Find the curvature and the radius of curvature at the stated poin r(t) = 11 cos(t)i + 10 sin(t)j+10tk; t = %3D NOTE: Enter the exact, simplified answers. 卡|2

Q: The parametric equations x= 3 - 8 sin 3t and y = 9 + 8 cos 3 t for 0 sts x/4 represent a curve C.…

A: Given data: x(t)=3-8sin(3t) y(t)=9+8cos(3t) for 0≤t≤π4 Solution: Length of parametric curve is given…

Q: Find the exact length of the curve described by the parametric equations. x = 1 + 6t2,    y = 5 +…

A: Find the exact length of the curve described by the parametric equations.x=1+6t2,y=5+4t3,0≤t≤3Using…

Q: What curves are represented by the following? Sketch them. [cos t, sin 2t, 0]

A: To Sketch: The curves represented by the parametric form [cos t, sin2t, 0].

Q: 1. Let C be a curve with a vector equation r(t) = (4 cos(t), -4 sin(t),-3t) where 0<t<÷. What is the…

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: Consider the unit circle given by x² + y² = 1. Which of the following parametric equations describes…

A: Introduction: In trigonometry, the unit circle has a radius of 1 and is centered at the origin.…

Q: Find the equation of the tangent to the function y = cos(2x) at the point where x = л/4.

A: equation of a tangent line

Q: Find dy/dx and d²y/dx². For which values of t is the curve concave upward?

A: x = t2 + 1 y = et - 1 dy/dx = dy/dt ÷ dx/dt

Q: 2. Sketch both parametric curves below. Then determine if they intersect. I they intersect, find the…

A: Introduction: All forms of curves that may be represented on a plane can be described by parametric…

Q: 1) Sketch the curve. a) r=-2 sin O Show All Work

A: Here we have to sketch the given curve.

Q: Find the length of the curve. r(t) (7t, 3 cos t, 3 sin t), -2 sts 2

A:

Q: (3) Evaluate f dz where C is the lower-half of the unit circle in clockwise direction.

A:

Q: Given the parametric equations x = 2(8 – sine) and y= 2(1 – cose). The second derivative of y with…

A: Let's find.

Q: Use symmetry to evaluate the followingintegrals.

A: The given integral is ∫-22x9-3x5+2x2-10dx.

Q: Given the parametric curve. x = cos t y = sin t 0 <t< 2T Please find the length of curve.

A:

Q: Eliminate the parameter for the given parametric equations to write an equation in the form of y=…

A: Given x=ln t and y=et

Q: Express in terms of "t" for the following parametric equation: da x = ln(t); y = = sin² (t) and…

A: Differential equation and it's solution

Q: Compute for the tangential velocity of a wheel rotating at a speed of 2000 rpm such that the radius…

A: Formula for tangential velocity Vt is: Vt=2πrt  here r is the radius of the wheel and t is the time…

Q: 1. Use a Trigonometric substitution to evaluate the following: Vy² – 25 -dy,y > 5 y Include a sketch…

A:

Q: Determine the intervals on which the function is concave up or down and find the points of…

A: For the point of inflection, we solve y"=0

Q: B. Find (Inx dx

A:

Q: Solve the problem. 10) Find the equation for the tangent plane to the surface 6x+5y - 5z = -9 at the…

A: