1. Find the determinants of the following matrices using Laplace Expansion and Triangular matrices (Upper and Lower). 9 07 i. A = -3 2 -1 2 4 1

Q: Verify Stokes' Theorem for F(x, y, z) = (y,-x, yz) and Sis 13.) the paraboloid z = x² + y², 0≤z≤1.…

A: Let S be a open surface bounded by a closed curve C and F=f1i^+f2j^+f3k^ be a continuous…

Q: (a) Assume that g(x, y) is a function of the form g(x, y) = 0 if (x, y) = (0,0). (i) Show that g(x,…

A: As per the policy, we are allowed to answer only one question at a time. So, I am answering the…

Q: Consider f(x) = sin(x²). Is the function even, odd or neither, and which conse- quence does the…

A: A Fourier series is a sum of sine and cosine waves that represents a periodic function. Each wave in…

Q: Jy Find the area of the inner loop of the curve r = 9 cos 0 - 4 by using double integral.

A:

Q: Use Green's Theorem to evaluate: [F F.n ds where F =(√x + 5y, 3x + 5y) and C' is the boundary of the…

A:

Q: 2. The value of ₁-² [Tn (x)]² a) b) √ EIN dx = ', for each Chebyshev polynomial Tn(x), n ≥ 0. c) 0…

A: Solution

Q: state explicity which ordered pairs are in A x B and which are in R?

A: The ordered pairs (x,y) such that x∈A, y∈B are in AxB. i.e.  AxB={(x,y) | x∈A, y∈B}

Q: 1. The set of functions {Po, P₁, Pn} in [a, b] is called a set of orthonormal functions, with…

A:

Q: Home Furnishings has contracted to make at least 220 sofas per week, which are to be shipped to two…

A:

Q: Q1. Locate and classify the singular points of the following functions: A: f(z) = z[1-e¹/z] B: f(z)…

A: We can solve this using definition of singular points

Q: 2. The value of f(x) dx = ..., for each Chebyshev polynomial T₁ (x), n ≥ 0. √1-x² c) 0 d) None of…

A: The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions,…

Q: Q1: The following two random variables x and y are linearly correlated: 1) specify their correlation…

A: Let us solve the statistic problem in the next steps.

Q: 1. Evaluate the following limits: |x+61 2. lim G(x) if G(x) = x-→-00 x+6

A:

Q: 41. Vertex e is OA) an incident vertex OB) insecure vertex OC) isolated vertex OD) adjacent vertex

A:

Q: “Assignment problem is a special case of transportation problem where the number of sources is equal…

A: To discuss: Assignment problem is a special case of transportation problem.

Q: Using the Laplace transform and showing the details of your work, solve the IVP: 8. y₁= -2y+3y2, y2…

A:

Q: Which of the following is NOT a circuit in the graph? B E F D CC OABFEA OBFDCB O None of the Above

A:

Q: Solve using method of variation of parameters: y" + 2y' - 8y = 2e-2x - ex, y(0) = 1, y'(0) = 0.

A:

Q: Evaluate the integral 1 C C sin(x²) dxdy.

A:

Q: - 4. Find the D₂R(t)|| and ||D,R(t)|| if R(t) = 2(e² − 1)i + 2(e² + 1)j + e¹k.

A:

Q: The function f:P (₂)→Xº for X is a two-element set (0,1) is?. a) Bijective b) Surjective c)…

A: Bijective

Q: Find where each of the following functions is discontinuous (a) tan(x) (b) cosec(x) (c) |x|

A: Solution a: Given function is y=tanx Since at π2 , tanx does not exist. Now, we will see it in graph…

Q: Which of the following statement is always false? (a) For all integer x, [x] = [-x] (b) For all odd…

A:

Q: Write the Mayan numeral as a Hindu-Arabic numeral. notation 4x10+6×10 The equivalent Hindu-Arabic…

A:

Q: Use chain rule to differentiate the following 1 y = sec+ (√x+;

A: To find the differentiation using chain rule :-

Q: Define a vector field in space as follows: F(x, y, z) = (x + 2z, y -cos z, x³ + 2z). Suppose E is…

A: Given  F→(x,y,z) =x+2z, y-cosz, x3+2z Then  div(F→) =∇.F→=i∂∂x+j∂∂y+k∂∂z.F→…

Q: 20 Multiply using Napier's rods. 4x735 Construct the blocks for multiplying 4 x 735 using Napier's…

A:

Q: 12. If the x-term is missing, then the quadratic equation cannot be used.

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 8. Suppose you revolve the region completely about the of revolution. Describe the solid and find…

A: Introduction: A stable of revolution is a stable determine created via way of means of rotating a…

Q: e) If a convex function f: R→ R satisfies f(10) = value for f(7)? = -4 and f(20) = 30, what's the…

A: Given that f:R→R is convex function with f10=-4, f20=30.

Q: 5. Determine the number/s

A: Given: Function F(x)=4-x2 To find : The point at which function is continuous.

Q: Suppose F(2) = 1, F(8) = − 1, and F'(x) = f(x). - 10 [ f(x) dz = 10

A:

Q: 4. Data from the National Vital Statistics Report reveal that the distribution of the duration of…

A:

Q: during typhoon ambo, Pagasa tracks the amount of accumulating rainfall.for the first three hours of…

A: Given- During typhoon Ambo, Pagasa tracks the amount of accumulating rainfall. For the first three…

Q: - Find the solution of the equation 3U, -5U, = 0 satisfying the condition U(0, y) = sin y

A: We have to find the solution to the given equation.

Q: umeral for the Roman n

A: Introduction: Manuscript numerals are a symbolic representation of numbers that do not have a place…

Q: Solve the initial value problem. -1 1 0 y' 1 -1 -2 y, y(0) -1 -1 -1 6 5 -7

A: This is a problem of system of differential equation.

Q: 1. How many grams of a drug are there in 850 ml of a 1 in 130 w/v solution ? state andwer to 3…

A: Note: according to our guidelines we can answer only first question  1)   Given solution is 850 ml…

Q: Solve the ordinary differential equation y'+4y-3x³, using Runge-Kutta method with Xe 0, Yo-1, X₂-2,…

A:

Q: Use induction to prove for every positive integer, 4 x 10 = 4 or 7 (mod 33)

A:

Q: 4. Prove that a permutation matrix is orthogonal.

A:

Q: a) Suppose you are given model with two explanatory variables such that: Y₁ = a + B₁x₁i + B₂x₂₁x +…

A: Given: yi=α+β1x1i+β2x2ix+ui To find: Coefficients

Q: 1. Suppose you invest P5,000 at 10% simple interest. How much money will you have after 5 years? O…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Find the consumer surplus at the equilibrium point. 29) D(x) = 5x +2; x = 0 A) $2 B) $5 C) $7 D) $0

A: Let D(x) be the demand function . Then the consumer surplus…

Q: Find a, b, c such that the following change of order of integration holds: 3 clnx LL f(x, y)dydx =…

A: The given integral is                 ∫13∫0ln xf(x,y) dydx

Q: What is 377 in Roman numerals?

A:

Q: (a) Assume that g(x, y) is a function of the form x²+y² g(x, y) = 0 if (x, y) = (0,0). (i) Show that…

A: (a) The given function is gx,y=x3yx2+y2  if x,y≠0,00             if x,y=0,0. To show: (i) gx,y≤xy…

Q: ind the all possible number of different multi sets of size '4' from -element set, in which at least…

A: In this question, the concept of permutation is applied. Permutation Permutations are frequently…

Q: Determine the nature and stability of the equilibrium points of the system dx = x = y + x², dt dy…

A:

Q: An isosceles triangle with a base of length b and height of h has a rectangle inscribed. Find an…

A: Given: An isosceles triangle with a base of length b and height of h has a rectangle inscribed. The…