Suppose a particle of mass m has position given by r(0) =< 1,0,0 > , and velocity given by v(0)0,1,-1 > at time t = 0. also, assume that for every time t 20 the particle experiences only the force given by the vector function f(t) = m < -cos(t), 0, sin(t) > . disregard units in this problem a) use newton's second law, f(t) = ma(t) (where a(t) is the acceleration vector of the particle at time t) in order to show that r(t) =< cost, t,-sin t > gives the particle's position at time t, for t 2 0. show all the necessary work to find this position vector function, do not simply check that it is correct b) sketch the particle's path for t 2 0 c) determine the curvature of the particle's path at time t d) assume a second particle is also present, and has a position given by the vector equation r2(t)sin(t)-1,n-t, cos(t) -1> , for t 2 0. determine at which times (if any) the particles collide. determine at which points in space (if any) the paths of the particles intersect

Which is not one of the major climate zones? question 3 options: rain forest polar tropical temperate

Use the frequency histogram to complete the following parts. ​(a) identify the class with the​ greatest, and the class with the​ least, relative frequency. ​(b) estimate the greatest and least relative frequencies. ​(c) describe any patterns with the data. female fibula lengths 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 0 0.05 0.1 0.15 0.2 0.25 length (in centimeters) relative frequency a histogram titled "female fibula lengths" has a horizontal axis labeled "length in centimeters" from 30.5 to 39.5 in increments of 1 and a vertical axis labeled "relative frequency" from 0 to 0.25 in increments of 0.05. the histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. the approximate heights of the vertical bars are listed as follows, where the label is listed first and the approximate height is listed second: 30.5, 0.02; 31.5, 0.04; 32.5, 0.05; 33.5, 0.13; 34.5, 0.22; 35.5, 0.25; 36.5, 0.13; 37.5, 0.06; 38.5, 0.09; 39.5, 0.01. ​(a) the class with the greatest relative frequency is nothing to nothing centimeters. ​(type integers or decimals. do not round. use ascending​ order.)

Infrared rays have a shorter wavelength than question 11 options: x-rays. ultraviolet rays. radio waves. gamma rays.