1. Plot the point with polar coordinates are given. Then find two other pairs of point, one with r > 0 and one with r<0. a) (1,) TC b) (-2,) c) (3,2) 4.

Q: The Cartesian equation of the polar curve r = 2sin0 + 2cos0 is Select one: O x² + y? = 2 O x + y = 4…

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Q: Without solving explicitly, classify the critical points of the given first-order autonomous…

A: Here is the Answer and Explanation

Q: 14. Polar coordinates. a. Write (x, y) = (-2,2) in polar form (r, 0).

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Q: 3. a) Find polar coordinates (r, 0) of the point (1, -/3), where r> 0 and 0 <0 < 2 p2 = x² + y?, tan…

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Q: 3. Given the point (x, y)=(-40/3,40). Convert this point to polar coordinates, (r.), with r>0 and 0…

A: given  (x,y)=(-403,40)in polar coordinates    x2+y2=r2and     tan(θ)=yx

Q: Consider the polar curves C₁ : r = 2 - cas 0 and C₂: r = 2 + 2 cos 0, 0 € [0, 2πC). (1.) Show that…

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Q: Convert to polar form. Then isolate r. (a) x² +y² -9= 0 (b) x² +y = 4x %3D

A: x2+y2-9=0 On simplification, we get ⇒x2+y2=9⇒r2=9         ∵r=x2+y2⇒r2=x2+y2⇒r=3

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.) Given the parametric equations: x=t'- 1 and y=f+t, find the 1ª and 2nd derivatives.

A: We will find the derivatives.

Q: 7. Use polar coordinates to evaluate: fe(x²-y²) dydx

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Q: #2) Convert each of rectangular pair coordinates to polar coordinates where r> o and o 4o < Zx. part…

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Q: 1.5 -1 X X 3 1.0 0.8 0.6 0.4 0.2 1 2 3 X

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Q: 3. Let (x, y) denote the usual rectangular coordinates. Write the following function f(x, y) in…

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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: Write a polar equation of the form r cos(0 – 0,) = ro for the line 3 x- y = 2.

A: Given: To find the polar equation of the form r cosθ-θ0 =r0 for the line 3x-y = 2.

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A: A point is expressed in polar coordinates as r, θ. To convert it into a point in rectangular…

Q: The Cartesian coordinates of a point are given. (a) (2V3, 2) (1) Find polar coordinates (r, 8) of…

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Q: 2 - y = 2 #8) A) Change equation x 4 to polar coordinates.

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Q: 1. (a) For the point (r, 0) = (3, T/2), find its rectangular coordinates. (b) For a point (x, y) =…

A: Relation between polar coordinates (r, θ) and rectangular coordinates (x, y) is given by, ⇒xr=cos θ,…

Q: Find polar coordinates with positive r and 0s 0 < 2n for each of the four points. (x, V) = (,8 (a)…

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Q: SHOW ALL WORK Change the polar coordinates, (r, 8) to rectangular coordinates, (x, y). (Leave…

A: Given the query is to find the rectangular coordinates.

Q: 6. Convert: a) Coordinates of point D(-1,-5) to polar coordinates, r> 0 and 0 <0<2n.

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Q: Convert the Cartesian equation to a Polar equation. Express your answer as r = 2y –x² = 2y– 3x

A: The objective is to convert cartesian equation to polar equation.

Q: 4. Find the equation of the circle (in polar) with center on the line a = and passing through the…

A: The general equation of a circle with centre at r∘, θ∘ and radius, a is given by r cos θ-r∘ cos…