Compute the line integral of the vector field F = (3y, -3x) over the circle x² + y² clockwise JcF. ds = = 81 oriented

Q: Explain why S is not a basis for R2.S = {(−3, 2)}

A: We know the definition of basis, let V be a vector space. Let B be a set of vectors in vector space…

Q: Suppose that u and v are two unit vectors in 3D and the angle between them is π 3 . i. What is |u ×…

A: We know that the vectors i, j and k denotes the unit vectors in the direction of x-axis, y-axis and…

Q: 2x3 Use the correct trigonometric substitution to evaluate the integral ſ- √√x²-16 dx

A: Evolution of integral by trigonometric substitution

Q: Determine the general solution of: 9y" - 6y + y = 0. No conditions are given. By calculation of the…

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Q: You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v = 1331. Find the…

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Q: The given Riccati equation is y'- y²-yeatr + sin²x = 0 Also it is given that, the particular…

A: Solving Riccati equation when one particular solution is given. y=y1+1/u

Q: If f(x) = ln(cos 2x) then find the slope of the graph of f(x) at x = π/8.

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Q: 1) Solve the following ODE using the power series method

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Q: The table time (z.) 1 2 3 4 5 6 infections (y = f(x)) 32 37 34 48 53 69 depicts the number of newly…

A: We will be solving first three question as mentioned. The given table is: Time xi 1 2 3 4 5 6…

Q: Consider the following. B = {(0, 1, 4), (-1, 1, -4), (-3, 3, -8)), B' = {(-3, -2,-4), (2, 1, 2),…

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Q: 6. Consider the functions f, g: R → R defined by the formulas 1 x² + 1 f(x) = and g(x)= x + 1. Let A…

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Q: Without the use of a calculator, calculate the determinant of the matrix. [-30 7 1 1. 2. 01 11 0 2 2…

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Q: Consider the simple model of labour market flows with the unemployment rate following Ut+1 = (1 −…

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Q: n² n→∞ √3n¹+1 (a) lim (b) lim √3+(-2) n 818 € IM8 IM8 n=1 n=0 2" 2" 1 32n

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Q: (e) Using ti = 4 and t₂ = 6, apply five iterations of the Bisection Method to find the value of c…

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Q: The curves f(x, y) = x³ + y - 1 g(x, y) = y³x + 1 rsect near the point (x1, 9₁). Using the point…

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Q: An arrow is shot from the ground into the air at an initial speed of vo = 108 ft/s. (a) Use the…

A: The bisection method is used to find the approximation of the root of a real valued function by…

Q: Find the maximum and minimum values of ƒ(x, y) = xy on the ellipse 3² + y² = 5. maximum value =…

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Q: Determine the area of the parametric surface S with equation R(u, v) = (u²+v², 2uv, u² −v²), where 0…

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Q: Show that the given transformation from R² to R² is linear by showing that it is a matrix…

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Q: identify the number of decimal places to which the approximation is correct, show

A: From the Maclaurin series of cosx upto sixth degree   The  approximate value of Cos(1/2) from…

Q: In what follows, the function f is given by f(x) = 3+1 (a) (i) Use Taylor's Theorem to derive a…

A: a) (i) Here we use Taylor's Theorem and two point forward difference formula is, f'(x) = f(x+1) -…

Q: Suppose a cyclic group G = with the older 12: (1). List all subgroups of G (2). List all those…

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Q: Find the local and global extrema for the graph of ƒ(x) = x3 – 6x2. a.There is no local or global…

A: We first find the critical points of function by equating derivative of f to 0. i.e.…

Q: In Z24, find a generator for each of the following subgroups. (a) (21) n (10). (b) (15) n (14). (c)…

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Q: nd the inverse Fourier transform of the signal given below. |G(f) = { otherwise -B≤f≤0 -π/2 0≤f≤B 06…

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Q: Functions f : [0, 2] [0, 4] and g: [0, 4] → [0, 6] are given by their graphs (see the pictures…

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Q: f(x, y) = e cos(4y). Find and classify all critical points of the function. If there are more blanks…

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Q: Determine whether the matrix is elementary. If it is, state the elementary row operation used to…

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Q: y' = =+ y x

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Q: Find all (real) values of k for which A is diagonalizable

A: The algebraic multiplicity of an eigenvalue is the number of times the number appears as the…

Q: True or False: (1) There is a solution of y' = 24, which is decreasing when x < 0. (a) m1 2

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Q: 7) For which values of the parameters 'a' and 'b' the system does have either i-unique solution or…

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Q: 4. Consider waves in a resistant medium that satisfy the problem u₁t = c²uxx-ru, for 0 < x <l u= 0…

A: Let, ux,t=XxTtuxx=X''xTtut=XxT'tutt=XxT''t Separation gives…

Q: The curves F(x,y) = x² + y - 9 and g(x,y) = y²³-x+1 intersect near the point (04, 4₁). Using the…

A: please find the attached image.

Q: Find the future value for a $85,000 investment for 15 years at a compounded continuously at 5%.

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Q: RICCATTI 1. y' =2 tanx secx y₁ = sec x -y²sinx

A: This is the question of the differential equations. Application of Ricatti and Bernoulli'es…

Q: 1. (a) Use the Fourier expansion to explain why the note produced by a violin string rises sharply…

A: 1) a)

Q: 9. Let R+ denote the set of positive real numbers. Define a relation E on R+ as follows: a Eb if and…

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Q: wice the base of the triangle. If the perimeter of the e of each side of the triangle. of a square…

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Q: Design a rectangular milk carton box of width w, length I, and height h which holds 494 cm³ of milk.…

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Q: Using double integrals, find the volume of the octahedron with the following 8 faces: z = ±1 + x z…

A: Please find the attached image.

Q: 7. Consider a line in 2-dim space y = ax + b and a given point (ro. 30) not on the line. Please…

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Q: Define complemented lattice. Let (L, *,Ð, ', 0,1) be a Boolean algebra. Then show the following:…

A: Given: (L,*,⊕,',0,1) is a Boolean algebra.We need to define complemented lattice and show that…

Q: Find the integrating factor and the general solution of the following differential equations. 1.…

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Q: Let S = (1 + (nx)²)−¹. a. Show that the series S converge on R \ {0}, but does not uniformly…

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Q: L. log 4 = 2-log (x + 5) 2. In (3x-1)=2 3. log (3x-7)= log (5x + 1)

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Q: Draw a Venn diagram that illustrates the relationships among the given sets. S = {Amazon, Hotmail,…

A: Given

Q: 8. Write an equivalent statement that does not use the if... then connective. Use the fact that p→q…

A: We know that, p → q is equivalent to ~p v q.  The given statement is        "If the sun comes out…

Q: BONUS. Write the Mayan numeral for 999,999.

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