How do you measure distance along a smooth curve in space from a preselected base point? Give an example.

Q: Find the length of the latus rectum of the curve rsin²x=cosx

A: The given curve is: rsin2x=cos x

Q: Draw a smooth curve starting at point C and tangent tő the line segments. Label the other end of the…

A:

Q: The exact value of the curvature of ƒ(x)=arcsin x when x= , can be expressed as the product of a/b…

A: Given,               f(x)= arcsin xDifferentiating both sides with respect to x…

Q: Prove that moments are independent of change of origin but not of scale.

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Q: Describe an Ogive curve in brief.

A: Answer: For the given question,

Q: Define tangency for general curves?

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Q: 4. Does there exist a simple closed unit-speed plane curve with curvature less than or equal to 2…

A: In a simple closed unit-speed plane curve, curvature =1r According to the question, Area of the…

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: A stream line is a line that is everywhere tangent to the velocity filed

A: Streamlines are a family of curves that are instantaneously tangent to the velocity vector of the…

Q: The change of the shape of continuum is called strain

A: Yes , The change of the shape of continuum is called strain .

Q: A tangent line from a point to a circle touches the circle in two points. True or False? O True O…

A: A tangent line from a point to a circle touches the circle in two points.True or False?Answer   :…

Q: Describe the transformation rules that map Circle F onto Circle F'. Translation rule: (x, y) -->…

A: We have to find dialtion

Q: How can draw a Lorenz curve ?

A: ANSWER: For the given question, we have,

Q: Plot a function for which every secant line has a parallel tangent in between the points of secancy.

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Q: Find all points of horizontal and vertical tangency to the curve: x = 3cos 0 y = 3sine

A: for Horizontal tangent put dydθ=0 for the vertical tangent put dxdθ=0

Q: Determine if line XY is tangent to circle Z. Please show work.

A: using pythagoas theorem

Q: (a) How do you find the slope of a tangent to a parametric curve?

A: (a) Assume a general parametric curve. Differentiate and find the derivatives.

Q: Use the guidelines of curve sketching to sketch the curve y = 1-x2 %3D

A: Given: y=x1-x2

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

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Q: What curves have zero curvature?

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Q: Eevery comPact and Ta- SPace is Tus Pa ce

A: Let us prove this theorem.

Q: A stream line is a line that is everywhere tangent to the velocity filed صواب İhi

A: Streamlines are a family of curves that are instantaneously tangent to the velocity vector of the…

Q: cally integra then in any ng curves is

A:

Q: Let F=-yi+xj and let C be a curve consists of the line segment C₁ from (0,0) to (4,0) followed by…

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Q: It is a line, ray. or segment that intersects the circle at exactly one point. O tangent line secant…

A: Let's find.

Q: Give a geometrical interpretation of torsion.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the distance between the points (-1,4) and (3, -6). Give the exact distance and an…

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Q: Dar Show that the length of the the Curve y=foor where Fox)= Insee t

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Q: What is a parametrized curve? Give an example?

A: A curve or a vector in three dimensional or in two dimensional space is such that it basically…

Q: Represent as a parametric curve the rotation of a rod of length 2 that makes 1 full turn every 3…

A: Rotation in a plane, let it be xy- plane. There are two possibilities, center of rotation is the one…

Q: Find the distance between the pair of points. Give an exact answer and a three-decimal-place…

A: In this problem we have to find the distance between given points.

Q: Find all points (if any) of horizontal and vertical tangency to the portion of the curve shown.…

A: Given  x=cosΘ+ΘsinΘ Y=sinΘ-ΘcosΘ We will find the vertical and horizontal tangent

Q: Show that the average straight-line distance to a fixed point on the surface of a sphere of radius a…

A: As per the hint we will assume the north pole (0,0,1) as the fixd point. Then in order to find the…

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: Define Central and Non-Central moments.

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Q: 4) The lemniscate curve (x² + y²)² = 4(x² – y²) was discovered by Jacob Bernoulli in 1694, who noted…

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Q: Find the tangent line to the curve 2y + " = ye"-2 at the point (2, ). %3D Please select file(s)…

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Q: 2.Proof that any tangent plane for the surface F(- point = 0 passses through a fixed

A: Given below clear explanation

Q: Sketch the curve y cu. = x sq.

A: Given the curve is y3 = x2 Put random value in the curve and we get the table which help to trace…

Q: curves. Decide whether to integ

A: The given curves are: 2y=5x, y=3, and 2y+2x=7 Find the area of the region and sketch the graph.

Q: Cannot solve

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Q: Let C be the curve of intersection of length of C from the origin to the poi

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

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Q: Use either a computer algebra system or a table ofintegrals to find the exact length of the arc of…

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Q: Find distance between point A(1,3) Perpenclicular the line L: 2y =2+X on

A:

Q: Are parametrizations of a curve unique? Give examples.

A: A parametric representation of a curve is not unique. That is, a curve C may be represented by two…

Q: must

A: When a curve changes from concave down to concave up or concave up to concave down , that means…

Q: What is a flat surface that extends infinitely in all directions?

A: Plane.

Q: À line that intersects a circle at only one point is called a tangent.

A: Determine whether the given statement is true or false.

Q: A stream line is a line that is everywhere tangent to the velocity filed ylgn ihi

A: The statement is TRUE