Evaluate the integral by making an appropriate change of variables. 3(x + y) cos (x2 - y2) da, where R is the rectangle enclosed by the lines x - y = 0, x – y = 6, x + y = 0, and x + y = 6 Hints: If we set u = x-y, v=x+y, how are x and y expressed in terms of u and v; which region D in the uv-plane is mapped to R in the xy-plane; what is the Jacobian of x,y with respect to u,v?

Q: )  Use composition to determine whether or not f(x) = 2? + 4 and g(x) = x-4/2 are inverses.

A:

Q: of o the genesal Solndion ot btain Solution y'tay'+y= e- inx y+2y'ty3= on(o,00)

A:

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

A:

Q: The number of carbon atoms in a fossil is given by the function y = 5100(0.95)x, where x represents…

A:

Q: A function f(x) is said to be continuous at x = c if the following three conditions are satisfied:…

A: Solution

Q: A set of data has a normal distribution with a mean of 100 and a standard deviation of 15. Find the…

A:

Q: Prove that: 3n > 2n + n2 for all integers n is greater than or equal to 2

A:

Q: 3(x + y) cos (x2 - y?) da, where R is the rectangle enclosed by the lines x - y = 0, x – y = 6, x +…

A:

Q: 6. Show that if f : X Y and g : Y → Z are both onto then fg : Z -→ Z is onto. (Note this is function…

A:

Q: 10 (2). Let f be a function that admits continuous second partial derivatives such that Vf (x, y) =…

A: Introduction: Like a single variable function, a multi variable function can also have extremum…

Q: 11. 2х, — 3х, = -7 x1 + 3x2 - 10x3 9. 3x1 Xz = 13

A:

Q: Find the least residue of 99! (Mod 101)

A: Introduction: In number theory, Wilson's theorem is a very significant theorem. It states that for…

Q: Consider the four intervals [a, b], (a, b), (a, b], and [a, b) whose endpoints are a and b. What is…

A: Consider the four intervals [a, b], (a, b), (a, b], and [a, b) whose endpoints are a and b. What is…

Q: t2 2t – 8 t 6. Find the Laplace transform of f(t) 2 te-2t

A:

Q: Use the indicated entry as the pivot and perform the pivoting. X1 X2 2 4 X3 S1 $2 S3 1 1 1 1 3 1 1 1…

A: Introduction: The simplex method is a method for testing vertices as potential solutions in a…

Q: EXAMPLE 1 Evaluate the triple integral SSSKYZ'dv, where B is the rectangular box given below. B =…

A:

Q: 5. 10 20 60 30 40 50 200 230 264.5 304.17 462.61 y 349.8 402.27

A: We have, For Linear the rate of change test is  y2-y1x2-x1=fx2-fx1x2-x1=m For exponential functions,…

Q: Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.  F…

A:

Q: Find the mass and center of mass of the lamina that occupies the region D and has the given density…

A:

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: 7) Use binomial theorem to expand (2x-1)^6

A:

Q: 3. If x and y are two n-vectors, then prove that 1 (a) |x*y|< ]], \»l, - +=1 (Holder inequality) 1…

A: Given that x and y are two n-vectors. We have to prove the following :                          (a)…

Q: power factorization

A: Introduction: A number is prime factorised or integer factorised when it is broken down into a set…

Q: Given the formula B VR, where statement B is true and statement R is False, the whole formula would…

A: Introduction: In sentential logic, a statement is constructed from simple statements by using…

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

A: Solution :-

Q: (b) If f is a bounded linear functional on a Hilbert space H, show that there is a unique y e H such…

A:

Q: A window has the shape of a parabola above and a circular arc below. Find the area of the window.…

A: As per our guidelines we are supposed to solve only first three subparts of the problem. For the…

Q: pivot in the simplex tabléäu. X1 X2 X3 $1 $2 S3 6. 2 4. 4 6. 1 1 6 1 1 1 - 3 1 0 1 e pivot is…

A: In this question, the pivot in the simplex table is determined. Simplex Method A simplex approach is…

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: e numeral is

A: In this question, the change of the numeral system is applied. Number System A number system is a…

Q: Q3. Find the solution ylt) of the initial value problem (1) Hat =0, l0\ = | Where ə is o postve…

A:

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: (x² + y)dx + (x+ y²)dy = 0

A: Use the given differential equation.

Q: Let X be the collection of all functions f : IR→ IR Show that there exists a one-to-one function G:…

A: It is given that X is the collection of all functions f:ℝ→ℝ. Prove that there exists a one-to-one…

Q: Solve the first order differential equation by separating variables

A:

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

A:

Q: t2 t 6. [34] Find the Laplace transform of f(t) 2t – 8 te-2t

A:

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

A:

Q: For #1&2, describe the end behavior of the graph for the polynomial function. y = 7x5 + 8x2 – 10 1.…

A: 1) The given polynomial is: y=7x5+8x2-10 The degree of the polynomial is 5 which is an odd number.…

Q: 1. 'Let X = {a,b,c,d,e} . Define ze P(x) by r={ø,X,{a},{c,d},{a,c,d},{b,c,d,e}}. ond nterore d) Give…

A: Let (X,τ) be a topological space and A be a subset of X, then the closure of A is denoted by cl(A)…

Q: Evaluate o(7000).

A:

Q: 9 (2). Consider the region R shown in the following figure, which involves the curves of equations…

A:

Q: sin x Use a CAS to plot the region of integrati on for 0 y dx dy. Then use this plot to switch the…

A:

Q: Chain rule and implicit differentiation Suppose that F(x,y,z) = 0 defines z as a function of x and y…

A:

Q: Let y = 3Ja. Find the change in y, Ay when x = 3 and Ar 0.2 %3D Find the differential dy when x = 3…

A:

Q: a to graph the region. Also if the evaluation of the double integral is very complicated, you can…

A: Introduction: The formula of the green's theorem is given by, ∫C(Pdx+Qdy)=∬D∂P∂y-∂Q∂xdxdy.

Q: Use Euclid algorithm to write (80,104) as a linear combination of 80 and 104

A: Introduction: Euclid's algorithm is a method for calculating the greatest common divisor of two…

Q: Multiple Select Question Select all that apply а Which of these are paths in the directed graph…

A:

Q: Suppose that F(x,y, z) = 0 defines z as a function of x and y and F is differentiable. Prove that дх…

A: