Problem 3. Calculate the first fundamental forms of the following surfaces: (a) x(u, v) = (u - v, u + v, u² + v²). %3D (b) x(u, v) = (cosh u, sinh u, v).
Q: 4. Find the equations of the line tangent to the intersection of the surfaces z = x´ + 2y and
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Q: Problem #6: The surface = 5 - 5 + V3 xy within the cylindrical region 15 x2 + y2 < has a surface…
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Q: Problem 4 B Find, by using polar coordinates in R?, the volume of the region bounded above by the…
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Q: Problem #8: Use Stokes' Theorem to evaluate F. dr where F = (x + 9:)i + (7x + y) j + (6y – =) k and…
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Q: Problem 1. Parametrize the following surfaces: (a) 2x + 3y + z = 6. (b) z = 9 – Vx² + y?. - (c) x² +…
A: As per Bartleby's answering policy, we can answer only one question with a maximum of three…
Q: 15 Problem 2: Find the area of the surface generated by revolving the curve x = 2/4- y, 0 < y< 4…
A: Given curve x=24-y ,0≤y≤154 revolving around y-axis Find the area of the surface
Q: Suppose surface #1 is defined by o =45° , 0 <ps9, 0 < z< 6 and surface #2 is defined by 0 =56.3° The…
A: given:
Q: Problem 2 You are in charge of erecting a radio telescope on a newly discovered planet. To minimize…
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Q: Find the area of the surface generated when the curve is revolved about the y-axis. y=4x-1, for 1 <…
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Q: 1. Find an equation of the tangent plane to the given surface at the indicated point. 2² + y? – 3z =…
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Q: Problem 3. Calculate the first fundamental forms of the following surfaces: (a) x(u, v) = (u – v, u…
A: Hi! You have posted multiple questions. As per the norm, we will be answering only the first one. If…
Q: Work Problem1 a) Find the exact length of the curve 1 ,1< < 2. y = 4 3x b) Find the exact area of…
A: Given curve y=x34+13x , 1≤x≤2
Q: Question 8. Consider the surface defined by x² – - = 1. Draw the traces of this surface…
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Q: Problem 1. Find Fn dS if S is the sphere (x-1)´+y+z=1 , S and F(x, y,z)= (x³, x²y , zy°) . 2
A: n = 820 , x=22 Po=xn=22820=0.0268 npo(1-Po)=820(0.0268)(1-0.0268) = 22(0.9732) = 21.41…
Q: Problem 3: Evaluate ff,F· dA using Gauss, where F = half of the sphere x2 + y? + z²2 = 9. (2²x, y³ +…
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Q: 1 15. Find the radius of curvature at 0 = n of the parametric equations x = 3(0 + cos 0), y = 3(1 —…
A: Given parametric equations are x = 3(θ +cosθ) y = 3(1- cosθ) We have to find radius of curvature at…
Q: Problem 1: Use spherical coordinates to evaluate the integral of Vr2+ y? + z2 over the ball of…
A: Since you have posted multiple question we are supposed to be answer only first one... kindly repost…
Q: 32. (sin y, x) • dr, where C is the boundary of the triangle with vertices (0, 0), 0 ), and 2' 2
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Q: dy h,p For problems 1-3 compute dx for the given set of parametric equations. and dx? 1. x = 7t2 –…
A: 1) Given that x=7t2-9t, y=t6+2t2We have to find the dydxand d2ydx2First we find…
Q: Practice Problem 5: Set up the arclength integral to compute the length of the parametric trajectory…
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Q: 3. Find the area of the surface generated by revolving the curve y = 2/x ,1Sx<2, about the x-axis(as…
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Q: 1. Find an equation of the tangent plane to the surface of z = sin(x - 2y) at the point (7,2,0).
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Q: Problem #1: Given X = x+ 2z?, and Y = p sin o a, (a) Express X in cylindrical coordinates and Y in…
A: Given X=x+2z2. In cylindrical coordinates x=ρcosϕ. So, X=x+2z2 in cylindrical coordinates is:…
Q: Problem 1: Find the area of the surface generated when the given curve is revolved about the y-axis.…
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Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².
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Q: Find the centroid of the region above the curve (shaded in green) in Figure 4. This region is ranges…
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Q: Problem 6: Find the surface area of the surface generated by revolving the graph of f(x) = Vx from x…
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Q: Question 4 Let w aXu(q) + bX.(@) € T,S such that |lw||= 1. Then the normal curvature to the surface…
A: Solution and explanation is below
Q: 1 4) Find the exact area of the surface obtained by rotating the curve x = + on the interval 6 2y…
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Q: 5. Discuss the bifurcations of the system ŕ = r(µ – sin r), 0 = 1 as µ varies.
A: Given that: This system has no fixed points, but r can take on zero values where μ≤0. Where equality…
Q: Problem 12 Find an equation for the plane that is tangent to the given surface at the given point…
A: In this question we have to find the equation for the plane that is tangent.
Q: Problem #4: Evaluate the following integral, xyz dS, where S is the surface with parametric…
A: We will find out the required value.
Q: 12.3 24 determine the curvature and the radius of curvature of the given curves at the specified…
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Q: Problem 2: Let C be the boundary of the triangle with vertices 0, 2+ i, and 3i. (a) Find the line…
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Q: Identify the surface whose equation is given. p = sin(8) sin(4) O a sphere of radius - centered at…
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Q: Find an equation of the tangent plane to the given surface at the specified poin 8x2 + y2 - 7y, (1,…
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Q: Problem 0.4. Give an orientation and orientation preserving parametrization to the following curve C…
A: Given that -
Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T =…
A: We have given; The temperature T at any point (x, y, z) in space isT = 400xyz2and the unit spherex2…
Q: Problem 3. Use cylindrical or spherical coordinates to evaluate the integral. 1* dz dy dr for a > 0.…
A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…
Q: Suppose that the Celsius temperature at the point (x,y,z) on the sphere x +y +z =1 is T= 1600xyz“.…
A: This is a problem related to maxima and minima. Based on the general formula we will answer the…
Q: 6. Find the area and centroidal distances of the curve that lies between the equations y-4-x^2 and…
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Q: Problem III Let B(v) = (f(v), 0, g(v)) be a curve with g(v) > 0 and v E (a, b) with a <b€R. Let S be…
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Q: Problem 4 The helix r(t) = (cos(xt/2), sin(xt/2), t) intersects the sphere x2 + y² + z² = 2 in two…
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Q: Problem 1. ad the points on the sphere r² + y² + z? = 9 that are closest to and farthest away
A: Given, x2+y2+z2=9 (1)
Q: 15) Consider curve C which is the intersection of the surfaces shown in the attached figure. The…
A: The equation of the graphs given are as follows: x=-34y2+3y=yz=y22 We are asked to evaluate the…
Q: Problem II We consider a parametrization of a regular surface S, given by X (u, v) = (u+2v, 2uv, 2u…
A: Here the equation of the tangent plane to the surface will be Xu×Xv.x-6,y-8,z-2=0 where X=Xu,v is…
Q: Problem 1: Determine centroid Y-bar with respect to the x-axis. A = 1.6 m B-3.9 m V A A B B
A: We have to find the centroid.
Q: Problem 2. Find the value of a > 0 such that the cone 22 = x² + y², z > 0 is orthogonal to the…
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- Find general solutions of the systems in Problem Attached. Use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system.In Problems 21–26, decompose v into two vectors v1 and v2 , where v1 is parallel to w, and v2 is orthogonal to w. 25. v = 3i + j, w = - 2i - jThe trace determinant plane in our textbook (and in We-bAssign) includes two border cases: (1) when τ = 0 (and ∆ > 0), wehave a center point and (2) when τ 2 = 4∆, we have a degenerate node.It does not include the other border case when ∆ = 0.(c) Suppose τ > 0. Is the (0, 0) equilibrium stable or unstable in thiscase? What if τ < 0
- Need help with a Jacobian ProblemLet a=<−5,0,−3> and b=<4,0,2> Show that there are scalars s and t so that sa+tb=<27,0,15>.s = ? t = ?: A parametric cubic curve passes through the points (0,1), (2.5), (3,5) (5,-3) which are parameterized at t=0.1, 0.3, 0.6 and 0.9 , respectively. Determine the geometric coefficient matrix and the slope of the curve when t-0.5.
- Can you help me find the unique vector described in problem 2?5. Given that, for some a, b, c, d, e, f, g, h, i E R, a b c d e f g h i = 8 evaluate the following deterimants: x = 3g 3h 3i d e f -2a -2b -2c y = d-5g e-5h f-5i a b c g+7a h+7b i+7c z = d -a 2g e -b 2h f -c 2iFind the standard matrix for the reflection T of R3 in the line { x=2t y=-t z= -2t Is T invertible?
- Let L be the line that passes through the origin in the direction of u = (1, 1, 1). Find the matrix for the rotation about L with angle 45 degree.I need to solve this problem without using matrices. We have a vector V whose components in the basis B = (v1,v2) are (3,-2) Which are the components of the same vector in the basis C = (u1,u2) if v1 = 4u1-u2 and v2 = 4u1-3u2? Remember, no matrices.1. Let a= (<5,3>) and b= (<1,-1>). Show that there are scalars s and t so that sa + sb=(<-3,-5>) 2. A child walks due east on the deck of a ship at 3 miles per hour. The ship is moving north at a speed of 1 miles per hour. Find the speed and direction of the child relative to the surface of the water. 3. A horizontal clothesline is tied between 2 poles, 10 meters apart. When a mass of 2 kkilo grams is tied to the middle of the clothesline, it sags a distance of 4 meters. What is the magnitude of the tension on the ends of the clothsline?