Show that the osculating plane at (x, y, z) on the curve of intersection of the cylinders x2 + z² = a², y² + z² = b² is given by xx²³ - z z² − a² _ y y² − z z² − bª - - a² B²

Q: Is that dot between the n and d1d2...dk meaning multiplication?

A: It is not multiplication.

Q: y" + y = e-t y(0) = 0, y'(0) = 0

A:

Q: Find infinite Sum [=> k=1 ka 2

A: The given problem is to find the infinite sum of series 1/k2 from k=1 to infinity.

Q: alculate the surface integral ff F. NdS, where F = S (u, v) = (uv, v, u) where 0 ≤ u ≤ 4, 0 ≤ v ≤ 3.…

A: The given function is, F=3xy i^ -3yzj^-4xz k^. Parametric representation of the surface S is,…

Q: Stokes’ Theorem for evaluating line integrals Evaluate theline integral ∮C F ⋅ dr by evaluating the…

A: The given vector field: F=x2-y2, z2-x2, y2-z2 The region is boundary of the square x≤1, y≤1 in the…

Q: [4] Use Gaussian elimination with back substitution to solve the linear system of equations x2 + x3…

A: First use Gauss Elimination Method.

Q: Make a scatter plot of the data and determine which type of model best fits the data.…

A: x 1 2.5 0.5 -2 0 1.5 y 3 16.5 1.5 0.1 1 5

Q: Use the graph of f(x). f(x) 5 x² + 5 x+1 to solve the ineq

A: Introduction: The circumstance of an illegal and/ or uneven distribution of openings and coffers…

Q: 2π tan@ elo

A:

Q: Evaluate the line integral by the two following methods. fxy dx + 2 dx + x²y³ dy C is…

A:

Q: g(n) := Σu(d)ƒ (d) = [I (1 − f(p)). II d\n p|n where product is over all primes which divides n.

A:

Q: Prove that n²¹ +n²+1 n = 0(n³).

A: To Prove: n4+n2+1n=Θ(n3).

Q: Consider the series R10 ≤ n = 1 (a) Find the tenth partial sum, $10. (Round your answer to six…

A:

Q: Solve using Laplace transform "+2y+5y=sin(3r), y(0)=1, y'(0) = -1

A:

Q: A scammer offers you a "deal" by which you can invest your money with them and earn returns. The…

A: We need to find rate of change in investment  i.e. return of investment according to scammer and…

Q: A. Recall that an undirected graph is connected when it has at least one vertex and there is a path…

A: Kindly refer to Step 2 for the solution.

Q: 4. Let R be a relation defined on Z as follows: For all m, n € Z, m R n iff 4 | (m² — n²). a) Prove…

A:

Q: Consider the following initial value problem. (A computer algebra system is recommended. If a…

A: Given That :  Initial Value Problem  y'=y2+2ty3+t2 , y1=2 To Find : a) Use Euler method with h=0.1 ,…

Q: the ellipsoid Show that the tangent at any point of the curve of the intersection of + =1 and the…

A:

Q: CNBC.com reported mortgage applications increased 9.9% due to a decrease in the rate on 30-year…

A:

Q: 2. Let D be a relation defined on Z as follows: For all x, y € Z, x D y iffx|y. Determine if D is…

A:

Q: 1. Encrypt the following Messages/words using the indicated method. A. Using cipher shift of 4 to…

A:

Q: 2. (Section 17.6) Given that = 2yî - xj+xzk, evaluate J. ds where S is the part of z = 3 + y inside…

A:

Q: y" - y' - 2y = 5 sin x y(0) = 1, y'(0) = −1

A:

Q: 7. f(x)= // at x = [0, 1]

A: Given: fx=1ex3 ,x=[0, 1] To find: n when error E=0.0002. To find: Approximate integral by using…

Q: Find the matrix A of the quadratic form associated with the equation. 4x2 - 6xy4y2 + 6 = 0 A = 4 -3…

A:

Q: dy For the differential equation = (y - 3) (+2) there is equilibrium solutions. The positive…

A: The given differential equation is: dydx=y-3y2+2. To find: The positive and negative equilibrium…

Q: Calculate the future value of a simple interest loan of 15,500 DHS at a rate of 2.5% for six (6)…

A: Principal amount is 15,500 DHS Rate is 0.025 ( in decimal) Time is 0.5 years We have to calculate…

Q: Let ^ - √/12 (11¹) "²-1 (²3) A R Find the eigenvalues and eigenvectors.

A: A=121-111 Let λ be the eigen value then…

Q: Suppose a 5x8 matrix A has two pivot columns. Is Col A =R2? Is Nul A=R6? Explain your answers. Is…

A:

Q: Q16. Consider a game in which a fair die is rolled. If the die comes up 1, the player wins $4. If…

A:

Q: M = -5 1 -2 -14 2 -1 1 8 0 1 -2 -9 -3 1 -2 -12 1. Explain why this matrix is or is not invertible by…

A:

Q: We have written the given differential equation in the form M(x, y) dx + N(x, y) dy=0 where M and N…

A: Given a differential equation Mx, ydx+Nx,ydy=0. Here Mx, y=y-8xex-6x2 and Nx, y. To find the partial…

Q: Calculate using polar coordinates. √4-7² 2 siste o x² + y² dy dx

A:

Q: with the curve Find the equation of the plane that has three point contact at the origin x = A - 1,…

A: We find the equation of the plane that has three point contact at the origin with the curve x=…

Q: Which of the following functions has a slant asymptote when graphed? 2x³ + 4x² - 6x x² + 2x-3 a)…

A:

Q: Solve the traveling salesperson problem for the graph below by finding the total weight of all…

A:

Q: of A5 A=14=44 A4 = -4 -2 5 A6-

A:

Q: Part Time Hours Hourly Rates 180 $62 186 $69 192 $76 198 $83   Using the labor supply…

A:

Q: Suppose the vector field v(x, y, z) = (3y + 2) i + (x − 2) j+ (2z+1) k represents the velocity field…

A: The given problem is to find the circulation of the given vector field over the path C where C is…

Q: Suppose you have a deck of 52 cards. a. How many different 5-card hands can be chosen from this…

A:

Q: Theorem 4.12. Gauss: Let n #0 (mod p). Consider the remainders mod p of the following (p-1)/2 many…

A: Let n≢0mod p. Consider the remainders mod p of the following p-12 many integers, n, 2n,......,p-12n.…

Q: 7.1.39. On the vector space R³, let R denote counterclockwise rotation around the x axis by 90° and…

A: To Find: (a) Matrix representation of counterclockwise rotation around x and z-axis by 90° and…

Q: Example 1: Complete the table for each of the following graphs. | Amplitude Period Equation of Axis…

A: Graph of the trigonometric functions are given, we have to find the equation of functions in both…

Q: The yearly amount of material recycled (in thousand tons) during selected years from 2000 through…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: You borrow 150000 DHS from your dad and promise to pay back 176550 DHS in thirty-six (36) months.…

A: We use the following:

Q: What are the x-intercept(s) of f(x) = x²7x+10 3(x-1)² a) There is no x-intercept. b) x = 1 (order 2)…

A:

Q: The recurrence relation for the Bessel function J₁(k) with the first coefficient C_1=1 leads to 1…

A:

Q: Determine whether the alternating series 80 Σ (-1)+1 2 converges or diverges. n=1 Choose the correct…

A:

Q: 5. Let R be an equivalence relation on a set A. Prove that for all a, b E A, a R biff [a] = [b].

A: