5 Let the torces vector field F: TR-TR" with a,6 € TR, where F(x,y, z) = (ax+xy, xb4+ 2Z (a) Proove that the field Fis astrobilo (6) Find a scalable potential

Q: that 10348+4303 is divisible by 47. the remainder of 123 is divided

A:

Q: 3. Find the inverse Laplace transform of the ff. а. (s+1)(s+2)2 10 b. s(s+2)(s+3)2

A:

Q: Let A = {(0, –1,6); (–1,0,2); (2,1,0)}. Then A is a basis for R4 the above vector space R3 the above…

A:

Q: 1. In the right triangle ABC, AB = 2, BC = 4 and ED is a line parallel to AB. Find the angle a =…

A:

Q: • MMD7;10 Let M = Then M is a basis for M2,3 O the above M3,2 the above None of the mentioned

A:

Q: Question 2 [14 marks]. Show, using truth tables, that (a) ¬(p V q) ^r = -p^ (¬g Ar), (b) ¬ q V (q V…

A: We will construct the truth table to show  Logical equivalence in part (a) and tautology in part…

Q: 2. Solve for the missing angle: 100 O x = 90 O x = 100 Ox = 80 O x = 40

A: Solution

Q: 10 Find the value of x: to 70° degrees

A: Centeral angle and intercepted angle of a circle are same

Q: 10 m 10 m

A: Solution

Q: Consider the following optimisation problem max f(r, y) = t/r y, subject to tx? + y 0, y > 0. a)…

A: Given: max fx,y=txysubject to x2+ty≤5x≥0,y≥0 To find: a) t=1 b) Envelope theorem c) Marginal effect…

Q: Consider the differential equation (10x³y* + e=Y +3 sin(4x + 3y))y' + (6x²y5 + 4 sin(4x + 3y) + 2) =…

A:

Q: Which of the following is a subspace of R? O A. All vectors of the form (a, 0,0). O B. All vectors…

A: Subspace of a vector space:  A subset V of ℝn is said to be a subspace of ℝn if 1. The zero vector…

Q: pプ PG2-2(6x)さ子エ theorem over the elosed hemispher defined bY Zz J25-x²_y?

A: Given that F→=x2+yi^-zyj^+z2k^ and z=25-x2-y2

Q: 5. Calculate the area contained between the curve y = cos x, -T < x < T, and the line

A: To calculate the area contained between the curve y=cos x, -π&lt;x&lt;π, and the line y=12. Note: As…

Q: Question 2 [14 marks]. Show, using truth tables, that (a) ¬(p V q) ^r = -p^ (¬g ^ r), (b) -q V (q V…

A:

Q: d'y dy Consider the second-order equation +p + qy = 0, where p and q are positive. dt 5. %3D dt2 (a)…

A:

Q: Which of the following is a subspace of R? O A. All vectors of the form (a, 0, 0). B. All vectors of…

A: To choose correct option we will use the following theorem Theorem: A non-empty subset W of a vector…

Q: Suppose that for a company manufacturing bluetooth and wireless headsets, the cost and revenue…

A:

Q: Find the Laplace transform of 0 2 (t – 6)² + 2 cos

A:

Q: (A 1a z arrs z and" For complex numbers z and w, if |z| w-|w² z = z-w, then which of the following…

A:

Q: (ii) o S(2xy + z)dx dy dz z=-1 :0 Jx=1

A:

Q: B. How many different ways can the letters of each word be arranged? 5. MISSISSIPPI 4. PHILIPPINES…

A: This question related to permutation and combination topic.

Q: Calculate: a) median b) first quartile

A: )a) find the median class interval frequency cumulative 90-105 24 24 105-120 62 24+62=86…

Q: what about part 5)?

A: Please find the answer innext step

Q: "COUNTING MADE REAL" (Performance Task) Situation 2 Grade 10 class with 40 There are 10 contestants…

A: To find for the given situation 1,2 &amp; 3.

Q: y"' + 3y" + 3y' = y y(0) = 7, y'(0) = -7, y" (0) = 11 %3D

A:

Q: When you throw a dice twice, what is the size of the sample space?

A:

Q: Does there exist an 8 x 8 matrix A - (a) satisfying the following three conditions? (1) If i 2j then…

A:

Q: Let V be a vector space of dimension 4, and let W be a vector space of dimension 2. Let L : V → W be…

A:

Q: solve the determinants of the vandermonde matrix using Newton Interpolant (incremental…

A: Given: The left-hand side of the linear system of equations, obtained by Newton's interpolation…

Q: . f(t) = -2cos6t + 5sin6t %3D

A: Solution

Q: a). Evalieteo lim foca+la -4 X-2 b). f(x){ de?+72, xこ 3x2+3d9x > a Contir at evesy ?

A:

Q: 1. lim f(x) = -1 and f(1)DNE 2. lim f(x) = 1 and f(0) = –3 4. lim f(x) = +o, 3. lim f(x) = -2, lim…

A:

Q: graphing the solution: 36. yi 3 2y1 + 4у2, у2 —D у1 + 2у2, У1(0) 3 — 4, У2(0) %3D — 4

A:

Q: if it was N-{cz,,z,»z,): 2z,-z, = o} Two subspaces of C³ space on field C find MON Then prove that…

A:

Q: - dimensional vector space V Let T be a linear operator on the finite condition that T be semi -…

A: Given: T is a linear operator To find: Theorem

Q: †3 – 12 +5t + 2

A: Laplace transformation of polynomial

Q: 2d 2e 21 Let a, b, c, d, e. f be real numbers, A = e fl, and B = d-3 If determinant of A is equal to…

A:

Q: If an converge to zero then the series -0 an is convergente Select one: True False

A:

Q: (2+i)Z = 3+4i Y-Z = 2+i

A:

Q: 1. Evaluate the following integrals. · | (csc 0)(1+ sin² 0 + sin 0 cot? 0) d0 а.

A: Properties of integration ∫sinθ dθ=-cosθ+C∫cosecθ dθ=-ln|cosecθ+cotθ|+C∫cosec2θ dθ=-cotθ+C

Q: Evaluate the integral using integration by parts rule if [x cos 2x dx 5) Express the integrands as a…

A:

Q: Solve the nonhomogeneous y'+ 2y equation

A:

Q: 3. 2 B -1 0 1 а) A = 1 -2 -4 5 -3 -3 b) A = 7 11 -11 13 A 28 43 -6 18 B = 22 -3 c) 3 7 4 3 12 B = d)…

A:

Q: function g defin g(x ,y) = cos (TX JG) Consider the (b) calculate the instanta

A: Given: Function g(x,y)=cos(πxy)+1log3(x-y) To find: Instantaneous rate of change of g at the point…

Q: Sand pouring from a container forms a conical pile whose height is equal to the diameter. If the…

A: Note: According to our guidelines we can answer only 5th question

Q: How to do the horizontal element of the area?

A: The area of the given plane region is calculated using horizontal strips as shown below.

Q: Let A = {(4,1,0);(1,0, –2); (0,1,–5)}. Then A is a basis for %3D R3 the above vector space O None of…

A: Given set of vectors is  A = { (4,1,0), (1,0,-2), (0,1,-5) } is subset of R^3  If A is basis for R^3…

Q: 27TT 5. x = y? and x + y = 2 is revolved about y = 1. (Answer: с. и. ) %3D 2

A:

Q: Suppose you flip a fair coin 4 times. What is the probability that they are either all head or all…

A: Coin is flip 4 times  that is totel outcomes will be 2^4 = 16