4. Does there exist a simple closed unit-speed plane curve with curvature less than or equal to 2 and length less than 3? Justify your answer in detail.

Q: Find a, b, c, and d such that the curve ?=??3+??2+??+? has its tangent line at(1, 1) and at (0, -2)…

A: The objective of this question is to find the coefficients a, b, c, and d of the cubic function y =…

Q: A variable straight line is drawn through the point of intersection of the straight lines x/a+y/b=1…

A: Given lines arexa+yb=1               ....(1)and  xb+ya=1               ....(2)Solving (i)and(ii) we…

Q: A highway has an exit ramp that begins at the origin of a coordinate system and follows the curve y…

A: A highway has an exit ramp that begins at the origin of a coordinate system. It follows the curve…

Q: What curves have zero curvature?

A:

Q: 4. Find the radius and center of curvature of the curve y=6x-x³ at the point (1,5).

A: This question is based on radius and centre of curvature formula.

Q: b. The y' of the curve y 4 Vx

A: The given function is y=4x. Obtain the first derivative as follows. y'=ddx4x=ddx4 x-12=4…

Q: Describe the condition for a curve to be rectifiable between two points.

A:

Q: Prove that the part of the tangent at any point of the hyperbola x²y² =1 intercepted between the…

A: We have to prove that the part of the tangent at any point of the hyperbola…

Q: 2) Find and sketch the circle of curvature at the point on the curve y = x² where the tangent line…

A:

Q: A parabola has an equation of y²=2x, compute the radius of curvature at point (2, 2)

A:

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: A hyperbola is defined by the equation x2 - y2 - 2x - 4y - 4 = 0. Its center is at the point (-1, 2)…

A:

Q: What is y = _ + x3 1 curve x = 1 and x = 2 the length of the part 12 х between the abscissa points?

A: We find dy/dx using the power rule

Q: 3 2 from Find the length of the curve a = 24 19 , 4) the point (, 2) to the point

A: