I dont wanna spam forum so I'll be lumping 4 problems in a post as to not clutter the forum, however I'll be happy to repost the questions seperately if im accidentally breaking a forum rule here.
Question 1. A particle moves along the y-axis so that at any time t is greater than or equal to 0, velocity is given by v(t)=3t^2-sin(t). At time t=1, the position of the particle is s(1)=8. Determine the position of the particle at t=5.
Question 2. f prime of x = ln(3x^2-5) and f(3)=pi. Find f(4)
Question 3. A cake with a temperature of 325 degrees fahrenheit is put into a 72 degree fahrenheit room when t=0. The cake's temperature is changing at a rate of r(t)= -4.2e^(-.12t) degrees fahrenheit per minute. Estimate the cake's temperature when t= 10 minutes.
Question 4. Road salt leaks out of a truck at a rate of dV/dt = 1/50(50-12t-9t^2) where dV/dt is measured in cubic cm per hour and t is measured in hours. If there are 1000 cubic cm of road salt in the truck at time t=0, how many cubic cm of road salt are in the truck when t=5?
Thanks in advance to anyone who gives these a shot.
