Let M = Q(V5). Determine the degree |M:Ql. Show that 2 € M and determine the degree [M(V2): Q]. Justify the answer.

Q: Derive and use the estimate 800 |u (x, t)| < 1 -7²t/10 re (2k + 1)* k=0

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Q: Let f(æ, y) axy + az?y+ y³. (a) div(grad(f)) = (b) Find a so that div(grad(f)) = 0 for all æ, y. %3|…

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Q: Find the nullity of T.T: R4→R2, rank(T) = 2

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Q: What is t' (x) if t(x) = ? ez

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Q: Find the value of c such that S xe = 3.

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Q: That is, T'(1) = %3D

A: Given, a recurrence relation T(n) corresponds to the natural numbers, but that "skips" multiples of…

Q: given f (z) = 32² – 6z + j3, what is the value of u(3, 2)

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Q: Use the cutting plane method to solve the following IP: max z = x1 + 2x2 x1 + x2< 10 s.t. 2x1 + 5x2…

A: First draw the line x1+x2=10 and mark the region for the inequality x1+x2≤10.

Q: sove for m in terms of r and T. [(1-m)(1+r)]T=1/2

A: The answer is given as follows.

Q: Use the convolution theorem to find f (t) 14 l(s+2)(s-5))

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Q: Given F(r, s, t) = r(3s4 – 6t°), compute: Frst

A: This is a partial differential problem

Q: Let T: P2(IR) → P2 (R) be defined by T(p(x)) = p(x) – 3p'(x). Given that %3D - T(1+x + x?) = a + bx…

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Q: For T: R5→R3 and nullity(T) = 2, find rank(T).

A:

Q: Q6. Given M = {(x, y), 1 < a² + y² < 4} c R². (a) Determine dM and aM. (b) Is M connected? Pathwise…

A: On the set M, we have to find the following results.

Q: ,use the linearity of L   determine L[f]. Q. f(t)=4cos(t −π/4).

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Q: the followms lineer pgramming Poblem: 3x, + Xe t 213 s.t. ズ」 X +2X3 s 20 2文,+ X』 Xる く(o 20. て apply…

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Q: Given F(r, s, t) =-r(8s³ +t³), compute: Frst

A: Given  Fr, s, t=-r 8s3+t3

Q: iven T: R2 -> R2, where T(x,y) = (x,y2), Is T linear? Explain.

A: Given: To explain the given statement as follows, R2 + R2, where T(x,y) = (x,y2).

Q: (b) Given that p(x, y) = xsin(y)+x²y, determine the following (i) F = Vo (ii) ²pp (iii) V.F (iv) VXF

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Q: 04. Show that T = satisfies the equation T + Tyy = T³. %3D

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Q: What is the domain of r(t) = e'i + j+ (t + 1)~³k?

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Q: Consider the basic AMM city with all the standard assumptions, except the introduction c transport…

A: From the given information, Cost per km, t, for each mode is given by, Walking, t=3xCycling,…

Q: c) Prove the following theorem (-(pvq) v(q v r)) Ɔ ~(p•r) V

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Q: Let T: P2(R) → P2(R) be defined by T(p(x)) = p(x) – 3p'(x). Given that T(1+x + x?) = a + bæ + ca²,…

A: Solution:

Q: (b) Let X = {A E Mat2(R) : A is upper triangular} and let Y = {A € Mat2(R) : A is lower triangular}.…

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Q: For the function f(x,y,z) = In (7x+ 2y +5z), find fy, fy, and f,. fx =口

A: Given,           fx,y,z=ln7x+2y+5z

Q: P is the midpoint of GH implies that GH = 2PG.

A: We have to prove that GH=2 PG if P is the midpoint of GH. Drawing the figure of given condition, we…

Q: Use the convolution theorem to obtain f(t) if : 3.1) F'{F(jw)} = %3D 7+ 8iw-w?

A: Note: Here, we shall find  F-1Fjω=F-167+8iω-ω2=ft using the convolution theorem. (∵If…

Q: Given F(r, s, t) =r(3s² + 9t°), compute: Frst

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Q: For the function f(x,y,z) = In (6x + 7y + 4z), find fx, fy, and f,.

A: Given: f(x,y,z)=ln(6x+7y+4z)To find the fx, fy, and fzddx (ln x)=1x

Q: Given that f(r, v) = xain v, determine fy(z, y).

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Q: Given F(r, s, t) = r(3s² + 3t²), compute: Frst

A: Solution of question is written in below steps.

Q: (b) Given that p(x, y) = xsin(y)+x²y, determine the following (i) F = Vo (ii) ²p (iii) V.F (iv) VXF

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Q: Show that the function f(x, y) = (y + ax)²ev+a satisfies the equation given by %3D a2

A: Please see the explanation below....

Q: The range of f(x,y) = 2 - x2 + 4y² is : O [0,2] O xy-plane Joo+7] O

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Q: (b) Given that (p(x,y)=xsin(y)+x²y, determine the following (i) F=Vo (ii) ² (iii) V.F (iv) VxF

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: The Proff+ P (in thou sends of $) fora company in terms of the amount $ Spent on advertising (in…

A: Point of diminishing returns is found by equating the second derivative of profit model equation to…

Q: . Evaluate F dr, where F(x, y) = ryi+z'y²j, and C is given by r(t) = ti+tj. 0sts1.

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Q: 2. Determine if each of the statements below is true or false. If a statement is true then prove it.…

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Q: Show that ||T(x)|| = ||x||, Vx E R². Show that T(x) · T(y) = x · y, Vx € R². Interpret the property…

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Q: Find the constants c0, c1, and x1 so that the quadrature formula Z 1 0 f(x)dx = c0f(0) + c1f(x1),…

A: Consider the given quadrature formula, ∫01fxdx=c0f0+c1fx1 here we need to determine the constants…

Q: Show that u(x,t)= f((x+a*t)+f(x-a*t))/2

A: Given PDE is utt=a2uxx subject to ux,0=fxutx,0=0 We know that the general solution of the PDE is…

Q: Evaluate F· dī where C F = = , and C is given by - T(t) = , 0 < t < T 0 <t<

A: Given

Q: The ordeng and transportation Cost C Cin hundred of dollars) for automobrle dealership is modeled by…

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Q: ニメ Find the eg uaton (x) 4a| %3D 3tan x when fo f the tor

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Q: PART C dy 12. Show that dx 2 for the relation %3D V%3D10, x, y X. # 0. y

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Q: If r(t) = (V10 – t, In(t – 1) - then the domain of r is

A: Domain = (1, 10]

Q: Let f(x, y) = x² + xy + y² where x = 3(t + s) and y = e2st, find . as

A: we have given f(x, y) where x and y are function of s and t.  We have to find the partial derivative…

Q: |- ri + 2r3 r3- 4x2 T:R R2, T 21, 22, r3 E R

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Q: fud the general Schiklen for the P+q =X+Y+Z

A: p=dzdx and  q=dzdy Let f(x,y,z,p,q)=0We can relate this equation to F(x,y,z,p,q)Then we have the…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.