Consider the equation (2¹ +64) = 32√/31³. Find all the roots and express them in rectangular form. Let a be the principal root. Show that the principal value of a³-2i is -8e-/3 [sin (2 In 2) + i cos(2 ln 2)].

Q: HD 7) Write each of these statements using "3": a) A is not empty. (Here, A is a set.) b) x is a…

A: ∃ is a symbol used for "Existential Quantifier". ∃ means "There exists", "There is at least one", or…

Q: & equation of ellipse is, 2²745²2=4 x² + y² = 1 1² 2²=4₁ 6=1 we know, two diameters Y=m₁ x and y=m₂x…

A: Equation of the ellipse is       x2 + 4y2 = 4     => x2/4 + y2/1 = 1     => a2 = 4 and b2 = 1…

Q: 3. We define the absolute value function by: for all î ¤ R, we have { |x| := X -X if x ≥ 0 if x < 0…

A:

Q: 11. and C. Find a counter example to show that the following statement need not be true for all sets…

A:

Q: c) For the 2x2 matrix C, find C-1 by hand using C-1 = decadjC, where adj is the adjoint operator. 3…

A:

Q: Let ƒ (x) = Ax² + Bx + C where A, B and C are real numbers. Prove that if f(x) is an integer…

A:

Q: Does Sn have a subgroup isomorphic to An, other than An (n ≥ 5).

A: A very famous result. Lot of techniques and theories about A_n will be used. The long solution has…

Q: What is the value of x that will give g(x) = 3-13x² - 6x³ a relative min value?

A:

Q: Question 9 Use the transforms in the table below to find the Laplace transform of the following…

A:

Q: m-1 1 If * Σ( ² ) = 4( ¹ - ₂ = ²/₁ ) ₁ ₁ k=1 2m m «£ () simplification of 04(1-2-²-1) 2m 04 (1+ 1 2m…

A:

Q: Prove the identity 1+z+z²+...+z"-1 th if = 1-z" 1-z on th noot of: 2 for z 1. ait other than 1 +

A:

Q: Find the area of the shaded region in specified by the graphs of the circles

A:

Q: 9. Translate the following statement into English, where the domain for each variable consists of…

A: Here the domain for x and y are real numbers.

Q: Determine the interval of convergence and the radius of convergence of the power series x2n Č n-2 n…

A: Given series is ∑n=2∞x2nnln n2

Q: 49. Using the map below, determine the number of direct routes (no backtracking) from point A to…

A:

Q: A qualitative look at a fish population Example. A population of fish is being monitored in a lake.…

A: At equilibrium points P'=0 . To find sign of P' we will take a value of t in that region and…

Q: You decide to make monthly payments into a retirement fund earning 4.75% compounded monthly.  Note:…

A: Given-  Monthly deposit, PMT = $240 Rate, r = 4.75% = 4.75100 = 0.0475 Amount, A = $338,000 Number…

Q: For ohy a <b, ony • ohy f: [dsb] → IR and any n=1 RIGHT (f. n)-f(x)d₂ ) ≤ = d bo | SIMP (f»n) -…

A: Given fx=2πe-x22 We have to find the  maxx0,2f'x f'x=-x2πe-x22f"x=-2πe-x22+x22πe-x22…

Q: but why we cant use formula I=integral(r^2dm) directly and get the same result? we can choose a…

A: You are calculating moment of inertia of sphere about z-axis using elementary disk. You are taking…

Q: Either f,g,h € F(R, R) the functions f(x) = sin(x)^2 And g(x) = cos(x) and h(x) = sin(x). Show that…

A:

Q: 101. The gamma function, which plays an important role in advanced applications, is defined for n >…

A: The gamma function is given as, Γ(n)=∫0∞tn-1e-tdt. To Prove: (a) Γ(n)=∫0∞tn-1e-tdt is convergent for…

Q: Consider the function f(x) √x-1. Find f(x) and sketch the graphs of y = f(x) y = f¹(x) on one…

A: Look at domain ,range of the function. If f is one one, onto in that domain then f has inverse.

Q: tell whether if the equation is a solution or not a solution to the differential equation. 1. y = 4…

A:

Q: Question 14 The current share price of a resources company is $6.85. (a) A shareholder owns 880…

A: Since you have posted multiple questions with multiple sub-parts, we will solve the first three…

Q: (9) Consider the substitution homomorphism given by My (Peas) = p (6₂) (You can assume it's a…

A: Given :  μ2 : ℤx → ℤ2 defined by  μ2p(x) = p2 is a homomorphism. a) Show that μ2 is onto. b)…

Q: Find the other order of integration. Determine which of the two expressions is easier to integrate.…

A:

Q: 2. Consider the curve y = (x²+2) ³¹/ 0≤x≤1 a) Find the length of this curve b) Find the volume of…

A:

Q: 1. Consider the region R bounded by y = x² and y = 3x a. What is the area of R? b. What is perimeter…

A: V=2π∫03x3x-x2dx   =2π∫033x2-x3dx   =2πx3-x4403   =2π27-814   =13.5π

Q: A question of medical interest is whether jogging leads to a reduction in blood pressure. To learn…

A:

Q: Find E₁ Consider the following Gauss-Jordan reduction: -139 20 0 -28 1 0 0 CD-LB-E-W-W- 1 → -28 4 0…

A:

Q: Find a fundamental matrix of the following system, and then apply x(t) = Þ(t)Þ(0) ¹x₁ to find a…

A:

Q: 3 + 6x² + 3x +

A:

Q: Determine whether the equation is exact. If it is, then solve it. 7 ]dy = 0 y cos (xy) + 7 [x cos(x…

A:

Q: .

A: Given: A=1111 To solve parts (a) , (b) and (c)

Q: Q"+wQ = sin wot,

A:

Q: 6. 5. Find the general solution of the equation xy" + 2y' + xy = 0, if we know that y₁ = solution.…

A:

Q: (-1)" Determine the exact value of the sum of the series ; (2n + 1)3n

A:

Q: W 1 wall Erin likes to fence 3 sides of a rectangular lot for his cat. The 4th side of the lot will…

A:

Q: Can you solve question 8

A:

Q: Problem 7 Let He Vam I tudom S = {(2,x) | x E I} CR², dT (81 Ing/ T= {(0,x) | x 1} CR², o ir aut

A:

Q: For ohny • ohy f: [dsb] → IR and ony n ≥ 1 RIGHT (f. m)-f(x)dz) ≤ (b-d) ² max [1/(20) n d | SIMP…

A: Given fx=2πe-x22 Therefore f'x=-x2πe-x22 For critical point f"x=0 ⇒x22πe-x22-2πe-x22=0⇒…

Q: 21. An mxn upper triangular matrix is one whose entries below the main diagonal are 0's (as in…

A: Solution : - Proposition : A triangular matrix (upper or lower) is invertible if and only if all the…

Q: (a) The curve with equation 2 y 3 + y2 - y 5   = x 4 -2x3  +x 2  has been likened to a bouncing…

A: Given: The curve with the equation 2y3+y2-y5=x4-2x3+x2 has been linked to the bouncing wagon. To…

Q: 17 Part 4 of 4 Required information NOTE: This is a multi-part question. Once an answer is…

A:

Q: 2 3 8 -5 [], 2 -5 8 -9 mine if w is in the subspace of R3 generated by v₁ and v₂. Let V₁ and w…

A:

Q: Find a polynomial p of degree 2 so that p(3)=13] p(5) = 35, p(-2)=-7, then use your polynomial to…

A:

Q: Problem 1. Let R be the radius of earth, M be the mass of earth, and G be the gravitational constant…

A:

Q: 2. Verify that the vector field F(x, y) = (2xy + x-3y)i + (x² −3x+y)j is conservative. Then use the…

A:

Q: Prove that √2 +1 is irrational

A:

Q: 3. For the curve r(0) = 6 2+6 sin 0 (a) Find the eccentricity and the directrix. (b) Describe the…

A: 3. (a) Consider the given equation of curve, rθ=62+6sinθ=31+3sinθ Compare with the standard…