Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.  F = xy i + x j; C is the triangle with vertices at (0, 0), (8, 0), and (0, 4)   a) 0   b) -80/3    c) 112/3   d) 64/3

Q: Write an equation for the function graphed below. The y inte 5+ 4 3.

A: Introduction: Asymptotes are imaginary lines that are very close to the total graph of a function or…

Q: Question 5: Use Euler's method with n = 4 to obtain an approximation of the the initial-value…

A: Introduction: The formula of the Euler method to approximate the solution of the differential…

Q: - the following sys 2z = 1 Bz = 3 az = b

A:

Q: Queston2 {e-x, xe-O onlo, c∞) a) shau that q fandamented Set

A:

Q: Let T: P2 P² be given by T(p(x)) = xp'(x) – x² S, p(x)dx a. Show that T is a linear transformation…

A:

Q: A computer store sells two types of laptops, an all-purpose laptop and a gaming laptop. The supplier…

A: The linear function that needs to be optimized(maximize or minimize) is called the objective…

Q: luate the surface integral. // (x + y + z) ds, S is the parallelogram with parametric equations x =…

A: Sub x= u+v  y= u-v  z= 1+2u+v

Q: Find a least-squares solution of Ax = b by (a) constructing the normal equations for x and (b)…

A: Given that A = 1-2-120339 and b = 51-23 . We have to find a least-squares solution of Ax = b by…

Q: You sell 600 shares of AVG Technologies (AVG). You purchased the stock at $2.99 per share and sold…

A: Solution

Q: 18 (1). Let f be a function that admits continuous second partial derivatives, for which it is known…

A:

Q: If A=2(1-cos 0)â, – pyâ, (1– cos ¢)â, – ppâ, +zcos² þ⸠, what is 4 8. V•A ?

A:

Q: Express (-2/3 + j2)

A: This is a problem of complex analysis.

Q: 6 (1). Consider the curve C of equation (x²-2y+y²)² = x²+y². Among the options listed, select the…

A: We know that a polar coordinate is represented by r, θ, where r is the length with r=x2+y2 and θ is…

Q: Find the present value of an ordinary annuity with regular quarterly payments worth P1,000 at 3%…

A: In this question, the concept of Compound Interest is applied. Compound Interest Compound interest…

Q: Use the general solution of x" + w?x = 0 given in Problem 7 to show that a solution satisfying the…

A:

Q: Iz, where * and C is the cu se. Then the valu

A:

Q: 1. Solve the differential equation (x² + y)d.x + (x+ y²)dy = 0.

A:

Q: If gcd(7, a) = 1, prove that either a +1 or a – 1 is divisible by 7. 20

A:

Q: Find the solution using Gaussian elimination: 7x + 5y − 3z = 16 3x − 5y + 2z = −8 5x + 3y − 7z = 0

A:

Q: Solve the initial value problems: (a) ý = 6 + 5y + y°; y(0) = 0 (b) y/ + 2ry + xy = 0; y(0) = 1

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find the maximum and minimum values of the function g(0) = 40 – 7 sin(0) on t Minimum value =…

A: Introduction: Let us suppose that y=f(x) is the function of variable x. to find maxima and minima of…

Q: 5. Given that X, - px, 2 = 4 where p and q are constants. a) Find the general solution of x in terms…

A: Note: As per our guidelines, we are supposed to answer only 3 subparts and rest can be resposted.

Q: Use pola

A: Introduction: To convert the rectangular coordinates x,y into the polar coordinates r,θ, we have,…

Q: B1. (а) The unfinished Histogram and Frequency Table give information about the times, in hours,…

A: Histogram: It is a diagram containing the rectangles, whose base is the range of the intervals and…

Q: Let W = Lin and U= Lin 2 (a) Show that R' = W U. Explain.

A: Note:- As per our guidelines, we can answer the first part of this problem as all the parts are…

Q: 2 Let L be the line in R³ that consists of all scalar multiples of the vector . Find the orthogonal…

A:

Q: Let f : A → B be a function. Prove that if C CA and D CA and f is injective, then f (C) = F (D) = C…

A:

Q: 7. 3 RR Thecross product with one factor kepT a Linear oprator Ti:R3DR°. similarly the c withe one…

A:

Q: 2ty t²+1 – 2t – (2 – In(t² + 1))y'

A:

Q: Sketch the path using the following parametric equations x(t) = 3t – 7 and y(t) = 4 sin t+1 0st55,…

A: Here we need to find different points for different values of t

Q: 4. Consider the autonomous ODE, y' = f(y) = -y(y² – y – 6). (a) Identify the equilibrium solutions…

A: Introduction: When the differential equation is prescribed in the form of dydt=fy, the equation is…

Q: Find the solution using LU Decomposition: w + 2x − y + z = 6 −w + x + 2y − z = 3 2w − x + 2y + 2z =…

A:

Q: what is the limit as n goes to infinity of enn! divided by nn?

A: Since e^n > n And rate of convergence (e^n × n!) > rate of convergence (n^n)

Q: For the demand function q= D(p)%3D 290- p, find the following. a) The elasticity b) The elasticity…

A:

Q: Write the equation of a sine or cosine function to describe the graph. D=0

A: Note: General form of sine function is y = A sin(B(x + C)) + D  A = Amplitude, Period = 2π/B  D =…

Q: 1. Firm 1 and Firm 2 are two producers of widgets. Each firm produces its own widget type at a…

A: p1=200-2q1-q2      c1=15 p2=200-q1-2q2      c2=30

Q: y b a a = 17 mm b = 4 mm C = 7 mm

A: Solution :-

Q: Consider surface S of the cone S : z= 2 + y at the point P(1, , V5). (a) Determine the vector normal…

A:

Q: J y'+2xyt.xy4 1 =D0; ylo) =

A:

Q: Find sine half range for f(x) = \cos x for -t< a <n %3D cosx for f(x) for 0<x <n. cosx

A:

Q: e Stokes' Theorem to evaluate o F dr. F(x, y, z) = z²i + 26xj – y°k ere C is the circle x? + y = 1…

A: Line integral of the vector point function

Q: By the Euler method with h= 0.1 we solve x(0) = 1, 3y = 2x + 3y², y(0) = 0, x' = xy – x, 0<t< 0.2

A:

Q: ) Obtain the general solution of y" + 2y + y = e² In r

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: divisors

A:

Q: Factorise x6 + 1 as a product of three quadratic polynomials with real coefficients.

A:

Q: 3/ = re";y(0) = 1

A:

Q: steps in the process of simplifying the given matrix to​ row-echelon form, with 1s down the diagonal…

A:

Q: For each of the following: a) Determine the intersection points. b) Draw a sketch of the graph. c)…

A:

Q: LITI Solve the following differential equations of cos(y)·y' + sin(y)=

A:

Q: ASS R use the FOCE that aereriime for integ ers to which x,kE IN 7os 0 し +1 =z5 we

A: