1. Change to polar form, then evaluate: -x-1 х — у dydx V1-x² /x² + y² -1

Q: Write the polar equation in rectangular form. r = 6 sin 0 Oy =-6x Oy =x- 3 O x² + (v – 3)² = 9 O (r…

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Q: 2. (3+j4)(6+)7) convert to polar form (Az0) Hint: x = en(x)

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Q: 12/2 Use polar coordinates to evaluate dydx.

A: The region is bounded by x=1,x=2,y=0 and y=x

Q: Convert the rectangular equation to polar form and sketch its graph. y = 5 A/2 A/2 6 10- 4 6 3 4 2 1…

A: The relation between rectangular and polar coordinates are: x=rcosθy=rsinθ then  rsinθ=5r=5cosec θ…

Q: Which of the following is equivalent to 1 dy dæ in polar coordinates? O 2 dr de O 4 C p?dr de OS S2…

A: In this question we have find which of the following polar coordinates is equivalent to given…

Q: Convert the polar equation r2 = -2 sin 20 to a Cartesian equation. O +y? = 2 xy O12+)² = -4 xy…

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Q: Determine whether the statement " If x > 0, then the point (x, y) on the rectangular coordinate…

A: Consider a point (x, y) on the rectangular coordinate system  Draw a line joining that point to the…

Q: 3. Evaluate/calculate using polar coordinates. -1/2 cV1-x² А. M-X" xy/x2 + y² dydx ху,

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Q: Give two possible pairs of polar coordinates (r, 0) for the rectangular (Cartesian) point (-6, –6V3)

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Q: Show that the polar equation for x2/a2 + y2/b2 = 1 is                                           r2 =…

A: Plug x=rcosθ and y=rsinθ

Q: 5. Find two sets of polar coordinates for the Cartesian point (-7, 7/3) such that 0<0<2T.

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Q: 1/A) Replace the polar equation by equivalent Cartesian equation r2cose + 2sino

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Q: Convert ff Incxag) dA.aver. the.regian.cx.<e. segian.e.x+y.c.e. -.to.polar.form. and.…

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Q: B/convert the points below to the polar coordination (r,e) 1. (2,-2V3)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Convert the polar equation r 2 cos 0 to rectangular form. O g2 + y? 2 x2 + y ? = 2x x² + y? = 2x

A: solution:-r=2cosθconversion equationspolar to rectangularx=r cosθx=r sinθr=x2+y2

Q: 13 Convert x 2 + y 2 - 2x = 0 to a polar equation. r = 2cosθ r² = 2cosθ r = 2sinθ

A: We have to find the polar equation

Q: Convert the glven polar equation into a Cartesian equation. =D3sin 0+4cos ở

A: Given below equation r = 3sinθ + 4cosθConvert this into a Cartesian equation.We know that the…

Q: Give two polar representations for the point (x, y) = (0, 1), one with negative r and one with…

A: Check the polar representation.

Q: Convert the polar equation r sing = 5 in Cartesian equation form. %3D O xy + y? = 5 x = 5 Oy = 5

A: Here we have to convert the polar equation into Cartesian equation.

Q: 11 Convert the Cartesian equation y = 5 to a polar equation. r = 5cscθ r = 5secθ r = 5sinθ

A: We have to find the polar form

Q: #7. Convert into polar equation form. ( 4 marks each ) a) y=5x+3

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Q: Convert the polar equation to rectangular form. r= -9sin O O x²+y?+9x=0 O x²+y?-9=0 O x²+y?+9y = 0 O…

A: Given polar equation ,r = -9 sin θ

Q: Match the graph with its polar equation. r = 3 (1 + cos(0)) T/2 1/2 4| -2 2 4 -2 -2 л/2 T/2 3- 2 1…

A: Topic :- Geometry As per our guidelines , In case of multiple different questios ,at a time only one…

Q: Use polar coordinates to evaluate 2/2 dydx. 3 1 0, (x²+y?)? O 5 Оз 6 O 2 O 1 O 4

A: To determine: The value of the integral  using polar coordinates, ∫12∫0x22x2+y232dydx.

Q: Prove that the distance, d, between two points with polar coordinates (r, 01) and (r2, 02) is d =…

A: Distance (d) between two points x1, y1 and x2, y2 is  d=x1-x22+y1-y22   ....1

Q: Convert the given Cartesian equation to a polar equation. 22. у%3D4 21. x= 3 23. у%3D 4x?

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Q: Find the distance between P1(1, –91°) and P2(3, 335°) on the polar plane.

A: We know that, Distance between two Cartesian coordinates is,  Distance , D=x2-x22+(y2-y1)2 We know…

Q: 7) Evaluate IT !! (x + y)dxdy y by switching to polar coordinates.

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Q: The Cartesian equation, x = 4, is equivalent to the polar equation, 1 = 4 cose 4 r = cose 43 r =…

A: Given is the cartesian equation x=4. The objective is to write the equivalent polar equation. In…

Q: Plot the polar point. (25. 푸) 4 2 3 4 2 4 4. 2. klN 3. 3.

A: To plot the given point

Q: Evaluate f" Na-*) /x² + y² dydx, using polar coordinate. -a

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Q: The alternative polar coordinates that satisfies r 0 for

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Q: Convert the polar equation to a rectangular equation. r= 3 cos 0+6 sin 0 O A. 3x+6y 0 O B. x+y 6x +…

A: Recall: Convert form Polar to Rectangular:      x= r cosθ and   y= r sinθ ⇒r2=x2+y2   and  tanθ=yx

Q: If z1 = 1 + 3j , and Z2 = 2 – j , which of the following options shows the product Z1 Z2 in polar…

A: Solution

Q: Convert the rectanglular equation to polar form. Assume a>0. (x^2+y^2)^2=7(x^2-y^2)   find: r^2=

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Q: - Change LAxy dydx to polar form.

A: Consider a cartesian coordinate and polar coordinate . Then the relation between these two…

Q: Write the following point in polar coordinates (r,0) into Cartesian coordinates (x,y) -8,-

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Q: Replace the Cartesian equations with equivalent polar equations and discusss its symmetries x2 + xy…

A: Given an equation in Cartesian form. We need to convert it into equivalent polar form and discuss…

Q: 4cscθ

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Q: 1. Convert the Cartesian coordinate (12,5) to polarcoordinate.

A: Given the cartesian co-ordinate(x,y)=(12,5)

Q: Which Cartesian equation is equivalent to the given polar equation? 3 r = sin 0 +7 cos 0 O y + 7x =…

A: We have to find Cartesian equation of given polar equation.

Q: 2. Use polar coordinates to evaluate 2 1. √4+7++5² dy dz. Jo

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Q: Find in polar form: Z2 Z1 = 21cis (135°) Z₂ = 3cis (75⁰) Z2

A: Given;  z1=21 cis(135) z2=3 cis(75).

Q: Q2:- find the polar coordinates for the fol 1:-(-2,2) 2:- (-1, /3) 3:- (2/3,2)

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Q: Which of the following is equivalent to fo J Tady dz in polar coordinates? So So dr de O SA SoPdr de…

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Q: 3 V9-y2 / / (x² + y²) dx dy

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Q: Change the following rectangular equations to polar form. Show work on separate paper. 14. x² +y°…

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