Draw the plane curve defined by polar coordinates r = sin(30), 0 2¹, and calculate the x-coordinate of the center of the plane area D bounded by 0 ≤ ≤ 1/3 between it: = [[ r dr dp, z = = = = [[ x A = r cos y r dr dy, =X (is the representation of area D in polar coordinates)

Q: Find an equation of the normal line to the parametric surface given by R(u, v) = ((2+ cos v) cos TU,…

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Q: If the slope of the tangent line to the polar curve r = 10 cos 0 at the point P is –1 and (r, y) are…

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Q: What is the slope of the line tangent to the polar curve r = ㅠ Ө - ? O 1 √√3 ✓ 2 T -||♡33 √√3 cos 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: 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: osen y

A: Is it sen y =x

Q: Find an equation of the tangent plane to the parametric surface R(u, v) = ((u - sin u) cos v, (1 -…

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Q: The polar equation r = a+a cos 8, where a > 0, has a tangent line at (0, 7)

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Q: Find the length of the curve given in polar form as r= e,- <o<a a)2/2 sinh(7) b)sinh(") c)2 sinh(7)…

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Q: III. Find the parametric equations of normal line to the surface given by f(x, y) = tan 2 V + y? at…

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Q: Find polar coordinates (r,θ) where r < 0 and 0≤θ≤2π of(√3,−1)

A: Given point in the rectangular coordinates is 3,-1. To find the polar coordinates r,θ, where r&lt;0…

Q: Identify the surface for ρ = 4 cos φ

A: The given curve is: ρ=4cosφ Multiplying both the sides by ρ: ρ2=4ρcos φ Now, converting it into…

Q: Sketch the parametric curve of r(t) =.Then, find and draw the tangent vector r'(0)

A: 2cos t, 2sin t,3To Find:a. Sketch the parametric curve.b. Find and draw the tangent vector r'(0).

Q: Find polar coordinates (r, 0) of the point (1, -V3), where r <0 and 0 s0 < 2m

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Q: Use polar coordinates to integrate under z=xy above the first quadrant of the unit circle on the xy…

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Q: x =9+2t² y = 4t 0St<2 about x-axis

A: SURFACE AREA OF PARAMETRIC CURVE:                    Consider the parametric curve given by…

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

A: Power rule ddnxn=nxn-1 Length of a curve with equation r=fθ , a≤θ≤b is given by  L=∫abr2+[drdθ]2dθ

Q: Find the distance on the xy plane between the two points, given below as polar coordinates (7,…

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Q: The curve (x-)*+Cy +1)*= 4, x 7,1 is given. First draw it in the Cartesian plore and then transtorm…

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