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- Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0 ≤ t ≤ 5. Please explain your steps. Thank you.Subtracting the two equations, find a vector equation for the curve of intersection between y= 4x2+(3/4)z2 and y-1= 3x2+(1/2)z2 for x>0. Find and simplify the tangential component of acceleration for your curve.
- How do you find the velocity and acceleration vectors at t=-1?Find the requested vector. The velocity at t=pi/4 for r(t)=4sec^2(t)i-5tan(t)j+10t^2kThe path r(t) = (t) i+ (2t + 5) j describes motion on the parabola y = 2x + 5. Find the particle's velocity and acceleration vectors at t= 0, and sketch them as vectors on the curve. %3D
- A particle started at A(1,0) circled the origin once an d returned toA(1,0) .what were the change in its coordinatesAt time t = 0, a particle is located at the point (8,4,7). It travels in a straight line to the point (3,9,6), has speed 3 at (8,4,7) and constant acceleration negative 5i + 5 j - k. Find an equation for the position vector r(t) of the particle at time t.At time t = 0, a particle is located at the point (4,8,6). It travels in a straight line to the point (1,7,2), has speed 2 at (4,8,6) and constant acceleration - 3i -j- 4k. Find an equation for the position vector r(t) of the particle at time t.
- Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0 ≤ t ≤ 1. Please show all your work.The path r(t) = (t) i + (3t2 +7) į describes motion on the parabola y = 3x + 7. Find the particle's velocity and acceleration vectors at t= - 4, and sketch them as vectors on the curve. The velocity vector at t= - 4 is v(- 4) = (D i+ (Di (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)The position vector r describes the path of an object moving in space. Position Vector Time r(t) 3ti + tj + 1 t²k t = 4 8 (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. =
