Test for symmetry with respect to the line e = 1/2, the polar axis, and the pole. (Select all that apply.) 12 = 36 cos(20) O symmetric with respect to the pole O symmetric with respect to the polar axis O symmetric with respect to e = T/2

Q: /25– x² 1. Evaluate (x2 + y? )3 dy dx by converting to polar coordinates.

A: Evaluate the double integral by using the charge of polar coordinates

Q: Q3/ Find the Z1*Z2 and the Z1/Z2 and leave the answar in polar form. z= 12(cos 84° +i sin 84°) and…

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Q: Test for symmetry with respect to a. the polar axis, b. the line 0 =, and c. the pole. 2' r= 5+3 cos…

A: We have to check the symmetry for the given curve…

Q: Test the polar equation for symmetry with respect to the polar axis, the pole, and the line Theta=…

A: Test the polar equation for symmetry with respectto the  polar axis, the pole and the line θ=π2…

Q: Test r = 1 - 4cos θ for symmetry with respect to the following: a) the polar axis. b) the line θ =…

A: a).

Q: Q1/ Find the area inside r = 3 + 2 sin 0 and outside r =2 Q2/ Graph the polar equation r = 1 – sin0…

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Q: Use a graphing utility to graph the polar equation, draw the tangent line at the given value of 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: re inequalities for ion to the right in polar coordinates.

A: Given,

Q: Test for symmetry with respect to the line 0 = T/2, the polar axis, and the pole. (Select all that…

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Q: Test r = 2 cos 2θ for symmetry with respect to a) the polar axis. b) the line θ= π/2  c) the pole.

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Q: Q1 Find the points of intersection of the polar curves rcos and 2-cos-r=0 Q2 Find the points of…

A: Introduction: The polar curve has the form r=fθ. When two polar curves intersect each other, the…

Q: Find the area of the region enclosed by one loop of the curve. r = 7 cos4e Select the correct…

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Q: Test for symmetry with respect to the line 0 = 7/2, the polar axis, and the pole. (Select all that…

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Q: Test for symmetry with respect to the line 0 = T/2, the polar axis, and the pole. (Select all that…

A: To solve the following problem

Q: 5. Calculate the area A between the orange circle and the blue rose shown in the diagram below if…

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Q: Test for symmetry with respect to the line 0 = T/2, the polar axis, and the pole. (Select all that…

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Q: Test for symmetry with respect to the line 0 = 1/2, the polar axis, and the pole. (Select all that…

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

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Q: Test r2 = 16 cos 2θ for symmetry with respect to a) the polar axis. b) the line θ= π/2.  c) the…

A: (a) To test for symmetry in polar coordinates with respect to the line θ=π/2, replace (r, θ) with…

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: r2 = 16 sin 2θ.Test for symmetry with respect to:a. the polar axis. b. the line θ =π/2. c. the pole.

A: Known properties: For a polar equation in the form r=fθ, If f-θ=fθ then the curve is symmetric…

Q: Q 1. (a). Express z=2+/2i in polar form. (b). Find the value of z if e² =1.

A: Q1. (a) given complex number is                                                              z=2+2i…

Q: r2 = 16 cos 2θ.Test for symmetry with respect to:a. the polar axis. b. the line θ =π/2. c. the pole.

A: We have the  polar equation given as r2=16cos2θ (a) Now testing for Symmetry about polar-axis,…

Q: r = 5 + 3 cos θ.Test for symmetry with respect toa. the polar axis.b. the line θ =π/2.c. the pole.

A: Properties: For a polar equation in the form r=fθ, If fθ=f-θ then the curve is symmetric about the…

Q: Test for symmetry with respect to the line e = 1/2, the polar axis, and the pole. (Select all that…

A: We will test for all three types of symmetry as following .

Q: Test for symmetry with respect to the line 0 = t/2, the polar axis, and the pole. (Select all that…

A: It can be find by putting the required condition of curve and the angle.

Q: Q 2. (a). Express z = 3 + V3i in polar form. (b). Find the value of z if e =1.

A: Given : a. z=3+3i

Q: Test the polar equation for symmetry with respect to the polar axis, the pole, and the line e = 1…

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Q: er.)Graplethe polar equation r=1-coae for "e in [0,360) 30 45 use the braplon the next page…

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Q: Test r = cos θ for symmetry with respect to a) the polar axis. b) the line θ= π/2  c) the pole.

A: Given polar equation- r=cosθ To test  the symmetry of this polar curve with respect to polar axis,…

Q: Find the slope of the line tangent to the polar curve at the given point. 5 7n 2' 6 r= 5 sin 0; dy…

A: To find the slope

Q: Find the length of the curve r= sin°(0/3), 0<O<3n/2. The length of the polar curve is (Type an exact…

A: The length of a polar curve r=f(θ) between θ=a and θ=b is given by the integralL=∫abr2+drdθ2dθ

Q: Test r2 = 9 cos 2θ for symmetry with respect to a) the polar axis. b) the line θ = π/2. c) the pole.

A: Test r2 = 9 cos 2θ for symmetry with respect to a) the polar axis. b) the line θ = π/2. c) the pole.

Q: Q2: Sketch the polar function r 3 6 cos 30 ,-n<0 < m

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Q: r = cos θ.Test for symmetry with respect to:a. the polar axis. b. the line θ =π/2. c. the pole.

A: Test for Symmetry about polar-axis: Replace ( r , θ) with ( r , -θ ) simplify the equation. If 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: Q4) Find plane area inside the polar function r = 2 and outside the polar function r = sin +1 in…

A: Here we use double integration to find the area.

Q: Use a graphing utility to graph the polar equation. -을 sin(s8) 37 2 Find an interval for e over…

A: r = 3π2sin5θ (I) is the correct graph of the above polar         equation. Interval for θ over which…

Q: Find the length of the curve r=1+ cos 20,0s0sn /2 /2. The length of the polar curve is (Type an…

A: We will solve the problem

Q: Find the slope of the line tangent to the polar curve at the given point. 5 7x r= 5 sin 0; 2 6 dy…

A: Slope of line tangent to the polar curve is given by- dydx=drdθsinθ+rcosθdrdθcosθ-rsinθ

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: (a). Express z = V3 + V3i in polar form. (b). Find the value of z if e =1.

A: (a) Consider the given function as z=3+3i It is the equation of complex number in the form of a+ib

Q: Find the polar equation of a line parallel to the line r cos (0 = 1 and lying at a distance d = 5…

A: The given line is: rcosθ-π5=1. A line parallel to it, will be of the form: rcosθ-π5=k

Q: Q23: Polar conversion of (v3, -V7) is? (a) ( V10, 2n + tan¬1 3 () (), (b) (V10, 2n – tan-1 3 (c) (…

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Q: V2 Evaluate x² dy dx by changing /4- to polar coordinates. Select one: O a. T A – а. л — 2 О. 2л — 6…

A: Given: ∫02 ∫-4-x2-x  x2  dy dx Evaluate the given integral by changing

Q: Test for symmetry with respect to the line 0 = t/2, the polar axis, and the pole. (Select all that…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.