The acceleration vector of a particle moving in space is a(t) = 2i + 6t j + 2k. (i) find the position vector r(t) provided that the particle has initial position r(0) = j and initial velocity v(0) = −5j. (ii) compute the curvature of the trajectory r(t) at the point (1, −3, 1).

Add, subtract, multiply, or divide as indicated. list any restrictions for the variable(s) and simplify the answers when possible. 1) x-2 / x+5 + 3x / 2x-1 2) x+6 / x-6 - x^2 / x+6 3) x+9 / x-4 + x+2 / x^2-11x+28 4) x / x^2-64 + 11 / 2x^2+11x-40 5) 5 / x + 11 / x-3 - x-4 / x^2+2x-15

Will mark ! (10 points also! ) if x varies inversely with y and x =6 when y= 10, find y when x=8 a. y=4.8 b. y=7.5 c. y=40/3 d. y=4/15

Graph the following system of linear inequalities. identify at least two points in the solution: y < 5 - 2x | x + 5y > -7