A circle C in the plane x+y+z= -1 has a radius of 3 and center (2,0, - 3). Evaluate F.dr for F = (0,4z,3y), where C has counterclockwise orientation when depend on the location of the center of the circle? .... F•dr = C (Type an exact answer, using x as needed.) Does the circulation depend on the radius of the circle? O A. Yes. The circulation is inversely proportional to the square of the radius. O B. Yes. The circulation is proportional to the radius. O C. Yes. The circulation is inversely proportional to the radius. O D. No. The circulation does not change with the radius. O E. Yes. The circulation is proportional to the square of the radius. Does the circulation depend on the location of the center of the circle? O A. No. The circulation does not change when the circle moves in the plane. O B. Yes. The circulation changes linearly with x. O C. Yes. The circulation has a complex relationship with the location of the circle. D. Yes. The circulation changes linearly with y. O E. Yes. The circulation changes linearly with z.

Q: The following matrix projects 2-vectors onto the unit vector v = (v1, U2): U2n ןU P = vv" = Also rec...

A: Given unit vectors v=v1,v2. Hence v=1. P=vvT=v12v1v2v1v2v22 (1) Observe that Pv=vvTv=vvTv=vv2=v1=v H...

Q: nstruct a truth table for each statement: a. If you do not study or do not go to sleep by 12 pm., th...

A:

Q: Let F be a finite field of  pn elements containing the prime subfield Zp . Show that if   alpha is i...

A:

Q: Using changing variables, calculate the integral -dA where D is the triangle of vertices (0, 0), (1,...

A:

Q: Use undetermined coefficients method to solve b. y" – 2y' + 5y = e* cos 2x %3D

A:

Q: What is the largest number of edges possible in a graph with 9 vertices? edges. What is the largest ...

A: The maximum  possible number of edges in a graph with n vertices is given by nn-12  The maximum  pos...

Q: Solve the following equation. For your answer, simply type the value "7"). If you determine that the...

A: An algebraic expression is obtained by combining numbers and variables together with arithmetic oper...

Q: Use the given graph of the function on the interval (0, 8] to answer the following questions.

A: Introduction: If f(x) ≤f(c) for all x ∈D, the function f defined on the domain D has a global maximu...

Q: Some experimentation has convinced you that the relationship between wages paid (x) and profits can ...

A:

Q: If the given solutions t2 - 2t %3D %3D 2t form a fundamental set (i.e., linearly independent set) of...

A:

Q: given: 20,000 shares cumulative preferred stock ($2.25 dividend per share): 40,000 shares common sto...

A: Given- Given: 20,000 shares cumulative preferred stock ($2.25 dividend per share): 40,000 shares com...

Q: Prove that if f(2) is an odd function, that is, f(-2) = –-f(2) for all z E C, and f is analytic in a...

A:

Q: Find the x-intercept of the following line. 3x - 6y = 18

A: Here we have to find x intercept of the given line.       3x - 6y = 18

Q: Consider the coupled linear system i = 3y – 4x ý = 5y – 6x 1. Write this system in the form dæ Ax. %...

A: Given:  x˙=3y-4xy˙=5y-6x To find: 1) dxdt=Ax form of a given system. 2) Eigenvalues and Eigenvectors...

Q: The following eight teams will be participating in Urban University's hockey intramural tournament: ...

A: Remark: the number of different permutations of n elements taken r at a time ( here the order of sel...

Q: Use green's theorem to calculate the integral Fdr, F(r, y) = (e* + x²y , e³ – ry² + sen(3) + 2) wher...

A:

Q: The demand curve of a firm is p=1200 – 2lq and its total cost is C(q) = 2q° – 66q² + 600q +1000 wher...

A: In this question, concept of maxima and minima of profit function is applied. Maxima and minima The ...

Q: Let R = {A € gL(2,Z;) such that B is an upper triangular matrix . Then R is a ring with order О 275 ...

A:

Q: 2. Let L:= D2 - x-D+4x2. Verify that Ly 0 where y(x) = sin(x). %3D %3D %3D

A:

Q: Determine if each of the following relations is a functions with domain A={1,2,3,4} and codomain B =...

A:

Q: 2 0 0 3 1 2 0 3 S Let A = (a) Solve the characteristic equation of A and show that A = 1, 2, and 3 a...

A:

Q: Problem 5.3 Prove that п(п + 1)(2n + 1) (Зп? + 3п — – 1) 30 j=1 whenever n is a positive integer.

A:

Q: - : : 1 -21+ Find the most general real-valued solution to the linear system of differential equatio...

A:

Q: What is the largest possible area of a right triangle whose hypotenuse is 5 cm long?

A: according to question,  hypotenuse of a right triangle is 5 cm let the base be b=x and perpendicular...

Q: (2) where f(x)= x3-2x²-5

A:

Q: 300,000

A:

Q: Suppose that P is a point on the line AB such that AP = k AB , where k is a constant. a Show on a di...

A:

Q: . Let B = {(1,–1),(-2,1) } and B' = {(-1,1), (1,2) } be basis for R² , and let A = 6 I be the matrix...

A: We will utilise the given diagram to solve the questions.

Q: Determine the periodic payments PMT on the given loan or mortgage. (Round your answer to the nearest...

A:

Q: dentify if the given statement is a proposition or not a proposition. If it is 11 a proposition, det...

A:

Q: If x and y are real numbers and x>1, prove that there exists a positive integer n such that x" > y

A:

Q: [ 2t ute the Wronskian to determine whether the functions y, (t) and y2(t) are linearly independent....

A: Introduction: Let y1 is a constant multiple of y2 if y1 and y2 are solutions of equation with W[y1, ...

Q: Discuss the following statements regarding the function → R, f(x) = tan x 2 2 I. >: If 0 <x<", then ...

A:

Q: 8) Use the appropriate coordinate system to compute the volume of the indicated solid. a) The solid ...

A:

Q: Find the (real-valued) general solution to the differential equation. z′′+7z′=0 (Use constants A, B...

A: To Find the (real-valued) general solution to the differential equation. z′′+7z′=0

Q: y y' + y? = x-2 X

A:

Q: The value(s) of 1 such that the vectors v1 = (4, 3 - 1.) and v2 = (-8, 2 + 2) are linearly dependent...

A: Two vectors U and V are set to be linearly independent if and only if their linear combination aU+bV...

Q: Find the periodic payments PMT necessary to accumulate the given amount in an annuity account. (Assu...

A: Given that Future values FV=$30,000 Rate of interest, r=6% ⇒r=6100=0.06 Since, payment is monthly, h...

Q: Given x sin x + 1 = 0, using Newton-Raphson method with initial guess X0 = 4, calculate the root of ...

A: Given that, the function is x sinx+1=0 and the initial guess x0=4. Note that, the formula for Newton...

Q: x³ + x2 lim 2x3 - 7x2 is The value of the function f(x) = %3D

A: Introduction :

Q: 1. Given: 1. Vector = (1,1,1) (in standard basis) 2. The linear transform (in standard basis) T: R→ ...

A:

Q: -5] 3] 9. 2'|-9 3. 3. Given the basis for a subspace W of R4. Use the Gram-Schmidt process to produc...

A: According to our guidelines we can answer only one question and rest can be reposted. 

Q: 3. A coupled mass-spring system is described by the differential equations x = -x, + x2 x- 2x, = 0 w...

A:

Q: It is not the case that if we are breaking up (B) , then we will find happiness in mount Jiri (H). *...

A: Not breaking up(B)       ~B Then we will find happiness(H)    -&gt;H

Q: h) Given vector field F (x, y, z) = (2x + 2y + 4z) i + (2y + 2x – 32) j + (2z – 3y + 4x) k. (a) Prov...

A:

Q: 8. Calculate the area of the region within the ellipse x2/a² + y²/b² = 1 parameterized by x = a cos ...

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as...

Q: about z = 1 is Taylor's series expansion of Z+1

A:

Q: Are the following statements true or false? ? 1. K6 is not planar 2. K3 is planar v 3. K3,2 is plana...

A:

Q: f(t) = t² – 3t + 5 Ans. 5s2 – 3s + 2

A: As per our guidelines we are supposed to solve only first question. Kindly repost other question as ...

Q: Find the Laplace transforms of the following functions: 3 -4 (s + 3)² + 16 4s2 – 4s + 2 (s – 1)3 13 ...

A: Since you have posted multiparts questions and we can answer 3 subparts. So answered 1, 2 and 3.