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Question: The Montgolfier brothers (Joseph and Etienne) were eighteenth-century pioneers in the field of hot-air ballooning. Had they had the appropriate instruments, they might have left us a record, like that shown in Figure 5.87, of one of their early experiments. The graph shows their vertical velocity, v, with upward as positive.
(a) Over what intervals was the acceleration positive? Negative?
(b) What was the greatest altitude achieved, and at what time?
(c) At what time was the upward acceleration greatest?
(d) At what time was the deceleration greatest?
(e) What might have happened during this flight to explain the answer to part (d)?
(f) This particular flight ended on top of a hill. How do you know that it did, and what was the height of the hill above the starting point?
Estimate the clutch size which maximizes the number of survivors per brood.
A helicopter flies 192 miles against the wind in 2 hours. With the wind, it can fly 288 miles in the same amount of time. Find the speed of the helicopter in still air.
Look up the original papers by Warshall and by Roy (in French) in which they develop algorithms for finding transitive closures. Discuss their approaches.
What other real-world factors might be important to consider in designing the simulation and making a recommendation?
Consider another example where a pack contains 4 blue, 2 red and 3 black pens. If 2 pens are drawn at random from the pack, replaced and then another pen is drawn. What is the probability of drawing 2 blue pens and 1 black pen?
Estimate the slope of the curve y = f(t) at t = 0 .2 . In principle, what is the relationship between this slope and the instantaneous speed?
On may 13, 2006, each euro was worth 1,43921 canadian dollars and each japenses yen was worth 0.00703195 euros. Find the value of 1000 japenese yen in canadian dollars on may 13th, 2006. Rround answer to two decimal places.
The purpose of this assessment is to help you determine whether you have a clear understanding of vectors and dot products. Answer the following questions to complete this exercise:
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or "washer." (Do this on paper.)
Sean's older brother is 16 years old. He runs between 15 and 25 miles each week. The sum of the digits of the total number of miles that he ran last week is eight less than his age. How many miles did Sean run last week?
In a Cartesian coordinate system, how many paths are there from the origin to the point with integer coordinates (m, n) if the paths are built up of exactly.
Review and reflect on what you learned in the past 8 weeks. What is the most practical and easily applied lesson you learned?
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