Using the result of the previous question, explain why 1 n sin" xdx = - sin"-2 xdx. n and hence show that: 2.4.6...2n sin2n+1 xdx 3.5· 7... (2n + 1)*

Q: 1+3i 5. Evaluate 1-41

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Q: R(-2,4) and S (6,–2) are the endpoints of the diameter of a circle K. Obtain a. The equation of the ...

A: (a) First we find the centre of the circle (which will be midpoint of the diameter) and the radius r...

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Q: Express the function below in rectangular form, (-1+i)-1+i

A: let z=-1+i-1+i applying log both sides  z =e-1+ilog-1+i    =e-1+ilog2e3π4    =e-1+ilog22+i3π4 simpli...

Q: Exercise 3.2.6 Show that if G and H are isomorphic groups, then G commutative implies H is commutati...

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Q: 7 7. Determine the solution to the I.V.P. y"+7y'+12y=2le*,y(0)=y'(0)=-10

A: Note: According to Company Guidelines we are providing the answer of first question. Kindly post oth...

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A: (1) In first part, we need to use population growth model which is given as follows P(t)=P0ektHere P...

Q: 1. Find the area of the shaded region. X = -y Ay 3 y = Vx x = 2 - y X X 4 -2 2 y = -x b. а.

A: Area bounded by the closed region

Q: dx (2) 3y sin x 2xy cos x = 0 dy (3) 3x²y² + 2x³y -= 0

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Q: 21. x+y-2x +4y-4=0 22. x² + y' +6x – 4y-3=0 A. Transform each equation into center-radius form. | ar...

A: Center and radius of the circle

Q: a) Given a function f(x) = = 4-2x 1-3x ) Find the x-intercept and y-intercept of f(x) (if any).

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Q: Q.1. Apply three steps of steepest descent to f (x) %3D 2(х,2 + х?2) +x;x, — 5(х, + х2) with initial...

A: The function given is as follows: fx=2x12+x22+x1x2-5x1+x2 The initial point given is x0=1-2. We will...

Q: B. Find the distance between each pair of points on the coordinate plane. 1. A(12,-2) and B(10,-2) 2...

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Q: (ex – 1)² | dx 3ex

A: We have to evaluate the integral

Q: Question 1. Suppose that the tangent line to the graph of f(x) = x(6") at x = 1 is equal to the tang...

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Q: determine the parametric coordinate of the critical point of the curve x=t^2+3t=2 and y=t^2-1.

A: Curve will have critical point if it have vertical tangent or horizontal tangent . Slope of horizont...

Q: 4. Adele is bird-watching. She spots a bald eagle in the sky and determines that it is a distance of...

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Q: The formula in finding the roots of an equation using False Position methoe (XL)*f(Xu)-(Xu)*f(XL) f(...

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Q: Question 3. Compute the integral - dz 8+z where y is the rectangle with vertices +3+ i with the cloc...

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Q: 2. On his fishing trip Justin takes the boat 12 km south. The fish aren't biting so he goes 4 km wes...

A: Let us consider a right angle triangle ABC Using Pythagoras theorem, AB2+BC2=AC2

Q: -. Find the exact solution y to the initial-value problem dy dr xy/2 y(1) = 4. . Calculate y(1-5) fr...

A: In this question, the concept of a differential equation is applied. Differential Equation A differe...

Q: Let M be a plane with the following properties: • M contains the point with coordinates (-1,-1,0) • ...

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Q: C A 1070 B. Solve. Show your solution. 1. Quadrilateral CALM is a trapezoid. If m z M = 67°, find: i...

A: Please find attachment for the details solution

Q: 3. Let W be a subspace of R" of dimension k < n. Use the Fundamental Theorem of Linear Algebra to pr...

A: We will solve Q.3 as requested. Given W be a subspace of ℝn of dimension k≤n. Since W is a subspace,...

Q: 4x -1 dx. b) x(x² + x- 6) J

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Q: 2. Let u e R" and v E R" be two non-zero vectors, in other words at least one component of the vecto...

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Q: Assume x is a particular real number and use De Morgan’s laws to write negations for these statement...

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Q: A 100 mg per L solution of drug is adminstered intravenously at a rate of 20 mL per hr to a patient ...

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Q: Answer Directly Choose the letter that corresponds to your answer Given: Let p. q, and rbe the propo...

A: Only part I asked and answered.

Q: 3. Let W be a subspace of R" of dimension k < n. Use the Fundamental Theorem of Linear Algebra to pr...

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Q: Consider the following sets U= {1,2,3,4,5,6,7,8}, A = {2,4,6}, and B= {1,2,4,6}. What is A' -B' ? a...

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Q: (d) If w E R" then the function fw : R" R defined by fw (v) =v•w for all v E R" is a linear form. %3...

A: Solution:

Q: (9.6) R 4. Let R be the region in the first quadrant bounded by the graph of y = 2, the horizontal l...

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Q: Let ?: Hwi win the first round and ?: Hwi win the tournament. a. Write “Hwi wins the tournament onl...

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Q: а). Solve the linear congruence of 231x = 147 mod 598 .

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Q: Consider the Pauli matrices 1 1 1 0 Show that the set of Pauli matrices with matrix multiplication d...

A: The given Pauli matrices are σ1=0110,σ2=0-ii0,σ3=100-1. Let A=σ1,σ2,σ3. Observe that  σ12=σ1σ1=01100...

Q: Determine by composition whether the functions are inverses. Show your work using the Equation Edito...

A: Please find attachment for the details solution 

Q: Use the laws of propositional logic to prove the following: -p - (q - r) = q (pvr)

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Q: sin(z) Sc (3z – 2)(z – 3) dz

A: Please find attachment for the 

Q: Is the given Differential Equation a homogenous? If yes, what is the degree?

A: We know that, A differential equation containing a homogenous function is called homogenous differen...

Q: Consider the following sets U= {1,2,3,4,5,6,7,8}, A = {2,4,6}, and B= {1,2,4,6}. What is (B' ∪ A' )'...

A: The given problem is to find the set relation from given sets.

Q: Assessment Directions Circle the letter of the comect answer. 1. What will be the quetient when we d...

A:   "Since you have asked multiple questions, we will solve the first question for you. If you want an...

Q: Express the function below in rectangular form, (-1+i)-1+i

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Q: The water level of a lake is increasing by h cm every week. Time (week) 1 3 water level (h cm) 10.5 ...

A: Richardson extrapolation formula for derivative  f'(x) =f(x+h) -f(x-h)2h

Q: A 100 mg per L solution of drug is adminstered intravenously at a rate of 20 mL per hr to a patient ...

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Q: 3. Let W be a subspace of R" of dimension k < n. Use the Fundamental Theorem of Linear Algebra to pr...

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Q: 2. Find the volume of the solid that results when the shaded region is revolved about the indicated ...

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Q: (5) Use the expansions (Maclaurin series) 1 (1) Ew", w| < 1 1- w n=0 1 (2) E(-1)"w", w|<1 1+ w n=0 t...

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Q: A. Find the linearization of the function f(x) at the x = 0. %3D Vx+1 dy B. Let y = u20 and u = x + ...

A: Applications of the diffraction, linear approximation and slope of the tangent line , total derivati...