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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?
What is the cost of manufacturing before any units are produced
De?nition of smoothness of functions on a smooth manifold is chart independent and hence geometric.
Prepare a Flexible Budget Gator Divers is a company that provides diving services such as underwater ship repairs to clients in the Tampa Bay area.
Find the break-even points and the maximum revenue.
Find the absolute maximum and minimum mpg
The first or second derivative test to show that the critical value is a relative maxima or minima.
Derive the Boolean Expression and construct the switching circuit for the truth table stated
Find the inverse of the matrix.
Satisfies the Cauchy-Riemann equations
Complex problems
Evaluate which equations are under-identified, just-identified, and over-identified.
Illustrate why the A and B are symmetric
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