Show that (cos+ i sin 0)" = cos no + i sin ne for 0 € R and n € Z.

Q: where F(x, y, z) = 7yzi - 2xzj+ek and C is the circle x² + y² = 16, z = 6 oriented counterclockwise…

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Q: The temperature at a point (x, y, z) is given by where T' is in degrees Celsius and x, y and z are…

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Q: Introduction to Discrete Mathematics Let A = {x ∈ Z | ∃k ∈ Z, x = 3k + 2}, B = {x ∈ Z | x ≡ 1 (mod…

A: Let A = {x ∈ Z | ∃k ∈ Z, x = 3k + 2}, B = {x ∈ Z | x ≡ 1 (mod 3)}, and C = {x ∈ Z | 3 | x}. We now…

Q: Suppose that g is a function of two independent variables that has continuous partial derivatives,…

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Q: A professor had students keep track of their social interactions for a week. The number of social…

A: Given, The number of social interactions over the week is shown in the grouped frequency…

Q: 10. Which denominations (or value) of stamps can be purchased using a combination of stamps worth 13…

A: This is a famous problem which goes by the name Postage Stamp problem. We shall show that any stamp…

Q: If (x + iy)³ = u + iv, then show that И V - | < + X y = (x² - y²).

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Q: Given: AB 1 BC DE LCD BD and AE bisects each other Prove: AB ED X D Statements Statamante Reasons…

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Q: An investment account promises yearly rate of 5,2 % compounded quarterly for the first 3 years and…

A: The following is given: An amount P is compounded quarterly at 5.2% for 3 years. Then it is…

Q: Use cylindrical coordinates to calculate : JS₁ ² + y² dv W: x² + y² ≤ 36, 0≤z ≤2

A: We need to convert cartesian to cylindrical co ordinate system  Relation between cartesian and…

Q: not correct

A: Given, The function  f(x,y) = 2x2-2x+4y+5y2   We have to find the critical point of the function.

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Q: P = Let D = A = If possible, find an invertible matrix P so that D = P-¹AP is a diagonal matrix. If…

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Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: Suppose that you have a curve C that is given by r(t) = (t2, 2t, t3) from t = 0 to t = 1. Let…

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Q: Jill's 2013 NC tax is: $ (Round to the nearest dollar.) What is Jill's effective tax rate? [Tax paid…

A: Given jill lived and worked in North Carolina in 2013 Jill gross income=$78000 Jill dedcution =$3…

Q: d) real numbers x, y s.t. there exist two disjoint neighborhoods of these numbers.

A: (d) For x,y any two elements.  To Prove or disprove: there exists two disjoint neighborhoods of…

Q: Use cylindrical coordinates in order dervive the formula for the volume of the following ellipsoid:…

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Q: Find an equation of the line that is tangent to the graph of f and parallel to the given line. Line…

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Q: sec */³3 2* * p² sin & dp de dø

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Q: Find the cylindrical coordinates. 1. The cartesian coordinates of a point are (-1, 1, 3).

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Q: 부 || S T x1(t) : = 여름을 0 || > T

A: As per our company guideline we are supposed to answer only first qs, kindly post remaining qs in…

Q: Find the Maclaurin series of the function ƒ(x) = 3x³ – 4x² - 6x +4 (143-144) CO = C1 = C2 = €3 C4 =…

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Q: {e-3t+ et cos 4t}

A: Evaluate Laplace transform:  Le-3t+etcos4t

Q: Find the surface area of the part of the sphere x² + y² + ² = 16 that lies above the cone z = √√x² +…

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Q: Let f be defined for (x, y) = R² if x #0 where f(x, y) = (x² + y²) x ,sin x + cos y Prove whether or…

A: Given: fx,y=x4+y4x,sinx+cosy, x,y∈ℝ2 with x≠0. To find: Whether or not there is a neighborhood U…

Q: A visitor is staying in a tent that is 7 kilometers east of the closest point on a shoreline to an…

A: We have to solve given Questions.

Q: Given F(t) = (cost,sint,t²), find the integral of f(x, y, z)=√z along the curve b-- from 0<=t<=2π

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Q: 7.1.8. Explain why the eigenvalues of A*A and AA* are real and nonneg- ative for every A Cmxn. Hint:…

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Q: The figure below shows that 4 one-inch segments are needed to make a 1 × 1 square, 12 one-inch…

A: 1×1 square require 4 one inch  segments 2×2 square require 12 one inch  segments 3×3 square requires…

Q: Use cylindrical coordinates to determine the volume of the solid that is enclosed by the cone z =…

A: Volume by cylindrical coordinates

Q: Let p be an odd prime. Show that if (p − 1) Xn, then 1 + 2 + + (p − 1) = 0 mod p

A: The given problem is to show that for p an odd prime if (p-1) not divides n then 1n+2n+...+(p-1)n=0…

Q: Graphing Quadratics Standard Form Identify y-int, x-int(s), axis of symmetry, vertex from the…

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Q: Can we make the polynomial a(x) = polynomials? h₁(x) = – 1 h₂(x) = x + 2 h3(x) = x² + 1 Answer: Yes,…

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Q: f(x,y)=x-y; x² + y² ≤ 1, x+y≥1

A: Note: Cartesian-polar coordinates relation: x=rcosθ, y=rsinθ .

Q: Find all the solutions to z7 = 1 - i√3, and plot them on the complex plane. Show that (cos 0 + i…

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Q: 4 AUB AUB, 6) AOB = AOB 524) JAN 28

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Q: (6) Use the series representation of the function to approximate the integral with € < 10-4. Hint:…

A: (6). (a) Given the integral is                                     ∫01e-x2dx.

Q: Analyze the continuity and differentiability of the function: at x = 1, calculating the…

A: Continuity of the function

Q: bad bna toort Problem 5 points). Consider the capital letters as unions of curves with wband to…

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Q: Show that is conservative by finding a potential function for F.

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Q: 9. Convert all complex numbers to trigonometric form and then simplify the expression. Write your…

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Q: Prove that the inner derivations ad x, x∈g are an ideal on Der(g)

A: Prove that : The inner derivative adx , x∈g are an ideal on Der(g).

Q: Calculate 11₁ S F.ds where F = (4x³z, 4y³z, 3z¹) and S is the surface of the solid bounded by the…

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Q: Suppose you plan to have $30,000 in 10 years from now and you can invest your savings at 2%…

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Q: Evaluate (x+y-52) dV where E = {(x, y, z) | − 7≤ y ≤0,0≤x≤y, 0≤ z ≤ x + y²}

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Q: Find the range of g(x) = 3x-7 2+5x What should be the domain of g(x)?

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Q: Suppose that A = 2 - 2 1 1 00 0 0 1 Find the eigenvectors of A (a) Eigenvector with respect to the…

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Q: 5. Using the above inequality, and note that for any point A(x, y), B(a, b) = R², we have ||A – B||…

A: Given : For any point Ax , y , Ba , b ∈ ℝ2 ,  A - B = x , y - a , b = x - a2 + y - b2   To prove :…

Q: 5. Make up sequences that have a. 3, 3, 3, 3, ... as its second differences. b. 1, 2, 3, 4, 5, ...…

A: To determine: (a.) Sequence with 3,3,3,3,... as its second differences. (b.) Sequence with…