Find the area of the plane z = 4x + 3y for all (r, y) E R where R is the region in the first quadrant which is bounded by the circle r = 10 sin (0) and V50 cos (20) both given in polar coordinates. Give your the lemniscate r = answer to the nearest four decimal places. A(S) = || () 1+ + dA, %3D ду R where R is the domain over which we are interested to find the area of the surface z. Sketch the region R before doing the integration. (In polar coordinates, dA = rdrd0)

Q: Show that the graph of the equation r = 2a sin θ, a > 0, is acircle of radius a with center at…

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Q: Consider curve given in polar coordinates by Find the derivative r = 8 cos 0,0 ≤ 0 ≤T/2, dr do -8…

A: The given curve is: r=8cosθ;  0≤θ≤π2. To Do: Find the derivative drdθ. Compute the surfaced area…

Q: Find the derivative dydx of the polar function r=1+sinθ at θ=π4.

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Q: Find the expression for the tangent slope dy/dx for points on the Polar curve r= 6 +12 cosθ

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Q: Find the point(s) of intersection between the following two polar curves on the interval [0, 360]: r…

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Q: Determine the area in the first quadrant bound by the polar function r(0) = sin (0) – 1.

A: Here, since the area is in the first quadrant, we can calculate the area with the help of integral…

Q: Find the area inside both the polar rose r = 5 sin (20) and the curve r quadrant. Enter an exact…

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Q: Identify the correct plot that describes the polar region R-{(r, e )| 2 srs 5, n/2 s 0 s 3n/2}. -3-2…

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Q: determine the slope of the tangent line to the polar curve r = 1+3 cos(20) at 0 6

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Q: Choose True if the statement is correct, otherwise False. The point (-13,–1107/4) is located between…

A: To convert the polar coordinates to the rectangular coordinates the formula used are x=rcos(θ),…

Q: cos(0) – sin(0) between the lines 0 = 0 and 0 = 4 Find the area under the polar curve r = 5.

A: Explanation of the answer is as follows

Q: Consider curve given in polar coordinates by Find the derivative r = 8 cos 0,0 ≤ 0 ≤ π/2, dr = -8…

A: We need to find out the area of the surface of revolution formed by the given function.

Q: Given r = 2(1-sin theta)  1. Find the tangent line equation at (r, theta) = (2, 0). Show all work to…

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Q: r = 5 +4 cos 0 3. Draw and determine the area bounded by the curve in polar coordinates

A: We have to find the area bounded by the polar curve r = 5 + 4cos(theta)..

Q: Find the slope of the tangent line to the polar curve r=2cos0 at O %3D 4

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Q: Find the area of the region lying below the x-axis and above the polar curve r = 1 + sin(0).

A: Given polar curve is: r=1+sinθ To find: Area of the region lying below the x-axis and above the…

Q: Find the slope of the tangent line to the polar curve 7 = 1-sin 40 at 0= 04 0- 12/12 O 5√3+4 1-4√3

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Q: Find the slope of the tangent line to polar curve r = 8 – 7 sin 0 at the point (8 %3D 2' 6

A: Given the equation of polar curver=8−7sinθ       .......(1)(8−72,π6)

Q: Q4) Find plane area inside the polar function r = 2 and outside polar function r = 2 sin * +0) in…

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Q: Q5: Find the area of region enclosed by the polar function r= 3+3 sin 0

A: Plot

Q: Find the area between 0 = 0 and 0 = π/2 of the polar curve r = 1 + sin 0

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Q: п 4. Find the slope of the tangent line to the polar curve r = 1 – sin40 at 0 = 4 : a. 3 b. 4 c. 2…

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Q: determine the slope of the tangent line to the polar curve r = 3 + 8 sin 0 at 0 =

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