A particle moves along a straight line. For 0 <= t <= 5, the position of the particle is given by s(t) = 3t + 4t^2 - t^3 What is the average velocity of the particle over the interval 0 <= t <= 4?
Find a general expression for the velocity of the particle as a function of time, v(t), and determine the value of v at t=2. Is the particle traveling to the left or the right at this point? Justify your answer.
Find all times t during the interval 0 <= t<= 5 that the particle changes direction. Justify your answer.
At t = 4, is the speed of the particle increasing or decreasing? Justify your answer

The roman empire fell around the 5th century, and as islam spread in the 7th century, trade between europe and china slowed. chinese traders were blocked from westward expansion into europe when the chinese army was defeated by muslim fighters in the area known as syr darya. the trade routes, known as the silk road, fell into disuse, and trade between the far east and europe nearly stopped. it wasn't until the 13th century when the mongols invaded and controlled central asia and large parts of the middle east that extensive trade along these routes was opened again. based upon the paragraph above and your knowledge of the mongols, which of the following statements is correct? a. the mongols unified regions along the silk road, allowing for safe transport of goods. b. muslims controlled busy trade routes into china from the 5th to the 7th centuries. c. without access to european markets, the chinese were unable to obtain raw materials. d. the mongols replaced the roman empire as the dominant force in western europe.

How can firms use marginal analysis to determine the price of a product? a) profit maximization can occur when the marginal cost exceeds the marginal revenue. b) the total cost of production can determine the individual unit price of a product. c) marginal analysis can be used to determine at what price profit maximization occurs. d) firms can calculate the marginal cost of a product and set the price lower than the cost.

You want free points & brainliest? answer this drivers ed question correctly and i got you in which of the following situations should you use your vehicle's hazard lights? a. you're stopped on the side of the road with an engine that won't start. b. you're driving toward the shoulder because you hear a strange noise. c. you're driving in the rain and your headlights aren't functioning. d. you're driving slowly because you just spilled coffee on your lap.