Find a polar equation in the form r cos (0 = r, for each of the lines in Exercises 49-52. 49. V2x + V2y = 6 50. V3x - y = 51. y = -5 52. х %3D— 4

Q: Convert the equation rsin 0 = ln r + ln cos 0 from polar to cartesian.

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Q: Use polar coordinates to calculate e-(z²+y²) dydx. roo Express -(2²+y²) dydx in terms of dr, and…

A: We will find out all the required values.

Q: Find two pairs of polar coordinates, one with r>0 and one with r<0,

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Q: 5. Eliminate the parameter to find a Cartesian equation of the following curves. et (a) x = vt+1, y…

A: Eliminate parameter t.

Q: Express y=x^2 in polar coordinates.

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Q: 2. Find the length of the curve represented by the following polar equation. 15050을=4 1 r ==,0s0sI…

A: In the question we have to find the arc length.

Q: find a polar equation for the curve represented by the given cartesian equation 5x^2 +y^2 = 8x (r is…

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

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Q: 2. Compute [²√x by first changing it to polar coordinates. 1 -√3x (x² + y²) ² dy dx

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Q: (3) Find a parametric equation for the line segment joining (1, 0, 1) and (0, –2, 1).

A: The direction vector of the segment is: (0,-2,1) - (1,0,1) = (-1, -2, 0) Initial point is (1,0,1).…

Q: 2. Find a set of parametric equations for a particle that oscillates on the line y = 6x - 5 between…

A: formula:

Q: 7. The polar equation of the curve r + y² = 2x is r= 2 cos 0 T= sin 20 T= 2 sin 0 D T= cOs

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Q: 4. Integrate L e-° dxdy by converting to polar coordinates, and ase that result to integrate J e dx.

A: This problem is convert to pollar form and then solve so,......

Q: Replace the Cartesian equation with an equivalent polar equation. x² + y² - 4x=0 O A. r cos²0=4 sin…

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Q: Consider the polar curves C1 : r = −3 sin(2θ) and C2 : r = 3 sin θ. 1. What is the equation of the…

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Q: Find the length of the curve r = 2 sin^3 (u/3), 0&lt;=u&lt;=3pai, in the polar coordinate plane.

A: To determine the length of the polar curve.

Q: Find a polar equation for the curve represented by x2 + y2 = 8cx, where c is a constant.

A: The given equation is x2 + y2 = 8cx   Known fact x=rcosθy=rsinθ

Q: Consider the curve given in polar coordinates by r = 0 + cos 0 . Compute the slope at 0 = 0. %3D O…

A: Slope of polar curve r=f(theta) is given by dr/d(theta) Differentiating r with respect to theta we…

Q: Find the slope of the polar curve r= e® at 0 = n/3.

A: Given:

Q: b. Plot the polar curve r=2(1- cos0) in interval n

A: r=2(1-cosθ) in the interval π , 2π

Q: 3. Express the equation y = mx + b, where m and b are constants, in plane polar coordinate.

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

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: Write a polar equation of the form r cos(0 – 0,) = ro for the line x + y = v2.

A: Given line, x+y=2

Q: 7- Find the length of the curve T = e", 30 - A<0<T given in polar coordinates. a)V10 sinh(37) b)2/10…

A: Given a curve : r=e3θ   ,-π≤θ≤π We need to find the length of the curve. Let's start.

Q: 2) Use polar coordinate dydx (1+ x² + y° )'?

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Q: 2. \ Evaluate •V4-2² dydx + dydx 2x-r2 using polar coordinates.

A: We have to evaluate the integral using polar coordinates.

Q: 9. Sketch the polar curve.r= 2 cos 2 0 ||

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Q: Find two sets of polar coordinates for the point for 0 s0 < 2z. (r, 0) = (smaller r-value) (r, 0) =…

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Q: Compute the length of the polar curve. r = 1 + θ for 0 ≤ θ ≤ π/2

A: It is given that,  r=1+θ  for    0≤θ≤π2

Q: Express the equation z = rroot2 cos2tita, which is given in cylindrical coordinates, in…

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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: Draw the polar curve to ((x-3)2/32) - (y2/32) = 1

A: We have to draw the polar curves to x-3232-y232=1.

Q: Find the exact length of the polar curve. = 02, 0s0 < T/2

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Q: Which of the following is Parametric equations for the line passing through the origin and A(3, -2,…

A: We will use Standard form of parametric equation of Line passing through two points

Q: (2. Plot the points with polar coordinates 2, and -3, 2 using the pencil. 6. 3 3n 4 5n 6. 4. 7n 6.…

A: topic - plotting of points in polar coordinate system

Q: Calculate the slope of the polar curve  r=4cos3θ  at the point where θ=5π/6

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Q: Calculate the length of the polar curve r=1- sin Oon the given interval (0, 2m].-

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Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

A: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

Q: 1. Find two sets of polar coordinates for (x, y) = (-V3,1, one with r> 0 and one with r< 0, both…

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Q: 2. Find a set of parametric equations for a particle that oscillates on the line y = 6x – 5 between…

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Q: Consider the curve. (금) 2 = 1 19 + Identify all possible parametric equations for the given curve. O…

A: In this question, we can check one by one parametric equation in the given curve.

Q: Find the corresponding Cartesian equation of the parametric equation       x=3cosθx=3cosθ.…

A: Given:           x=3 cos θ,   y=4 sin θ            0≤θ≤2π From: x= 3 cos θ            cos θ=x3 From:…

Q: Give an example of two polar equations, r1(0) and r2(0), whose graphs intersect in at least two…

A: According to the given information, it is required to give an example of two polar equation whose…

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

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Q: Give a parametrization of the left half portion of the polar curve described by the equation r = 3.

A: Give a parametrization of the left half portion of the polar curve described by the equation r = 3.

Q: 2. Evaluate Vr2 + y? dy dx by switching to polar coordinates.

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Q: Write a polar equation of the formr cos(0 – 0) = ro for the line x - V3y = 2.

A: We have to solve given problem: