Find the volume of the parallelepiped defined by the vectors u=(1,-8,2), v=(5,0,-3), w = (1,5,-3)

Q: L Look for the values of t in which the given curve is concave upward and downward: x = (t + 3)³ and…

A: Given that, x=t+33y=3t+32 Differentiate both sides w.r.t. t. dxdt=3t+32dydt=6t+3 So,…

Q: Proposition 4.1.2. If ƒ : A → Rn satisfies the lower-Lipschitz condition on E, i.e., if there exists…

A: We will prove all by using the definitions

Q: Suppose that f(x, y) = -2z4+3 zy2 + 3y2, z=rcos (t) and y=rsin (t). Find af af and (write your…

A:

Q: metric on R² is d: R² x R² → R$, given by fo 0 ifr=y 1 if x #y. d(x, y) =

A:

Q: (b) By Parseval's formula ΣΙΑ*(v)||2 = ΣΣΚΑ*(vi), v;}/2 = ΣΣΚυ;, A(v;)}2 = ΣΙΑ(v;)||2 < 0. ji…

A: To Explain: The mentioned part of the proof:

Q: olve the following system of linear equations by applying the Gauss elimination: 6x - y = -13 -x +…

A:

Q: Explain why Newton's method doesn't work for finding the roof of the equation x³ 3x+6=0 if the…

A: Answer :- We also know that F(1)=1-3(1)+6 F(1)=4

Q: [(cos y + 3xy²)dx +(4x²y-xsin y)dy Use Green's Theorem to evaluate the line integral (0,0) to (0,1)…

A:

Q: 1. 2. 3. A restaurant offers 10 appetizers and 25 main courses. In how many ways can a person order…

A:

Q: 14. The hydrogen ion concentration of rain water is about 0.00001. What is its pH?

A:

Q: Matrix A is factored in the form PDP. Use the Diagonalization Theorem to find the eigenvalues of A…

A:

Q: Hi school track teams long jump record is 22 feet 3 1/4 inches this year Bruce's best long jump is…

A:

Q: 1) Give examples without justification. a. An open cover of (0,∞) that has no finite subcover.

A:

Q: Proposition 4.1.3. Let A CRn be open. Iff: AR" is C¹, then f is locally Lipschitz.

A: Given: A function f:A→ℝm which is C1, and A⊆ℝn is open. To Prove:  f:A→ℝm  is locally Lipschitz.

Q: use a property of the real numbers and explain how the property is being applied =14(3+(-x))+15x-51…

A:

Q: For Set [le₁>= (1), 1e₂) = (b), (₂) = (?)] then by Gram-Schmidt procedure chevye the above Set to…

A:

Q: 7. Let V be an n-dimensional vector space over the field F and let B = {V₁, V2, ..., Vn} be an…

A:

Q: For each of the statement below, decide whether it is true or false, and prove your claim. (a) For…

A: Sum, difference, product and division of non zero rational numbers is rational

Q: Find the flux of the vector field F = (z,y^, - x) through the helicoid with parameterization r(u, v)…

A:

Q: The following illustrates an application of optimization using parabolas. The concentration C in…

A:

Q: Rotate the quadratic function 5x^2 + 3y^2 + 2z^2 + 4xz = 14 to its principal axis. ( express as a…

A:

Q: A body falls in a medium offering a resistance proportional to the speed at any time. If the…

A:

Q: 2. Suppose you analyze a 2D linear system x = Ax and find complex eigenvalues λ = λr ±iλi where X₂ =…

A:

Q: Determine whether the following graph represents a function. -10 -8 -6 -4 -2 10 8 6 4 2 -4 -6 -8 y…

A:

Q: A = -27 32 -18 8 -8 5 -24 23 -18 Recall that for x € C, e^x= Σæk/k! = 1+x+x²/2! + x³/3! + ... k=1…

A: Given matrix is: A=-2732-24-1823-188-85 Using ex=∑k=1∞xkk!=1+x+x22!+x33!+ . . .  we will define…

Q: 1. Show how to multiply (25)(32) using a generic rectangle. Fill in all dimensions and areas on the…

A:

Q: Match each sequence below to statement that BEST fits it. STATEMENTS Z. The sequence converges to…

A:

Q: For the vector field G = (yeay + 4 cos(4x + y))i + (xeªy + cos(4x + y))) , find the line integral of…

A: Given That : Vector field G→=yexy +4cos4x+yi^ +xexy +cos4x+yj^ . To Find : The line integral of G→…

Q: Examples and similar. c) There exists a Cauchy sequence that does not converge in some metric space.…

A: c) "There exists a Cauchy sequence that does not converge in some metric space". Consider for…

Q: If a 6 x 3 matrix A has rank 3, find nullity A, rank A, and rank AT.

A:

Q: Q1: The distance x of a runner from a fixed point is measured (in meters) at intervals of half a…

A: t x ∆x ∆2x ∆3x ∆4x 0 0             3.65       0.5 3.65   -0.5         3.15   0.45   1 6.8…

Q: Find the distance between the point P = (-3,2,1) and the plane 3x-2y+z-6=0.

A:

Q: ‘or the system below, find the general solution, sketch the trajectories, being careful to nclude…

A: Convert given system into matrix form Find eigenvalues and eigencectors Find general solution State…

Q: Determine whether each of the following vector fields F is path independent (conservative) or not.…

A:

Q: Q20C. In what order are the vertices visited in a pre-order traversal of the tree below? (Enter…

A: Q20C. In-order traversal of a tree is in the order        Root - left child tree - middle child tree…

Q: Let G be the solid bounded by y = z, y = x², and z = 4. If it has density function p(x, y, z) = xyz,…

A: The value of integral is zero.

Q: Let L be the line through the point Q = (- 6, - 9, - 10) and direction vector d = [- 1, - 2, - 2]^T.…

A:

Q: A manufacturer produces three products: Product A, Product B and Product C. To be able to produce…

A:

Q: A 30-year-old woman wants to purchase a $300,000 one-year life insurance policy. What should the…

A:

Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

A:

Q: Q5C. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f, g, h, i} E =…

A: To explain why given graph has Euler trail or why given graph doesn't have Euler trail.

Q: Eliminate the parameter and describe the shape of the curve: :=√√x+4; _y=3√t; for 0≤t≤16

A:

Q: (a) Briefly explain why each of the series below either converges or diverges. (-1)"-1 1/2 n=1 n²…

A: According to guideline we need to solve one question. The rest of the question should be reposted.

Q: Use cylindrical coordinates to evaluate the integral where D is the solid bounded above by the plane…

A:

Q: coefficients.) 3 y"+10y' +29y=16t³-5t e sin 2t What is/are the root(s) of the auxiliary equation…

A:

Q: Use Green's Theorem to calculate the circulation of F = 3xyi around the rectangle 0 ≤ x ≤ 2,0 ≤ y ≤…

A: By Greens theorem ∫C[Pdx+Qdy]=∫∫R[∂Q∂x-∂P∂y]dxdy, where R is the region bounded a simple closed…

Q: Give a scalar equation for a plane at distance 9 from the plane P with equation 2x+y+2 = 4 0=0

A:

Q: Find the dimension of the subspace spanned by the given vectors

A: The rank of a matrix is the number of nonzero rows in the reduced matrix.

Q: solve the following give the general solution : question 1.  y'=y^2•x^3 , y(0)=1

A: Note:  "Since you have posted multiple questions, we will provide the solution only to the first…

Q: Show the (sum of) integral/s equal to the length of the portion of  from X to Y traced…

A: