This is calculas and vectors homework and i need answers for it to check if i am right

Short Answer 1. Describe the particle's acceleration at time ? = 2 s if its position is described by the function s(!) = (21 - 1)?. 2. Let s(1) = -51" +401 + 1 describe a toy rocket's motion as it is launched vertically into the air. Determine the maximum height, in metres, that it reaches over the time interval 1 S / $ 5. 3. Let the graph below represent an object's velocity as it moves away from a sensor. At what time, in seconds, is the object furthest from the sensor? 2 -It -2- 4. Determine the maximum height a baseball reaches as it is hit if its height can be represented by the function s(1) = -512 + 551+2. 5. A pizza shop is having a special, for one week all large pizzas will only cost consumers $6.00. If the cost to the shop to produce the pizzas is represented by the function C(x) = 10- 15x +0.15x, how many pizzas can the shop sell before they begin to lose money? 6. Let A(x) = = x+3 x2 - x - 12 . What is the equation of the vertical asymptote of f(x)? What is the sign of f(x) as x approaches the asymptote from the right? 7. Calculate f "(x) for the function f(x) = 4". It may help to first determine a pattern.Name: ID: A Problem 8. a. Graph the function with a local maximum at (-1, 2), a local minimum at (1, -2), an absolute maximum at (3, 18), and an absolute minimum at (-3, -18). b. Determine the domain of the function. c. Where is the function increasing? decreasing? 9. Suppose the population (in thousands) of a certain species of insect after / months is described by the function P(1) = 4/ + = 1001 + 500. Determine the maximum population in the first three months. 12 + 400 10. A document is to contain 80 square centimetres of print. The margins at the top in bottom of the document are each 2 centimetres wide and the margins on each side are 3 centimetres wide. What should be the dimensions (in centimetres) of print so that a minimum amount of paper is used? 11. The decay of a certain substance is modelled by the function N(t) = 100(3 + e '), where the number of particles is represented by N in a time of t hours. a. What is the initial number of particles? b. Determine the rate of change in the number of particles at time t. c. How fast is the number of particles changing when t = 3 hours