Define plane curve?

Q: What is the relationship between the tangent unit vector and the orientation of a curve? Explain.

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Q: simple contour that is not closed can cross itself. True or false ?

A: Answer is true

Q: Find the length of the arc of the curve from point P to point Q. 25 -5, 2 5, 2 У

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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 parametric representation of a straight line through (1,1,1) and (4,0,2), and sketch it.

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

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

Q: Find a parameterization for the line segment joining points (0,3​) and ​(6​,0) using the angle θ in…

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Q: Find a parametrization for the curve described below. the line segment with endpoints (4,4) and…

A: Given,  A line segment with endpoints 4, 4  and  6, 1  We have to find the parametrization of the…

Q: There are exactly two tangent lines from an exterior point to a circle. True or False? O True O…

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Q: About family of curves. Draw the curves in one Cartesian plane.

A: We draw the family of equation of the lines y+5=mx-3 for different values of m. [Blue lines] And we…

Q: define trapezoidal rule

A: To Define The Trapezoidal Rule

Q: Where an Interior point Exists?

A: Interior point: Let S⊆ℝn.  A point a∈ℝn is said to be an Interior Point of S if there exists an…

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: 3. What are the new coordinates of line segment AC if the triangle is dilated using a scale factor…

A: What are the new coordinates of line segment AC if the triangle is dilated using a scale factor of…

Q: Use Clairaut's theorem to draw the geodesics of the catenoid

A: Solution :-

Q: Calculate the mean curvature of the catenoid

A: Given; z=ax2+y2a

Q: y=csinx  Identify the curves that intersect the curves under a right angle.

A: Given- y = c sinx To find- Identify the curves that intersect the curves under a right angle.

Q: find the length of the latus rectum of the curve rsin^2x=cosx

A: rsin2x=cosxLet us change into cartesian coordinates uvPut u=rcosx and v=rsinxr×v2r2=urv2=uThis is…

Q: What are the three Properties of the bell shaped curve?  *in paragraph form, minimum of 6 sentences

A: Here we have to explain the 3 properties of bell curve

Q: Point F is 50 mm from a vertical straight line AB. Draw locus of point P, moving in a plane such…

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Q: Demonstrate how a central projection can transform parallel lines into intersectin lines.

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Q: Exercise 2. Find a formula for the curve which is traced by the motion of a fixed point on a wheel…

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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: Explain in words the meaning of the curvature of a curve. Is it ascalar function or a vector…

A: According to the question, we have to explain the meaning of curvature of a curve. It is defined as…

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: Explain Curvature of a Plane Curve?

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

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Q: Find the curvature of the curve =.

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Q: Discribe the topology through diagrams of surface and curves

A: Describe topology through diagrams of surface and curves.

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 of the curve ,4=3+3, OLtbl length 3+3, 0Ltbl 大こ 4モ2

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Q: A rectangle us reflected across a vertical line. What is the resulting shape?

A: A rectangle is reflected across a vertical line:

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

A: Here,

Q: A simple contour that is not closed can cross itself

A: Contour means simply a curve and simple means curve that doesn't intersect itself. If a simple…

Q: Cannot solve

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Q: by fev ving the curve in the indicated Coordinate plane about the given axis. Equation of Curve 22 -…

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Q: How to use the trapezoidal rule to approximate distance travel?

A: The trapezoidal rule is used to estimate the area under the curve. The expression for the…

Q: Point F is located at (4, 7) and point G is at (-3, 10) what is the midpoint of segment FG?

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Q: 1. Find the distance from the point to the given line by using the distance theorem…

A: Suppose the line l is Ax+By+C=0 and any point is P0x0, y0. Then the distance from the point P0 to…

Q: What is the locus of the center of a penny that rolls around and remains tangent to a half-dollar?

A: Concept;   Similar to circle sphere is a two dimensional space where the set of points that are at…

Q: Find a path that traces the circle in the plane y=5 with radius r=2 and center (-1,5, -4) with…

A: The radius if circle = 2 and center (-1,5,-4) The equation of such circle is given by: The…

Q: Define corner point?

A: Corner points are the vertices of the feasible region. When there is a system of liner inequalities,…

Q: What is the curvature of a straight line?

A: Consider an equation of straight line, f(x)=mx+b Hence, f'(x)=m   and    f''(x)=0 Therefore,…

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: What is the significance of arrows along a plane curve?

A: What is the significance of arrows along a plane curve?

Q: Find the curvature of the curve ř= .

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Q: G find the distance between fwo point (-6, 1,4), (4,0,-5)

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

Q: Is this curve a twisted cubic, parabola, line, or helix?

A: The objective is to check whether the curve is a  twisted cubic, parabola, line, or helix.…

Q: What is the definition of curvature?

A: