r(cos0+isin 0) with 0 (exact) in (0°,360°): а. z = 12-12i Z, =-3-3i z, =-4V3+ 4i b. с. Z3 = %3D

Q: Assume z =x+ iy = re® , i = /-1

A: Topic:- algebra

Q: Find the speed at the given value of t. r(t) = (sin(3t), cos(6t), cos(7t)), t = %3D (플) = 프2

A: Given:

Q: Find the length of the astroid x = cos3 t, y = sin3 t, 0 ≤ t ≤ 2π.

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Q: Two waves travelling in the same directio are given by: y1 = 0.2 sin(2ttx-20t+0) and

A: Given,  two waves travilling in the direction are                     y1=0.2sin(2πx-20t+φ)…

Q: Express the number -5 in the form R(cos(0) + i sin(0)) = Reil where R>0 and 0 <0 < 2T.

A: rewrite -5 as -5=-5+0i comparing with z=a+bi a=-5 , b=0 R=a2+b2=-52+02=25+0=25=5 now…

Q: Convert to polor coordinates with  r ≥ 0 and 0 ≤ theta < 2pi (4,0)  (r, theta) = ?

A: Polar coordinates (r, θ)            where r ≥ 0 and 0 ≤ theta &lt; 2pi Cartesian coordinates (x, y)…

Q: points

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Q: Find the cubic root of z = v27+ 3i in the form of r cis 0. (Hint: tan- = 6.

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Q: Show that cos 120 cos 40 – 3 cos 40 sin? 40 and use this identity to find an equation in rectangular…

A: We have to show that cos12θ=cos34θ−3cos4θsin24θ Consider  cos12θ=cos34θ=cos3P        Let P=4θ We…

Q: Find the angle(s) that satisfy the given values in the interval (0, 2r) 1. cos I = 2. secz = V2 3.…

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Q: * If r(t) =8 cos(6t)– 3sin(31), find and sketch R(j@). *

A: Since, you have posted multiple question, we will solve the first for you according to the Bartleby…

Q: Find all angles between 0 and 2T satisfying the condition COS X = 2 Separate your answers with…

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Q: - 77T then use the rectangular coordinates of P(t) ft= to fin 6. sint = %3D cost = %3D

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Q: : Find the length of the cardioid r = 1 + cos 0 0 < 0 <T

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Q: Which of the following images depicts the su y = 3 sin x, defined on [0, 7], is rotated about the…

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Q: Replace the Cartesian equation x² + y² equation. OA) r sin² 0 = 4 cos 0 B) r = 4 sin 0 Oc) r = 4 cos…

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Q: A bumblebee is flying so that its position is given by~r(t) = cos(2t), cos(3t),sin(5t) for the…

A: Before we start the problem let us get to know the formula first.

Q: Find the principle solution of sec(4z) = 2. If there is a distinct solution from the other half of…

A: sinπ3 = 32 and  sinπ-π3=32 cosπ3=12   and   cos2π-π3 = 12 .

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: First we write the components form of u and v .

Q: Find the area of the intersection of the circles r = 3 sin(0) and r = 3 cos(0).

A: Given the equation of curves r=3sinθr=3cosθ

Q: Convert the ! √ √4-1² 2 0 following to rectangular 32 r³z² sino cos o dz dv do dz dx dy

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Show that cos21θ=cos^3(7θ)−3cos7θsin^2(7θ )and use this identity to find an equation in rectangular…

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Q: Let z x = 2 cos u, and y 3 sin v. Find dz in terms of u and v. %3D Provide your answer below:

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Q: Assume the center of the motion is the origin, the motion is counterclockwise and that t = 0…

A: This is basic equation of motion problem

Q: = Replace the polar equation 8r cos 0 + 9r sin 0 Cartesian equation. OA) 8x +9y = 1 B) 8y + 9x = 1…

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Q: d the area of the surface generated by revolving the curve x =cos (2t), y = 7+ sin ( 2° - xis. .....…

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Q: If D is the region in the third quadrant between x +y? = 1 and x2 + y? = 4, then using the polar…

A: We have to convert given double integration into polar coordinates integration.

Q: A standing wave on a 2-m stretched string is described by: y(x,t) = 0.1 sin(2rtx) cos(50tt), where x…

A: Solution :-

Q: Consider the parametric equations x sin 2t and y -4+c ost. which of the following dy7 represents 2…

A: We are given that x=sin 2t y=4+cos tWe need to find dydx

Q: Transform C = cos p a, - sin p a, + cos p sin p az into spherical coordinates and then at P (2, T/4,…

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Q: Determine the surface area of the object obtained by rotating r = cos 8,-303% about the y-axis.

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Q: The values of C, and C, so that y(x) = C, sin (2x) + C2 cos (2x) satisfies the following conditions:…

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Q: Under what conditions for the contants a,b, k,e =) is (aa+by) da + (ka + ly) dy = 0 exact? Solve the…

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Q: The x and y coordinates of particle P, executing simple harmonic motion, are [x = A cos wt, y = A…

A: Given statement is "The x and y coordinates of particle P executing simple harmonic motion, are…

Q: Show that the substitution 1- x a = -1, b = l+ 1, c = 1 2 converts the hypergeometric equation into…

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Q: Compute the length of the cardioid r = 9 – 9 cos(0).

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Q: Determine the exact measure(s) of 0, where 0° < 0 < 360°. and Cos 0 = 1. %3D

A: To find:- Determine the exact measure(s) of where 0°≤  θ ≤ 360° Given equation cos θ = 1.

Q: 6. Find the length of the parabolic segment r %3D 1+cos 0'

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Q: Use an appropriate local linear approximation to estimate the value of cos(59°). cos(59°) ~

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Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y(pi/8) = 0…

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Q: Given, a(x,y,2) = 23x3 tan (y) + x*29 %3D Find the expression for Izyz and Caleulate it at the point…

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Q: A particle moves along the polar curve r =1– 2 cos 0 so that = 2. Find the value of d at e = , and…

A: We are given that,                     Now,              When          , Then

Q: Find the length of the cardioid r = 1 – cos 0.

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Q: Let z(1, y) ry where a = r cos(30) & y = r sin( – 70). az дл ду дл ду az & ae Calculate by first…

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Q: 3) Use polar coordinate to evaluate S'S_√x² + y² dxdy.

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Q: Convert to rectangular coordinates. x = 1+ sin t, y = 1 + cos t for t in 0, 27

A: The solution are next step..

Q: z2 = 2(cos7pi/12+isin7pi/12) what is (z2)^2 ? use de moivre law if needed

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

Q: 1. Given y + 0=90°. Find the measurement of angle 0 in the triangle below using cofunction…

A: Given,

Q: If the coordinates of any two points ₁ and ₂ are (x₁, y₁) and (x2, ₂), respectively, then prove that…

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