kT -글,-글 (1±icot 뚫), 8 = 0 has roots z Show that the equation (z + 1)° – z 1ti cot E), where (a) 2' 2 k = 1, 2, 3.

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A: Given the position vector: rt=3cost,3sint,t2 Rewrite it: rt=3cost i+3sint j+t2 k

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A: We know that,  90° counterclockwise rotation: (x,y) becomes        (-y,x)

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Q: By using Laplace trans formations Solve : - -2X 2X +3 e Cos3X y(oJ=0, ýw=| %3D

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Q: Write the parametric equations x = = 5 sin² 0, y = 3 cos² 0 e given Cartesian form. 3sqrt(1-x^2/25)…

A: Given query is to find the Cartesian equation.

Q: A hang glider is spiraling upward due to rapidly rising air along the curve r(t) = (3 cos t, 3 sin…

A: Given:          r→(t) = <3 cost, 3 sint, t2>   To find:           The time when the glider's…

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A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: cos(2z) dz c = |Z| = 1 Evaluate where at oriented 5-4 cos(z) counterclockwise?

A: Let fz=cos2z5-4cosz Singularities of f are those points where the denominator is zero. So, put…

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Q: x = a(0 – sin 0), y = a(1 – cos 0). %3D %3D urve followed by the particle as a function of 0.

A: The given parametric equations are, x=a(θ-sinθ)...............(1) y=a(1-cosθ) .............(2)

Q: 18.) Suppose x = R cos(0) sin($), y = R sin(0) sin($) and z = x² + y? + z? = R²Y R cos(). Verify the…

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Q: Calculate F-dr in the case when F(z,y) = (7y - sin (y) + 8)i+ (72 -e cos (y))jis conservative, and A…

A: Given that: F=7y−exsiny+8i+7x−excosyj and, rt=2tsinπt2i−π2sinπt2j for 0≤t≤1

Q: 6. Find the slope of the tangent line to the polar curve r = 2 cos 0 when 0 %3D You may use sin ,…

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Q: 8) roțațion 90° counterclockwise about the origin

A: topic - rotation

Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

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Q: 7a6(cos +i Si ) IF USE DE MOIURES TheoREM To Find Z. 23

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Q: Consider J sin'x cos²x dx. If we let "=cos x , the integrand can be transformed to. A 2u2 - - | (u²-…

A: The given integral,     ∫sin5x cos2x dx

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A: As per our guidelines, we can answer only three sub-parts in a single request. Kindly re-post the…

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Q: 7 Jlgull sin(2) = e-e- 2i eiz-e-iz 2 et +e-iz 2i e -e-i: 2i

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A: Hey, since there are multiple questions posted, we will answer third question. If you want any other…

Q: 3 19-x ? 2 b) Use the polar coordinate to find the integral J ] sin(x´+y´) dydx -3

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Q: Find the points (x,y)at which the polar curve r=1+sin(θ), −π/4 ≤θ≤π/4  has a vertical and horizontal…

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Q: Find the general solution to the hypergeometric ODE #(1 – 2)y" + (; - 2-) a - - 0. 3 ) y y = 0.

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Q: 213 If cot 0+ tan = and sece - sece = y, Prove that (x'y)° (xy²)*° = %3D

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Q: 2.11 Let A = p cosa, + pz² sin o a (a) Transform A into rectangular coordinates and calculate its…

A: Given A=ρcosθaρ+ρz2sinθaz

Q: 31. Find parametric equations for the tangent line to the curve of intersection of the cylinders x2…

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Q: 2. Prove that, V{(sec 0 - 1)/(sec 0 + 1)} cot 0. = cosec e

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Q: using the Cauchy- Riemann equations in polar Coordi'nates to find out whether the funchons are…

A: Let us denote the function by fz i.e.  fz=z2                     (i) Suppose, z=reiθ  , r>0,…

Q: Find the distance traveled by a particle with position (х, у); Cos t, y = (cos t)², 0 < t < 4TT X =

A: To solve this we have to use two point distance formula

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A: The given complex number is  z2 = 2(cos7pi/12+isin7pi/12)

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Q: QI/B/ Prove that cos y 1- 1+ sin y 1+sin y 2 sec y -= cos y

A: Question 1 is solved. Solving more questions are against the policy of bartalby and Post other…

Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, ± 3i.…

A: Solution is given as below:

Q: F- dr in the case when F(z,y) = (7y -sin (y) + 8) i+ (72 - cos (y))jis conservative, and Ais the…

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Q: 74. A particle moves in the xy-plane along the elliptical path x = 2 cos t, y = sin t, where x and y…

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Q: Integrate counterclockwise dz by Cauchy's formula 9. - 3 counterclockwise around the circle C : |z –…

A: Given that integrate counterclockwise  ∮Cz2z2-9dz by Cauchy's formula where  C : |z-3-3i|=32π.…