2)

A: You want intergral of e^-ct/m. I am assumig the variable of integration is "t". That is, the task in…

Q: For positive integers n and k (k sn+ 1), the kth term of (a + b)n is given by

A: The binomial expansion of (a+b)^n is

Q: (6) 3 Scary TRUE Military Ston x D Ranboolive - Twitch D BoomerNA - Twitch…

A:

Q: Prove m3 – n° = (m – n) (m² + ²). - N m - n (m – n)(m² + mn + n° Enter your next step here %3D 2.

A:

Q: Consider the following LP Min z = 3x, + 2.x, +7x, s.t - x, + X, =10 -2x, + x, - x, <-10 *,X,,x, 2 0…

A: Hi! As per norms, we will be answering the first question. If you need an answer to others then…

Q: Determine if the following is a fundemental set of solutions to  y'' -6y' + 25 = 0 Given that…

A: If the Wronskian of two solutions is not equal to zero, then the given set of solution is…

Q: paper 2 4. INDICES AND S 2007 N Q3 (i) Express 9x+1 as a power of 3. (ii) Express V272 as a power of…

A:

Q: ()if pis in fact larger than 0.301, t would seem there are too many numbers in the file with leading…

A: Given: n=223 r=85 α=0.05

Q: 15. prove that L. d= nd(n)/2

A:

Q: Show that E(x-a) = E(x; -x) + n(x- a), squares about a = is smallest. other words, show that the sum…

A: The answer is as follows :

Q: and such that the sum of their squares is as small as possible. Give the sum of the squares.

A: Given problem:- 2. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such…

Q: A cubic spline S is defined by: (So(x)%D 1+x- x (5,(x) = 2 - 5(x – 1) + (x – 2) if 0 SxS1 if 15xS2…

A: As we all know that Natural Cubic Spline is a piece-wise cubic polynomial that is twice continuously…

Q: 20 + 7)* Evaluate the integral dæ + 7)* * by making the appropriate substitution: u = dx (2x + 7)4

A: Let's find integration of given function.

Q: 3 If [E dx = In(7x - 6) - +C, find f (1). 7x - 6 Enter an integer or a fully reduced fraction such…

A: Given that:-∫f(x)xdx = ln(7x-6)-37x-6+CTo find: value of f(1)

Q: d. What happens if P < M for all t?

A:

Q: The Wronskian of the two solutions of ty-2t y -t8y3D0 is ct?. Select one: O True O False

A: Here we have to given a differential equation and we have to check is the given wronskian is right.

Q: In ALMN, LN is extended through point N to point 0, mZMNO = (5x – 13)°- mZNLM = (x – 4)°, and m/LMN…

A: Solution-

Q: Show that for any n E N, n(n + 1)(2n + 1) %3D k=0

A:

Q: Given the function z = In (2xy + e3x) - 5y, %3D az a. ax

A: Since, we have to find the partial derivatives ∂z∂x and ∂z∂y of functiongiven by z=ln…

Q: Suppose A is 1x4, B is 2x5, C is 4x2, and D is 3x1, then the dimensions of E= DACB are: О 3х1 O 1x2…

A:

Q: Assume C and D are chosen at random from {1,2...,n}. Let pn be the probability that C + D is a…

A: The number of pairs (c,d)  with sum m2 is m2-1 for m2≤n and 2n-m2+1 for n&lt;m2&lt;2n. Hence,…

Q: Suppose that it is estimated that t months after January 30, 2020 (first COVID-19 case in the…

A: Use the initial conditions to calculate the values for A and B . Use the values for A and B to…

Q: #02:-Discuss all the cases of reducible to hamggenou D.E form.

A:

Q: 1 Calculate the integral: k *. (a² +x²)3/2

A: Topic- integration by substitute

Q: 9. Suppose that N(h) is an approximation to M for every h > 0 and that M = N (h) + K,h+ K,h? + K3h…

A:

Q: 2. The square of any integer can be written in the form 3k or 3k + 1, for some k E Z.

A: True. We use the fact any integer is of the form 3q,3q+1,3q+2.