Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions. r 2 5, - 10 10 - 10 10 -2 -2 -4 -6 -8 -8 - 10 - 10 10 10 8- 6F 6 4 4 2 2 10 -5 5 10 10 -5 5 10

Q: 12 3. 5. 13 18 -1 For what value of hs in the plane spanned by j and i? Preview Answers Submit…

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Q: (a) Find and identify the traces of the quadric surface x2 + y2 - z2 = 36 given the plane.

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Q: Show that the points A = (1, 2), B = (1,0), and C = collinear and express P = (-7,0) in barycentric…

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Q: 2. Find the distance of the point A : (1,0, 2) from the plane P: 3x +y+ z = 9.

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

Q: (A) Determine the plane that contain the point A(2,5,1) and the line L, t=x-2, 3t =y-1, t=z+1

A: The equation of the line L given in the parametric form, that is, Thus, the above equation of the…

Q: Given, (2z – z) dz along the directed line segment from -i to 1. What is a parametric form of z(t)?…

A: We have to find the parametric form of directed line segment from -i  to 1

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,,n2, n2),B(m,,m2,m3),C(r,,r2, 13).

A: Please see the explanation below

Q: 14. State whether the following pairs of planes intersect. If the planes intersect, determine the…

A: Two planes are given by, π1: x-y+z-2 = 0  and π2: 2x+y+z-4 = 0. The objective is to check whether…

Q: Find the symmetrical point of point P(-1,-3,5) with respect to the plane D:3x-2y+z+6=0

A: Point P(-1,-3,5)  plane D:3x-2y+z+6=0

Q: Find equations for the planes The plane through P0(0, 2, -1) normal to n = 3i - 2j - k

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Q: 9. Let the affine map A : R? → R² be defined by A(x, y) = (3.x + 4, 2y – 3). Show that %3D the image…

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Q: 10. Find all the planar and hyperbolic points on the surface o(u, v) = u-3uv².

A: A point on a surface is said to be a hyperbolic point if the Gaussian curvature at p,i.e., κp<0.…

Q: B. Sketch these Cartesian products on the x-y plane R² (or R for the last two). 9. {1,2,3} x…

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Q: EXERCISE 4.3. Let S be a connected regular surface such that the image of the Gauss map is a great…

A: The answer is given below thank you for the question upvote is really appreciable

Q: Let r() = (In1, 1, 5). Find the equation of the osculating plane corresponding to1 = 1.

A: Find the point at t=1 the vector r(t)=lnt,t,t22 corresponds. lnt,t,t22=ln1,1,122=0,1,12=0,1,0.5…

Q: The parametric equation of the segment [AB] with A(1,0,5) and B(3,1,2) is: O x=1+2t y%3Dt z-5-3t -o<…

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Q: 26. ƒ(x, y) = ye*; R is the rectangular region with vertices (0, 0), (In 2, 0), (In 2, 3), (0, 3).

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Q: Find the symmetrical point of point P(1, 3, 4) with respect to the plane D:3x-2y+z+6=0.

A: Symmetrical point at plane problem....

Q: 3 Let aj = -1 a2 аз bị 5 5 3 -1 3 b2 -3 b3 2 and n = and let %3D -2 -2 A = {a1, a2, a3} and B = {b1,…

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Q: G' are centroids of the two triangles ABC änd A' B'C! Show that AA' + BB' t CC =3GG' %3D

A: If G and G` be the centroids of the triangle ABC and triangle A`B`C` respectively then show that,…

Q: 12. Let R be the region of the plane R= {(r, y) : # 2 0 and ²+ y? < 2}. Describe R using polar…

A: Here, the given region is: R=(x,y):x≥0 &amp; x2+y2≤2

Q: The equations for the plane through p0(0,2,-1) normal to n =3i - 2j - k O 3x-3y-3z=0 O 3x-3y=z O…

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Q: 4. Find the area of the surface S where S is the part of the plane z = 3x +y that lies above the…

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Q: Find the symmetric equations of the L that is parallel to the two planes x+y-z= 2 and z + 3y+ z =…

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Q: Find a parametric representation of the line through the point P(3,1,-4) and perpendicular to the…

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Q: H-w) find thi surf ace area for the Dlane 6x+44-22= 14 if this plane in the finst octant? S-A = |…

A: Surface area of the, in the xy-plane

Q: Зу — 2z 3D 6

A: Use a graphing utility to plot the plane, 3y-2z=6 .

Q: 2. Which of the following describes a different plane than the other three? (a) x + 2y + 3z = 6 (b)…

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Q: The part of the plane 2x 5y + z = 10 that lies above the triangle with vertices (0, 0), (0, 6), and…

A: Double integration need to be done.

Q: Find the number of points of intersection of the polar curves r=2cos0 and r=1+2sin0. O 1 3 O 2

A: Number of point of intersection of polar curves r=2cosx and r=1+2sinx

Q: Find a parametric representation for the surface: The plane through the origin that contains the…

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Q: O Find the equation of the plane that palses through the points A - (2,4,-3), B = (3,-1,5) and 2 :…

A: In the given question we have to find the equation of the plane passes through the points A ,B and…

Q: R) show that the pints ACI,l,4), B(2,2,2), c (o,1,5) and D(1,0,5) are coplanear (in the Same plane).

A: Form the three vectors and take the determinant of them. If determinant equal to zero it means all…

Q: 9. The Whitney umbrella surface is given parametrically by I= uv, y = v, 2= u. A picture of this…

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Q: Given, | (2z – z) dz along the directed line segment from – i to 1. What is a parametric form of…

A: Given integral is ∫Γ2z-z¯dz where Γ is line segment from -i to 1. i.e. it is a line segment from…

Q: Consider the planes z1+2+33 =4 and z +2z2+ 4z3 5 in R'. Find parametric equations for the line of…

A: Please see the answer in step 2

Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…

Q: find the centroids of the triangleswhose vertices appear . Assume a, b &gt; 0. (0, 0), (1, 0), (0,…

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Q: The part of the plane 3x + 2y +: - 6 that lies in the first octant

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Q: Verify that the line r(t) = [1 + t, 1 - t, t] is part of the one sheeted hyperboloid x^2 + y^2 -…

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Q: Sketch the following surface: (2+4)² + (y − 1)² = 1 a.) Draw the projection on a xy plane Show…

A: Disclamier: Since you have posted a question with multiple sub-parts ,we will solve first three sub…

Q: Find b such that B = (0, b) has hyperbolic distance of u from the point A (0,0).

A: Given: B=(0,b) has  hyperbolic distance of u from the point A=(0,0) Formula used:

Q: The part of the surface z-1+ 3x + 2y that lies above the triangle with vertices (0, 0), (0, 1). and…

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Q: 9. f(z) = e'n/4z %3D

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Q: EXERCISE 3.2 A parametric surface is P(u, w) = [0.5(1 − u)w + u, w, (1 − u)(1 − w)]. 0 ≤u, w ≤ 1.…

A: We have  parametric surface is P(u, w) = [0.5(1-u)w+u, w, (1-u)(1 − w)]. 0≤u, w≤ 1.   We have to…

Q: Find the centroid (, j) of the triangle with vertices at (0, 0), (8, 0), and (0, 9). x=

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Q: 2 Let w = z². Find the image of the first quadrant in z-plane

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