Consider R = {x:x>0}. We define the following operations: xBy xy Show that V= (R+,,D) is an R-vector space. cx x for c ER

Prove: iv. If (x, y) = 0 for all x & R², then y must be the zero vector. e

Please solve this linear algebra problem with a good explanation.

You are on a rollercoaster, and the path of your body is modeled by a vector function r(t), where t is in seconds, the units of distance are in feet, and t = 0 represents the start of the ride. Assume the axes represent the standard cardinal directions and elevation (x is E/W, y is N/S, z is height). Explain what the following would represent physically, being as specific as possible. These are all common roller coaster shapes/behaviors and can be explained in specific language with regard to units: a. r(0)=r(120) b. For 0 ≤ t ≤ 30, N(t) = 0 c. r'(30) = 120 d. For 60 ≤ t ≤ 64, k(t) = 40 and z is constant. e. For 100 ≤ t ≤ 102, your B begins by pointing toward positive z, and does one full rotation in the normal (NB) plane while your T remains constant.