. Calculate the projection of å along b and projection of b along å when: d = 3î + j – k , 5 = -21 – j + k

Q: Consider the hypergeometric equationx(1−x)y′′+[c−(a+b+1)x]y′−aby = 0,…

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Q: By how much will f(x, y, z) = e" cos yz change as the point P(r, y, z) moves from the origin a…

A: Given function is At origin,

Q: 1. In the following diagram, PA is tangent to 00 at A. If mBC = 50' , m/BEC=60', mBD=x and mAC = 2x+…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

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: B. Evaluate sin z z²+j2z dz, C the boundary of the square with vertices ±1, tj clockwise.

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Q: Which of this is a parametric representation of the unit circle? * O x=sin t, y=cos t O x=3sin t,…

A: The solution of the problem is given in the next step.

Q: (iv) Find [z dz along the contour C given in Figure. 1+i

A: Given ∫Cz¯2dz

Q: Calculate the value of x in the figure: AB = BC = DA and BD = DC (Not drawn to scale). %3D %3D 21 2x…

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Q: The parametric form of 3x - 2y + 10 = 0 is: O x = 2t y = 5 + 3t O x = t y = 5 + t O x = 3t y = 5 +…

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Q: EX, chang to polar and evaluate I= f dy hpxpx

A: Find Your Solution Below

Q: Consider the shaded square region on the s-plane, as shown in Fig. Q1. Let p =-Co, + j@, 1-5?, S'-…

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Q: Consider the following. C: line segment from (0, 0) to (4, 8) (a) Find a parametrization of the path…

A: Given:

Q: the xy-plane, centered at the origin, oriented clockwise so that the point (5,0) corresponds to t =…

A: we have to find parametrization of circle.

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

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

A: Solution:

Q: Given the line segment from the point (13, 7) when t = 0 to the point ( – 1, – 9) at t = 1, find the…

A: When t=0 then point (13,7) and t=1 then point (-1,-9)

Q: Y=V Cos 2O

A: The given function is, rθ=cos2θ The interval of θ is 0, π4 The axis of rotation is y-axis To find…

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: Part 4 of 8 Since we want the portion of the sphere which is above this circle, we return to the…

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Q: Given the funchisns fyl= 3y-y cnd 8y)=-y; 9. Sketch the frunckons cnd label then nteuseckon points

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

Q: Re(z) dz, where C is the right half circle |2| = 3, from z 2² – 2i (Ъ) -3i to z = 3i.

A: To Determine :-  An upper bound of the absolute value of the integral. ∫C Re zz2 - 2i dz  where C is…

Q: Suppose r'(t) has units of m/s. Explain why T(t) = r'(t)/ | r'(t) | is dimensionless (has no units)…

A: Suppose r'(t) has units of m/s. To explain why Let r(t) be a differential vector valued functionNow…

Q: 1. Name two points collinear to point D. 1 1)

A: As per our guidelines  I am supposed to answer  one question from eight question which question…

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: -2 Find the projection of v = 1 onto the line l of R³ given by the parametric equation l = tủ, where…

A: We will find out the required projection.

Q: Find the length of the following two-dimensional curve. π 3 r(t) = (3 cos ³t, 3 sin ³t), for Osts- 4

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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: Find the direct and opposite plane motions that map AB to ÁC where these three oints have the…

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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: Which of the following graphical representations shows the intersection curve, in the first octant,…

A: We have to choose which one shows the intersection curve in first octant between a cylinder of…

Q: Ex.9. An ellipsoid y2, z2 = 1 is surrounded by a luminous a? b2 ring x = 0, y2 + z² = a². Show that…

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

A: Any complex number is of the form z=x+iy The complex integral is converted into the integral of one…

Q: Use the diagram below for questions 19-22 in which G is the centroid of AABC, FC = 35, AG = 42, BF =…

A: Use property of median of triangle

Q: 8- of What is the value of (z + e22) dz, where C is the positiv C oriented circle |z - 1= 1 in the…

A: Since z-1=1 ⇒z-12=1⇒z-1z-1¯=1⇒z-1z¯-1=1⇒zz¯-z¯-z=0⇒z¯z-1=z⇒z¯=zz-1

Q: Find the unit fangent sector t for the currve : r=ti -2tj + 3t°k Y =a sin wt i +a Ceswt j %3D 2- r…

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Q: Find the projection of v = -7 onto the -2 e of R' given by the parametric equation e = tu, [-11

A: Introduction: The formula of projection of the vector v onto the vector u is given by the formula,…

Q: 5. Evaluate (y +tan x)dx+(x -2ry+y)dy, where C is the circler +y' =4 and is oriented in a positive…

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Q: O is the centre. EO = /3 . OF = 2 and OE I DF. Calculate the length of DE. (b) %3D F. E V3 2]

A: From the given problem:   EO=3 ;OF=2  OE⊥DF.   As we know that perpendicular from the center of the…

Q: If z(z, y) = 2x +y?, z = e", and Y = ue", find . %3D %3D Provide your answer below:

A: Put the expression of x &amp; y in z than calculate partial derivative of z with respect to v. When…

Q: B. Evaluate sin z z²+j2z dz, C the boundary of the square with vertices +1, tj clockwise.

A: Evaluate the integral ∮Csin zz2+j 2z dz, where the path C represents the boundary of the square with…

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: Find T, N, and k for the plane curve r(t) = ti+ In (cos t) j. -5<t<5. T(t) = i+Oi %3D

A: Given: r(t)=t i+lncos tj,  -π2&lt;t&lt;π2 Formulas to obtain T, N and k are given as:…

Q: If the angle at which the radius vector cuts the √√²-a² 2 1 a curve 0 = COS be o, then a r cos o…

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Q: If the analytical function f(z) = u(x, y) + iv(x,y) is expressed in terms of the polar coordinates r…

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Q: find the volu me of the o bócct Caused by the rotation oftne bouncled ared be twen y= aQ ,y=X…

A: Integrals and derivatives are considered as the inverses of each other. For example if we have a…

Q: " | and F(x.y) = <y-x, x+3), then TE If C is the curve parametrized by 7(1)= <2sint, 2cost), te 0,-…

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Q: 6. If r = and 2+ cos 0 (c, 0) is a focus expressed in rectangular coordinates with c+0 then c =

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Q: Evaluate z dz, where the contour C goes from z = 0 to z = 1 to z = 1+i.

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