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Problem 1: You are standing at the edge of a slow-moving river, which is one mile wide, and wish to return to your ground on the opposite side of the river. You will swim at 2 mph and walk at 3 mph. You must first swim across the river to any point on the opposite bank. From there walk to the ground, which is one mile from the point directly across the river from where you start your swim. What route will take the least amount of time?
Problem 2: A cylindrical can is to hold 20 m3. The material for the bottom and top costs $10/m2 and material for the side costs $8/m2. Evaluates the radius r and height h of the most economical can.
Problem 3. Show that an equilateral triangle provides the most area for a fixed perimeter.
Problem 4. The sides of an equilateral triangle are decreasing at a rate of 4 in/hr. How fast is the area enclosed by the triangle decreasing when the sides are 3 feet long?
Problem 5. What angle should my son aim his stomp rocket to get the maximum range? Justify your answer using methods from this class.
Problem 6. If he sets the launcher on a chair and goes for maximum range, how high will it go and at what time will it hit its apogee?
There is a difficult question on my assignment regarding the Mandelbrot set. It asks for me to develop a general rule for the set of c values that will be part of the set.
Consider a seven-game world series between team A and B, where for each game, what is the most likely number of games to be played in the series for p=0.6?
Determine the braking force required to slow the train of cars by this ammount by using the following method; the laws of motion and d'alemberts principle.
Suppose postal requirements are that the maximum of the length plus the girth (cross sectional perimeter) of a rectangular package that may be sent is 200 inches. Find the dimensions of the package with square ends whose volume is to be maximum.
A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is π/3, this angle is decreasing at a rate of π/6 rad/min. How fast is the plane traveling at that time? (Ro..
The interest formula shows how interest, rate, and time are related. It gives you a way of finding one of these values if the other three values are known. Even though you try to be careful in your calculations, there will always be that occasion ..
The value of EFX Corp. began the day at $17.68 per share and dropped $1.63 per hour for 8 hr. What was the price of the stock after 8 hr?
Find the dimensions of the largest acceptable box with square front and back. (Let x be the measurement of one side of the square front. Let y be the length of the box.)
Find the Fourier series for the odd extention of the function
What is the cost for both the ePhone and SmrtPhone if 28 hours are used?
Explain Stock probability, We have been informed that the stock has gone up 20%. What is the probability of a rise or fall in the GDP?
Discuss an example of a way you use, or can use, a system of equations in your life? Describe a situation where a system of equations has no solution, and prove it mathematically.
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