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Q: 12.17. Question attached. Thank you for answering my question!

A: The model for the two-way layout is as follows:

Q: (a) find a parametrization of the path C, and (b) evaluate (r? + y?) ds.

A: Here we have to find the Parameterization of path C, Counterclockwise around the circle x2+y2=1 from…

Q: 2. Evaluateſ. a+ (z+30:) dz along C which is the circle |z + 3i| = 3, counterclockwise. %3D (z+3i)

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Q: Find the angle (in radian) between the planes 2x + Z = 3 and x + 2y + Z = 2y z = 2.

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Q: Given: polar curves C₁ : r = √2- cos 0 and C₂ : r = √2+ sin intersecting at A(³√2, 37) and B(2,7) 2…

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Q: Let θ be the angle between the line y = mx +b and the x-axis. Prove that         m = tan θ.

A: The slope of a line is the rate of change of the y-axis with respect to x. Formula for slope=riserun…

Q: - 77T then use the rectangular coordinates of P(t) ft= to fin 6. sint = %3D cost = %3D

A: Solution:

Q: In the given figure , the common tangents AB and CD to two circles with centres O and O' intersect…

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Q: Consider the curve given in polar coordinates by r = 0 + cos 0 . Compute the slope at 0 = 0. %3D O…

A: Slope of polar curve r=f(theta) is given by dr/d(theta) Differentiating r with respect to theta we…

Q: Sketch the plane curve r(t) = a cos3 ti + a sin3 tj and find its length over the given interval [0,…

A: The curve is r(t)=a cos3ti + a sin3tj   Interval is 0, 2π

Q: 4. Let C be the circle |z| = 2 traversed once in the positive sense (counter clockwise). Compute :…

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Q: 6. Given a rule x² + y? = 9, its image rule x² + y² – 2x + 6y + 1 = 0 under a translation, state a…

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Q: Find the areas of the regions in Exercises : 1. Shared by the circles r = 2 cos 0 and r =2 sin 0

A: First find the common point or point of intersection of both the curves by equating both the…

Q: Let C be the line segment connecting 0 to ni. Then f. 1-e22 dz = a. 0 b. -0.5 + ni c. ni d. None of…

A: Given C be the line segment connecting 0 to πi Then we have to calculate ∫C1−e2zdz Hence,…

Q: Find the areas of the regions in Exercises : 1. Shared by the circles r = 2 cos 0 and r = 2 sin 0

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Find the exact length of the polar curve described by: r = 8e 3 on the interval a <o< 9n. 2"

A: The length of a polar curve r=fθ in the interval α≤θ≤β is given by L=∫αβfθ2+f'θ2dθ. The given curve…

Q: Consider the parametric curve defned by r=3+5t and y=1+ Over which values of y does t curve has a…

A: Given problem:- Consider the parametric curve defect by   x = 3 + 5t and y = 1 + 3t   Over which…

Q: Evaluate |(z - z+ 2) dz from i to 1 along the contour C given in Figure.

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: Graph the curve r2 = 4 cos θ in the Cartesian xy-plane

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Q: 3) Consider the line L in R? spanned byp = (6). Let PL(u) be the orthogonal %3D projection of the u…

A: b = 4

Q: refer to Figure 16.. Calculate the projection of −→AC along −→AD.

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Q: 4. to 1 What is the location of point A after a reflection across the y-axis and a translation of 4…

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Q: Compute the following: = 4 located in the first quadrant. (a) S x ds where C is the portion of the…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Draw the isoclines with their direction markers and sketch several solution curves, including the…

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Q: 9. What is the resulting image of D' after a reflection about the line y3Dx? ty D Rule: A B

A: Topic - symmetry and geometry

Q: 12. Use Greens Theorem to calculate P y'dx -a'dy C where C consists of the arcs y=x² and y =x1/2,…

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Q: Sketch the curve r= cos 20

A: Let us make a table for the given function θ 0 π/4 π/2 3π/4 π 5π/4 3π/2 7π/4 2π r 1 0 -1 0 1 0…

Q: use the distance Formula tO Find the distance between e) and(3,2)

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Q: 4. In the diagram of the collinear points, DE = 2, EF = 3, and DE = FG. Find each length. * FG. & DF…

A: As this is a multiple subpart question according to the Bartleby Answering rule, only first three…

Q: 4. Let C be the circle |z| = 2 traversed once in the positive sense (counter clockwise). Compute: .…

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Q: ) Let à = psin(4)u, + p² Ug %3D Evaluate $ Ã. dl given that L is the contour of the following…

A: Given, A→=ρsinϕup→+ρ2uϕ→ The given diagram can be drawn as,

Q: Sketch the graph of the following parametric (a) x = 1+t , y= 2t – 3, 2<t< 5 1 (b) x = 2t , y = 1+…

A: Here we have to draw the parametric equations:- a) x=1+t,    y=2t-3,   2≤t≤5b) x=2t,    y=11+t2c)…

Q: Graph the Plane Curve defined by: I = 3 cos(t) - t + 5. y = sin(t). for t in [0, 37]. x Clear + Undo…

A: Plot the points for different values of t from [0,3π]. Draw the curve passing through the points.

Q: The circles r (V3/2, 7/3). Show that their tangents are perpendicular there. V3 cos 0 and r = sin 0…

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Q: 63. Let e be the angle between the line y = mx + b and the x-axis [Figure 29(A)]. Prove that m = tan…

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Q: 5.) In the diagram of the collinear points, HK= 9, 1. Find the following lengths. = JK, and IJ a. HI…

A: Given,           In the diagram of the collinear points, HK=9, HI=JK and IJ=1.

Q: In the following sketch, O is the centre of the circle. AE= ED and DT=TC. %3D Prove that (1) Ê =Ô¡…

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Q: Show that = sin t if t>0 and C is the circle z] = 3. 2mi Jz+1

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

Q: In three-dimensional space, the graph of the equation z = sin(x) is: O a Line O a cylinrical surface…

A: Given,    Z= sin(x)    Sine curve is the curve of the sine function. It is also known as sinusoid.…

Q: 3) Use polar coordinate to evaluate S'S_√x² + y² dxdy.

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Q: Find the areas of the regions in Exercises: 1. Shared by the circles r= 2 cos 0 and r=2 sin 0

A: `1) Intersection   2 sin θ = 2 cos θ ⇒ sinθcosθ = 1 ⇒ tan θ = 1 ⇒ θ = π4   A = ∫ ∫A r d r d θ   A =…

Q: Find the are length of one turn of the helix, t=0 to t = 2r , given by 7(t) = (bcost, b sin t, V1 –…

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Q: Find the areas of the regions in Exercises : 1. Shared by the circles r= 2 cos 0 and r= 2 sin 0

A: You have posted multiple questions. As per the instruction, we will be solving only one question. We…

Q: Find an upper bound of the absolute value oI e +1 (a) dz, where C is the right half circle |z| = 3,…

A: Note:  Since you have posted multiple questions, which are independent, as per our policy we are…

Q: Find the angle (in radian) between the planes 2x + 2y Z = 3 and x + 2y + Z = z = 2.

A: Consider the two planes: 2x + 2y - z =3  and  x + 2y + z =2. We have to find the angle between the…

Q: 4. Let C be the circle |z| = 2 traversed once in the positive sense (counter clockwise). Compute : .…

A: Cauchy integral formulae: Let f(z) be analytic in a region D, derivatives of all orders are also…

Q: Find the exact length of the polar curve described by: r = 7e-0 3 on the interval 10

A: r=7e-θ,    310π≤θ≤6π Differentiating with respect to θ, we get drdθ=7-e-θ=-7e-θ