find the frenet apparatus of curve 3u-u3  , 3u2 , 3u+u3 and  Find equations of tangent, normal and binormal lines of this curve at the point 1

Q: An unsymmetrical parabolic curve has a forward tangent of 5% and a backward tangent of -3%.The…

A: Given G1=−3%, G2=5% And l1=120 m, l2=90 m PVI station=5+040 And PVI elevation=101 m PVC station=PVI…

Q: Find the distance from the point (3, 2, 5) to the plane whose general equation is 2x + 3y - z = 0.

A: we have to find the distance from the point (3,2,5) to the plane whose general equation is 2x+3y-z=0…

Q: 5) Find the orthogonal trajectory of the family of curve given by y = In(r+b) %3D

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Q: find a parametrization for the curve. the line segment with endpoints (-1, 3) and (3, -2)

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Q: find a parametrization of the curve. The line passing through (1, 0, 4) and (4, 1, 2)

A: Given: A line is passing through the points 1, 0, 4 and 4, 1, 2.

Q: Find the intersection between the plane  4x−y+5z=18  and the line through the points  (0,0,1)  and…

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Q: An angle with its vertex at the origin of an xy-coordinate plane and with initial side on the…

A: We know, An angle with its vertex at the origin of an x-y-coordinate plane and with initial side on…

Q: Find the slope of the tangent line to the ellipse = 1 at the point (x, y). 16 slope = Are there any…

A: consider the equation of the ellipse, x24+y216=1 differentiate the equation using implicit…

Q: Where does the line through (1,0, 1) and (4,– 2,2) intersect the plane x+y+z = 6?

A: It can be assumed that the vector for the coordinate 1,0,1 is 1,0,1 and the vector for the…

Q: Find the distance from the point (3, -4, 2) to thea. xy-plane b. yz-plane c. xz-plane

A: The 3D view of the point is as below

Q: 11) Find the distance between point A(-3, 1,1) and the line of symmetric equations x = -y = -z.

A: This question is related to coordinate geometry, We will solve it using given information.

Q: Find the equations of the tangent plane and the normal line at point (1,1,-2) to surface z^2 =…

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Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, - 1, 2) is parallel | to the line x=…

A: Given that points are (2,1,-1), (0,-2,0) and (1,-1,2) The parametric equation is,…

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: What does it mean for two families of curves to be mutually orthogonal?

A: Two families of curve are said to be mutually orthogonal if they intersect at right angles. Angles…

Q: sketch the curve ƒ(x, y) = c, together with ∇ƒand the tangent line at the given point. Then write an…

A: sketch the graph of x2-xy+y2=7

Q: 4 Find a parametrization for the line segment with endpoints (-1,3) and (3,-2).

A: 4) To find the parametric equation of line segment with endpoints (-1,3) & (3,-2)

Q: Find the slope of the tangent line to the ellipse = 1 at the point (z, y). 36 slope = Are there any…

A:

Q: Find the tangent and normal lines to the curve ペー9ーチ at the Pomt (-62)

A: Given, The equation of the curve  x2-xy+y2 = 7  We have to find the equation of tangent and normal…

Q: Find the point-normal form equation of the plane containing the point (1, -3, 5) and the line with…

A: Solution: P(1 , -3 , 5) (2 - x ) = (y+1)/2 = -z/3 = t

Q: Find the orthogonal trajectories of the family of circles with center at the point (0, 1) and radius…

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Q: Find the shortest distance from the point P(2,-1, 1) to the plane with =quation x - y + 2z = –1 and…

A: Shortest point of the given plane and point P.  Distance from the point P and Q

Q: Find equations of the line through the point (1, −1, 1) perpendicular to the line 3x = 2y = z and…

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Q: Straight lines with slope twice the x-intercept.

A: Let us assume x-intercept is a. That is, x = a when y  =0. So,  slope  =2a. Let us assume that the…

Q: A line segment bounded by two points (0,0,0) and (2,2,0) is rotated about the y-axis by 270 degrees.…

A: We will first parametrize the line as a function of t , then with the help of rotation (u) matrix we…

Q: Find a parametric representation of a straight line through (1,1,1) and (4,0,2), and sketch it using…

A:

Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

A: Equations of the curve in the given question is: Slope of tangent line is given by dy/dx, hence…

Q: Obtain the dirfferential equation of the family of curves:  1. All circles passing through the…

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Q: 3. Find an equation the plane curve about the inc

A: INTRODUCTION: In mathematics, functions are the most fundamental aspect of calculus. Functions are…

Q: Find the tangent plane to surface 8x2 + y2 + 4z2 = 25  at the point ( 1, -1, 2 )

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Q: Chebyshev's theorem is used when there is a bell shaped curve

A: Chebyshev's theorem is used when we want to find the the upper bound  of the probability. And they…

Q: The line through the origin whose projection on the xy-plane is a line of slope 3 and whose…

A: In this type of questions we assume a line an points on that line. Suppose we have a line and points…

Q: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: Find an equation of the tangent plane to the surface at the given point. 5x2 + 2y2 + 5z2 = 73,    P…

A:

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 − 7z2 = 27,   (−3,…

A: Differential equations are those equations of mathematics that involve dependent variables ,…

Q: Calculate the distance between the points M=(-9,8) and L=(-1, 1) in the coordinate plane. Give an…

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Q: Find parametric equations for lines passing through point Pand parallel to vector n: (а) Р(3, — 1,…

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Q: Write the equation of the plane passing through point (3, 8, 3) that is parallel to the xz-plane.. X…

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Q: Does this curve go through the point (-1, 1, -1)?

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Q: 2. Obtain an equation for a plane a that includes straight line(2--5) and 1: point(-2,1,1)

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Q: The 50 g bullet travelling at 100 ms-1 strikes the 2 kg block centrally and is embedded within it.…

A: Please check step 2 for the solution.

Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, -1, 2) is parallel to the line x 1-t,…

A: equation of plane for non collinear points , x-x1y-y1z-z1x2-x1y2-y1z2-z1x3-x1y3-y1z3-z1 we will use…

Q: Find the length of the curve. (Hint: u-s

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Q: Find the distance from the point (3, -4, 2) to the xy-plane

A: Given: 3,-4,2

Q: find the slope of the tangent to the curve of intersection between 6z=3squareroot(20-x^2) and the…

A: the cylinder equation is given by  and the plane is given by  We want to define each variable in…

Q: Find the orthogonal trajectories of the family of parabola described by the equation (x+2} = cy.…

A: Explanation of the answer is as follows

Q: .3 The curve y3Dx+ x*-x has two horizontal tangents. Find the distance between these two horizontal…

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Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

A: Given:

Q: Where does the line through (-3, 1, 0) and (-1, 7, 4) intersect the plane 2x + y -z = -2?

A: