Use de Moivre's Theorem to find the following. Write your answer in standard form. (√2 cis 77)

Q: Given that g(x) + 7x sin(g(x)) = 35x² + 24x − 35 and g( ² ) = 0, find g'( ² ). g ( ½¾7 ) =

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Q: Find all the roots of the given function. Use preliminary analysis and graphing to find good initial…

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Q: Eight years ago, Natalia purchased a 8.25% bond for $1,000 plus brokerage fees totaling $150.…

A: The objective of this question is to calculate Natalia's rate of return on her bond investment. The…

Q: When a mass of 2 kilograms is attached to a spring whose constant is 32 N/m, it comes to rest in the…

A: When a mass of 2 kilograms is attached to a spring whose constant is 32 N/m, it comes to rest in the…

Q: SOLVE STEP BY STEP DONT USE CHAT GPT 3. In the following problems use the appropriate algebra and…

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Q: Exercise 2. Consider the following metric defined on R by d(x, y) = inf {z-yl, 1}. 1. Is (R, d)…

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Q: b) W is the subspace of R³ with basis vectors 1 and 0 The vector in W closest to 3 [] 3 3 is O

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Q: -2 8 6

A: The graph has no branch for negative value of x.So, Given function is not defined on therefore, we…

Q: Assume that sin(x) equals its Maclaurin series for all x. Use the Maclaurin series for sin (8x²) to…

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Q: In each of Problems 8 through 16, use the Laplace transform to solve the given initial value…

A: The given initial value problem is y"-2y'+2y=0  with the given conditions y(0)=0 and y'(0)=1Now we…

Q: We are interested in the first few Taylor Polynomials for the function f(x) = 4e + 9e¯ centered at a…

A: Given: The function . To find the Taylor polyomials of degree one and degree two for the given…

Q: f(x) = √²+36

A: A function is concave (or concave downward) on an interval (a, b) if f"(x)<0 for all x in (a,…

Q: You purchased 500 shares of stock six years ago at $21.25 and incurred brokerage fees of $345.  You…

A: The objective of this question is to calculate the rate of return on an investment in stocks. The…

Q: 2. Gamma function - Express the following integral in terms of the Gamma function 3 1 = [* dra²…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Let R denote, as usual, the set of all real numbers. Consider the following two functions: ƒ : R → R…

A: Given:The functions and  are given as: given by ; given by ., where  is the set of all real…

Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 20 inches above the…

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Q: -10000) Say for what values of a and b the set A is a basis of R4 Consider the set

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Q: Use the Alternating Series Estimation Theorem or Taylor's Inequality to estimate the range of values…

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Q: congruence class d'+mZ has order d.

A: To prove that the congruence class has order , we need to show two things:raised to the power of is…

Q: Let f(x) = 8 + 2x2. (a) Estimate the area under the graph of f, the x-axis, and the lines x = −1 and…

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Q: How many triangles can be formed whose corners lie on the grid? A triangle has to have nonzero area.

A: A triangle have 3 vertices. So for draw a triangle it need to 3 distinct points. The given grid have…

Q: 4. Consider the binomial (a + b)^n and calculate what is asked below. a) Use De Moivre's theorem to…

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Q: Let 7= X1 Describe all solutions of a₁₁ + a₂2 +33 + 44 = Ō. I2 X3 C4 18 = x2 13 ā₂ - [3]₁03 = [27],…

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Q: Consider the function f(x) = arctan(3x). Show that the graphy = f(x) and its tangent line y = g(x)…

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Q: Consider the following differential equation y" - 2y' + y =0. (a) Prove that W = {ƒ€F : ƒ" − 2f' + f…

A: The objective of the question is to solve the given differential equation, find a basis of the…

Q: P.) Consider the topology r = {GCR: 0 € G or G=0} on R. Is [0, 1) compact in (R, 7)? Explain why.

A: Given, topology  on defined by, Consider the open cover of  in (Since,  is open set in  for every…

Q: For each of the following functions f, determine if it is injective (one-to-one), surjective (onto),…

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Q: How many functions are there from the set {1, 2, 3} to the set {7,8}. Enter your answer =

A: and We have to find how many functions are there from the set  to the set .

Q: A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the…

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Q: Use Green's Formula, S A given integral: aQ - bỹ) dxdy = = $(P dx + Q dy), to evaluate the JA 3…

A: where C is circle centered at origin with radius 1 .We have to evaluate the given integral using…

Q: In x x→ x-1 25. Find lim " ln x In x given that log₂ (x+1) ≤· -≤1-— as x⇒1¯¯. x-1 X

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Q: restaurant is being built on the side of a mountain, the plans are shown below. (a) The vertical…

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Q: f(t) = ・ƒ(1) = f(t) (4 0 <1≤7 26 127 f(t) 0 ≤1<8 128 (1) = {cos[2(1-7 0 ≤t</ cos[2(1-7)] 12 an

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Q: Four gallons of gas cost $13.70. Write a unit rate that fits with this statement for 1 gallon, you…

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Q: Show all calculations. Show that the following competition model does not admit closed orbits when…

A: We have a competition model represented by a system of differential equations.The goal is to…

Q: 'I' F. ds for the given vector field F and the oriented surface S. In other words, find the flux of…

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Q: Find bases for the column space, the row space, and the null space of matrix A. You should verify…

A: Here we have to find the column space, row space and null space of matrix A.

Q: 1. is this given problem belowe com be considered as lineau programmning? If not, convert or Find an…

A: The objective of the question is to determine whether the given problem can be considered as a…

Q: Compute the following coefficients of the Fourier series for the 27-periodic function f(t) = 3…

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Q: Several oil companies are jointly planning to build an oil pipeline to connect several southwestern,…

A: Given information:Given a network of 10 cities in the southwestern, southeastern, and midwestern…

Q: 12. Consider the vectors x(¹) (t) = and x(2) (t) - (2) a. compute the Wronskian of x(¹) and x(2). b.…

A: Note that : Since you have posted a question with multiple sub parts, we will provide the solution…

Q: Numerical analysis Find an interval [a,b] that contains the root of the function f(x)=x^3-4x-9?

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Q: x1 x2 x3 Assuming that A is invertible, use Cramer's Rule to find the value of 2 in the solution of…

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Q: 2) Let T: R³ R³ be a linear transformation such that T(1,0,0) = (2,-1,4) Determine T(2,3,-2)…

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Q: Write six different iterated triple integrals for the volume of the tetrahedron cut from the first…

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Q: 1. Calculate and draw the y[n] = x[n] *h[n] using the following signals. x[n]= 8[n] + 8[n-2] +…

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Q: 4. The Fibonacci numbers are defined as: f0 = 0 , f1 = 1 , and fn = fn−1 + fn−2 , for n ≥ 2 Provide…

A: Given, f0=0,f1=1 and fn=fn−1+fn−2,n≥2 .Let P(n) be the statement such that 3|f4n .That is,…

Q: (a) 1·1! +2·2! + . . . + n •n! = (n + 1)! − 1 - (b) if n > 6, then 3″ <n!

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Q: Given vector field F = (x³, y³,75z) and the surface S which bounds the solid described by x² + y² ≤…

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Q: 5. For the system of differential equation ¹ = A x, with coefficient matrix given by, (i) A = =…

A: Note: As multiple questions have been asked, so only first question i.e., (i) has been solved…