5. Sketch the vector-valued equations r(t)=2costi+3sintj. Then, find the curvature of the ellipse at the endpoints of the major and minor axes, by using formula K =!

Q: vector-valued function 7(t) the parametric equations of the line.) b) Find the distance of the point…

A:

Q: how was it determined that the equation of the yz plane is x = 0?

A: The objective is to explain yz-plane equals .

Q: Find the distance between the point (p, 4p) and the parabola y? = 2px, where p is a fixed positive…

A: let the point on parabola be A= (x, y)  B = (p, 4p) Thus,  AB = x-p2+y-4p2 but parabola is y2=2px…

Q: Find the curvature of the ellipse with major axis's length (12) and minor axis (6) at the point…

A: The curvature K of a curve y=fx is given by, K=d2ydx21+dydx232⋯⋯1 where, f'x and f''x are the 1st…

Q: A bee starts at the point (5, 7, -3) (with units in meters) and travels at a constant speed of 9 m/s…

A:

Q: Determine the direction angles for the line with parametric equations x = 5 + 2t, y = 12 - 8t, and z…

A: Direction angle

Q: 1 Write the parametric equations x = 1 + ½ 2, y = t − 2 as a vector function, and then plot the…

A: Step 1: Step 2: Step 3: Step 4:

Q: Li Syaoran is riding an airplane which departs from an airport located at (360, 0) miles in the…

A: The westward speed of the airplane = 480 miles/ hour The northward speed of the airplane = 120…

Q: Abee flies around a room at an altitude of 2 2.3 meters making circles, so that its a coordinate…

A: Solution :  To write the parametric equation to describe the motion

Q: Find the parametric equations for the line through the point (5, 2, 9) and perpendicular to the…

A: The parametric equation of a line passing through the point and has a direction cosines <a , b…

Q: tangent plane at the point (-2,1 – 3)

A: Equation of the tangent plane = dfdxx-x0+dfdyy-y0+dfdzz-z0 Let f=x24+y2+z29-3 (given)

Q: Find the angle between the two planes x- 2y + z = 29, 2x + 3y – 2z = 6. And also find the parametric…

A: here we will find angle between two planes and parametric equation of plane's line of intersection,

Q: π The path r(t) = (6 cos t) i + (6 sin t) j describes motion on the circle x² + y² = 36. Find the…

A: Given, r(t)=(6cos t) i+(6sin t) j Path of the motion described by x2+y2=36 To find : velocity and…

Q: 64. Find equations of both the tangent lines to the ellipse x² + 4y2 = 36 that pass through the…

A: Given: The Equation of the ellipse is x2 + 4y2 = 36