46. Match the polar equations with the graphs labeled I-VI. Give reasons for your choices. (Don't use a graphing device.) (a) r = v0, 0< 0 < 167 (b) r= 0², 0 < 0 s 167 (d) r= 1+ 2 cos e (c) r = cos(0/3) (e) r = 2 + sin 30 (f) r= 1+ 2 sin 30 I II III IV V VI

Q: Q7:- sketch the graph of the following polar equation. 3- r = 6 cos 6 1- 0 = 6. 5- r= 3(1- sin0) 2-…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: 4. Consider the polar curve C1 given by r = sin(0), for 0 e [0,27), (a) Find the area of the region…

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Q: 19 A curve with polar equation r = 8 sin 0+17 cos 0 represents a line. This line has a Cartesian…

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Q: 1. Let C be the polar curve given by r = 2+ sin 0, –T/4<0 <#/2. Sketch the curve. b. Indicate with…

A: Given : C: polar curve=r=2+sin θ,      -π4≤ θ≤π2 (a)   The  graph of the polar curve and  (b)…

Q: 1 By first changing to polar coordinates, evaluate 1+ x + y dA, where R is the quarter-disk region…

A: Given integral is ∫1+x2+y2dA over the region R where R is quarter disk region shaded above. Use the…

Q: - A tangent at the pole to the polar curve = V2 – 2 cos0 is 0 = r = A 3

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Q: The polar equations for the curve + =1 is Select one: O z= 2 sin t, y = 3 cos t, 0 st< 2n. O=4 sect,…

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Q: What is y2 = 3x in polar form? r = 3 sin 0 sin 0 O Option 4 r = 3 csc 0 cote Option 2 r = 3 sin 0 -…

A: Given y2=3xTo find polar form:

Q: 25) Evaluating in polar coordinates: 6*L*(x² + y²)dydx

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Q: 39 A curve with polar equation r = 3 sin 0 + 25 cos 0 represents a line. This line has a Cartesian…

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Q: 3 4. Sketch the region described in polar coordinates by r < Cos e

A: We need to sketch the region.

Q: 2. Determine the area of the region that is simultaneously interior to the curve r = 2 + cos (38), e…

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Q: (). 3 Calculate the length of the polar curve r = 8 sin' 3 in the interval 0 < 0<.

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Q: 10 Convert the Cartesian equation 2 xy = 1 in polar equation form. r²cos2θ = 0 cosθsinθ = 1/2…

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Q: 3. Consider the curve C of equation 4ry r² + y²" Among the options indicated, select the one that…

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Q: 6. Consider the curves: r = 2 + cos 2θ and r = 2 + sin 2θ, a) Sketch a graph of both curves on the…

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Q: 1. Let r(0) = 2sin(0) + cos(Ⓒ) be the polar definition of a planar curve. Find, in standard x-y…

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Q: r cos 0 = -3 2n 5Tt 2 3 Check for symmetry line 0 = = pole polar axis

A: rcosθ=-3 Now when θ=0, rcos0=-3⇒r1=-3⇒r=-3 When θ=π6, rcosπ6=-3⇒r32=-3⇒r=-23 When θ=π3,…

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

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Q: 12. (a) Sketch the curve in the polar coordinate system with directions, (b) Find the values o for…

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Q: 12 A curve with polar equation r = 4 sin 0 + 33 cos 0 represents a line. This line has a Cartesian…

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Q: 6. Consider the curves: r = 2+ cos 20 and r = 2+ sin 20, a) Sketch a graph of both curves on the…

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Q: 7) Find the points at which the polar curve r = 1+ cos® have horizontal or vertical tangent lines.

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Q: Consider the polar curves r = 3 and r = 3 + cos 3θ. Both curves are symmetric about the polar axis.…

A: We have to set up the integral for the given region.

Q: 5. Consider the two curves r= / cos(0) and r= V2 cos(0), -T/2<0ST/2,whose polar plo 0.6 0.4 0.2 0.2…

A: Here, the given curves are: r=cos θ &amp; r=2cos θ

Q: 2) Sketch the graph of the curve with the polar equation: r=2- sin(20).

A: The given polar equation is r=2-sin2θ. Draw the graph of the given polar equation in detail.

Q: 33 A curve with polar equation r 9 sin 0 + 55 cos 0 mx + b,where m and b are represents a line. This…

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Q: 44 A curve with polar equation r = 7 sin 0 + 36 cos 0 represents a line. This line has a Cartesian…

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Q: 8. the same graph as the polar equation r-6cos0 =0 and graph on the xy plane. Find an equation in x…

A: The given polar equation is r-6cosθ=0 The equation in x and y is to be calculated and graphed in the…

Q: Q/ sketch r:2 sinlo -)cos(0-) in polar system. ExPlav e is the graphic symme trical and wribing a…

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Q: Find the points at which the polar curve r= 5+ 10 sin 0 has a horizontal or a vertical tangent line.…

A: the equation of the given curve in polar form is: r=5+10sinθ we have to find the points to the curve…

Q: 6 (1). Consider the curve C of equation (x²-2y+y²)² = x²+y². Among the options listed, select the…

A: We know that a polar coordinate is represented by r, θ, where r is the length with r=x2+y2 and θ is…

Q: 11 Final the directrix of the polar curve r = 9-2 cos 0 11 99 x = 2 99 2 0 x = - 11 x = -

A: To find- directrix

Q: 31 A curve with polar equation r = 3 sin 0 + 7 cos 0 represents a line. This line has a Cartesian…

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Q: Find the length of the curve over the given interval. Polar Equation Interval r = 8a cos 0 16 16.

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Q: What is (x - 12)² + y² = 144 in polar form? r = 24 sin 0 r= 24 cos 0 O Option 1 r= -24 sin 0-144…

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Q: A curve in polar coordinates is given by: r = 12 + 5 cos 0. Point Pis at 0 = 297 24 (1) Find polar…

A: Given polar curve r=12+5cos(θ)θ=29π24 (a) To find out polar coordinate r for the given P,  Plug in…

Q: 8. Find the equation (in terms of Cartesian variables r and y) of the tangent line to the polar…

A: Given curve is Firstly, we find slope of tangent to polar curve is

Q: 4. a) Express the given rectangular equation in polar form. Solve for r or r2 if possible. x? = y? +…

A: Use x= rcostheta Y= r sin theta X2+y2=r2

Q: Q1/Replace the polar equations with equivalent Cartesian equations and vice versa. (Three only) 1. r…

A: We are given equations in polar and cartesian. we have to change them.

Q: 7 A curve with polar equationr = 5 sin 0 + 31 cos 0 represents a line. This line has a Cartesian…

A: topic - change in coordinate system

Q: 3. Let r = 1+ sin(0). Determine the rectangular point(s) (x, y) where the polar curve has a…

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Q: 15) Find the slope of the tangent line to the given polar curve at the point specified by the value…

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Q: The graph of the polar equation r(0) = 0 cos(0), o ses. with derivative = cos(e) – 0 sin(0), is…

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

Q: 23 A curve with polar equation r : 4 sin 0 + 13 cos 0 represents a line. This line has a Cartesian…

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Q: 7) Sketch the polar curve r = 2(1+ sin 0). In your graph, label the points corresponding to the…

A: We have to find out the graph and points according to value of θ