1. [3/10 Points] DETAILS PREVIOUS ANSWERS SCALCET9 3.7.003. A graphing calculator is recommended. particle moves according to a law of motion s = ((t), t 2 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) At) - sin (a) Find the velocity (in ft/s) at time t. v(t) - cos(2 ). () ft / s (b) What is the velocity (in ft/s) after 1 second? v(1) - cos ( =) .( 7) ft /S (c) When is the particle at rest? (Use the parameter n as necessary to represent any integer.) t = 0,2,4,6 (d) When is the particle moving in the positive direction for 0 s t s 6? (Enter your answer using interval notation.) (e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds. (f) Find the acceleration (in ft/s") at time t. a(t) = ft/s Find the acceleration (in ft/s ) after 1 second. a(1) = At / s (9) Graph the position, velocity, and acceleration functions for 0 s t s 6. is 0-3 Do-3/ (h) When is the particle speeding up? (Enter your answer using interval notation.) [2,4 ] When is it slowing down? (Enter your answer using interval notation.) Need Help? Read It Watch It Submit AnswerSuppose a sample of a certain substance decayed to 73.6% of its original amount after 300 days. (Round your answers to two decimal places.) (a) What is the half-life (in days) of this substance? (b) How long would it take the sample to decay to one-third of its original amount? Need Help? _' The half-life of cesium-137 is 30 years. Suppose we have a 140 mg sample. (a) Find the mass (in mg) that remains after t years. y(t)= Hog(i) " m9 (b) How much of the sample (in mg) remains after 140 years? (Round your answer to two decimal places.) - mg (c) After how many years will only 1 mg remain? (Round your answer to one decimal place.) r=-x w Need Help