5. (12 points) Find how many positive integers between 1 and 99, inclusive, have the following properties. a. Are divisible by 7: b. Are divisible by 5: C. Are divisible by 5 or 7. d. Are divisible by neither 5 nor 7.

Q: Calculate truncation error for e^2 with two and three terms in taylor expansion

A: Truncation error formula The truncation error of the Taylor series approximation for e^2 depends on…

Q: Consider the following matrix A: 1 3 -3 A = 26 -4 1 3 -2 For each of the following vectors,…

A:

Q: Let S denote the surface of the box [-2,3] x [-4,2] × [0,3], ori- ented outward, minus the disc that…

A: Given that the surface S denotes the box [−2,3]×[−4,2]×[0,3].The orientation is outward and the…

Q: 2. Let W be a finite-dimensional subspace of an inner product space V. Prove that if P is orthogonal…

A: To prove that I−P is the orthogonal projection onto the orthogonal complement W⊥, where I is the…

Q: 2. Solve the integro-differential equation for f(t) t –2f(t) = 2 | sinh(w)f(t – w)dw + 1 2 f'sir

A:

Q: 2. For each nonlinear autonomous system, find all equilibrium solutions: x' = 2y - xy and y' = y −…

A: 2.(B)The given non-linear system is .Find the all equillibrium solution as follows.Put  as…

Q: / /-1/-// 1/ 1 / 1

A: Clearly slope field is parallel to x axis at y=0,1Hence .dy/dx=0 at y=0,1Forms two factor…

Q: The diagram on the right is a floor plan. Letting vertices represent the room and the outside, and…

A:

Q: 35. Find the area of the part of the plane 4x-2y-z4 that hesabuvo the root)c [-1, 4]X[3, 7]. a. 51…

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

Q: 2 2 2 Consider the matrix A = 0 2 0 0 1 3 (a) Find the eigenvalues and bases for the corresponding…

A:

Q: Let A = [3 -3 0 14 20 1 We want to determine if the columns of A span R². To check this we add times…

A:

Q: Sandra has at most $100,000 to invest in stocks, bonds, and money market funds. She expects annual…

A:

Q: (0,。) - V (10)

A:

Q: 4. Suppose that p is a prime integer. (a) Show that if [x], [y] € Zp and neither of which is [0],…

A: Let's consider a prime integer and the set (integers modulo ).(a) To show that if and neither is…

Q: In Exercises 27-30, calculate ||x||. 1+i 2 27. x = 28. x = 3+i 2-i

A: Norm:

Q: #4: Consider SSC (V x F).ndS where F = 9x²¹²₁ + 8e²²³₁+ ln(+5)xos, k and S is the top half (20) of…

A: For F and ellipsoid S we have to find p(a) and q(a).

Q: We say that a set A is denumerable if there exists a bijective function f : N→ A. Suppose that A and…

A:

Q: 1. Prove, by giving a bijection to or from N, that the following sets are countable. You do not need…

A:

Q: 14 16 3x +5x (x³+x²+1) -dx 4

A: We have given, Let  and  be polynomials, where  has repeated roots and  is a proper fraction, i. e.…

Q: Let Q(x) = 143x² – 34x2 – 34x² – 36x1x2 – 36x1x3 — 72x2x3. Find a unit vector x in R3 whose first…

A:

Q: 2. Which one of the following functions will result in the following graph? M 2 A. 5+ 4 sin[3(x -…

A: Put x=0 and see the function values and then decide which will be the graph

Q: 0 3. Let {e₁,e2, e3} be the standard basis of C³, and {V1, V2, V3} be the basis v₁ = 1 V3 = 0 V2 =…

A: Let E={e1,e2,e3,⋯,en} and V={v1,v2,v3,⋯,vn} be two bases of a n dimensional vector space V.Then the…

Q: Problem #3: Let F(x, y, z) = (3y, 4x, 3y). Use Stokes' theorem to compute Sc F. dr where C is the…

A:

Q: N Shown above is a slope field for which of the following differential equations? A dy = x² + y² B C…

A: The given slope field is:We need to identify, which of the following differential equations has this…

Q: [3 0 -9 -25 -33 We want to determine if the columns of A span R². Let A = To check this we add times…

A:

Q: Consider a connected graph G and let e = wv € E(G) such that G' = G-e is disconnected. Let G₁ and G₂…

A:

Q: (4) Suppose f(x) is increasing on [a,b]. Let P₁ = {xo, ₁,...,n}, where xk = a + k (b − a), k = 0,…

A:

Q: Consider the predator/prey model x' y' 0): = = 3x - x² - xy -2y + xy. Find all critical points and…

A: Given predator/pray model is the following :So we get critical points for given system from which…

Q: Find the centroid of the region bounded by the curves y = sin(2x) and y = sin(x) for 0 < x≤².

A: We use the formula for centroid to solve this problem.

Q: (2) Suppose ƒ is continuous on [a, b] with f(x) ≥ 0 for all x € [a,b]. If | f(x) dx = 0, show that…

A:

Q: 5.1. THE LINEAR CONJUGATE GRADIENT METHOD 10 set of nonzero vectors {Po, P1, ..., Pi} is said to be…

A: Given that : Set of non-zero vectors    is  said to be conjugate with respect to symmetric positive…

Q: Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are…

A:

Q: Question 4. Money flows to the new Ponzi scheme at a rate proportional to the square root of the…

A: Since there are more than three parts, find the solution of the first three parts.A rate…

Q: #8: Use Divergence theorem to find the outward flux of F = (3x², e¹², cos³(x²+x)) of the cube in R³…

A:

Q: Linear algebra: please solve q6 and 8 correctly and handwritten example 2 are also attached

A:

Q: Problem #1: Q(x) = 3x² +x² + x² - 6x1x2 - 6x1x3 - 2x2x3. Find a unit vector x in R³ whose first…

A: The unit vector that minimizes the quadratic form subject to is the eigenvector corresponding to…

Q: Consider the function ƒ (x₁, x₂ ) = 5 x² + 4 x² defined on (x₁, x2 ) = R². X2 i=1,2 Match the first…

A: The objective of the question is to find the first and second order partial derivatives of the…

Q: In Exercises 1-18, s = 1 + 2i, u = 3 – 2i, v = 4 + i, w = 2 - i, and z = 1+i. In each exercise,…

A:

Q: Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated…

A:

Q: Divergence Theorem

A: and S is the surface of the cube.[-1,1][-1,1][-1,1]

Q: dy Let y = f (a) be the solution to the differential equation d = 3x + 2y with the initial condition…

A:

Q: Use diagonalization to find matrix A, assuming that A has the following eigenvalues and…

A: Given eigen value and corresponding eigen vector are

Q: Consider the following matrix: 2 -2 4 6 6 A = -1 1 3 2 -3 -1 1-3 -3 1 Give a basis for each of…

A:

Q: Use the Euler-Gauss method with h = 0.5 to approximate the solution of the following problema…

A: Given differential equation is                        Let    and h = 0.5…

Q: 14. УА y = x + 1 y = 2x + x - 1

A:

Q: 4. Solve the following ODE system using Euler's method, assuming that at x = 0, y₁ = 4 and 1/₂ = 6.…

A: Euler method is given by:yn+1=yn+hf(tn,yn)

Q: Suppose that in a certain state, all automobile license plates have three uppercase letters followed…

A: Since, all automobile license plates have three uppercase letters followed by three digits.Total…

Q: The graphs of f(x) and g(x) are shown in the figure below. Region R is bounded by f(x), g(x), x=-1,…

A:

Q: The linear tranformation L defined by L(p(x)) = −6p' - 12p" maps P4 into P3. (a) Find the matrix…

A:

Q: Consider the function f(x) = -x² + 4x + 10. 1. Explain how to determine appropriate scales for the…

A: