Show the following for any subset P of R": (a) If P C Q, then P^ 2 Qª and P^A C Q^A (b) РС РАД (c) P^ and PA^ are convex, (d) 0 e Pª and 0 € P^^. PÅ is the polar over P.

Q: Calculate by changing to polar coordinates. а) О 3пе4 - 3п - b) 0-3пе-4 + 3 3п c) 0-6пе d) O e) ( Зп…

A: see below the answer and calculation

Q: 5) y = 3cot- 2 ||~ 2 20 Зл 2T 5л 2 350 Period 2TT Amplitude

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Q: Draw the polar curve given by r^2 = 4sin(30). Show any necessary computations. No calculator.

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Q: ut pu!t(o ( polar. points of the f(Z) and calculate %3D 2. at these points lesidual Values the

A: Given,  fz=1zz2+1z-22

Q: Question 12 Compute the orthogonal projection of u onto v. Use the square root symbol 'V' where…

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Q: 65 7 4 8 9 10 12, 11 13 14 171 15 16

A: The UCS origin (0, 0), which is the point where the X and Y axes meet, serves as the starting point…

Q: Is there a polar equation that is equivalent to, " r = ( 9 * log(e)^ (theta / 3) + 1 ) with 0 =<…

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Q: Convert each equation from polar to rectangular form. 9) r= 4csc 0 10) r= 2sin (0 +") 11) r² = 5sec…

A: We have to use relation between cartesian and polar co ordinate system  x = r cosθ  , y= r sinθ…

Q: Q1) Consider two rotations, one about X by 30 degrees and one about Y 60 degrees: Are Rx Ry = Ry Rx…

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Q: 10. Derive CRE in polar coordinates Ur = r-1v0 ug = -rvr Using x = r cos 0 and y = r sin 0 and chain…

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Q: Let a = (5,2,-5) Find the projection projā b =< and 6 = (-5, -3,2). of b onto a.

A: Given: a⇀=5,2,-5 and b⇀=-5,-3,2.We need to find the projection of b⇀ onto a⇀.

Q: Convert 4-j9 to polar form √972-1.1526 Option 1 √972-1.9890 Option 3 √97 21.1526 Option 2 √9721.9890…

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Q: 相 3. Let S = and T = be ordered basis for R. Let v = 5 (a) Find the coordinate vectors of v with…

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Q: Let f be a rotation with center O and angle of rotation a. If lines AB and A'B' intersect at point…

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Q: 8. The point ( 5, can also be represented by which of the following polar coordinates? » (s -) s-똥)…

A: Given, Polar Coordinates 5,π6

Q: 2. Convert the rectangle coordinate (1,-√3) to a polar coordinate (r, 0) with r>0,-2л ≤0<2.

A: Given query is to convert rectangular to polar coordinates.

Q: 6. Convert 5,5/3] to polar coordinates with r positive and between 0 and 27

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Q: How does an image compare to its preimage after a -45 degree rotation?

A: Query- How does an image compare to its preimage after a -45 degree rotation. Answer-As reflection…

Q: 1) reflection are equivalent to a rotation. True or False: Three consecutive reflections across…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: When A is multiplied by a plane rotation Qij, which entries of A are changed? When QiJA is…

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Q: Give an isometry on C taking AABC to AA'B'C' for (i) A = A' = 0; B = B' = 2, C = i and C' = -i. (ii)…

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Q: 9.5. If s1 = aj + ib¡ and s2 = a2 + ib2, and s182 = (a¡a2 – bịb2) +i(a¡b2 +azb¡) use the fact that r…

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Q: 2) If z = -1 + √3i 2 2π 3 || then the angle 0 in polar form 0 True False O

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Q: Give all possible polar coordinates for the point (1, –V3) given in rectangular coordinates. | 57 a)…

A: Polar coordinates to rectangular coordinates