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1. An airplane ticket costs $200 if there are 50 or fewer people on the plane. But for each passenger over 50, the price per ticket is reduced by $2. (For example, if there are 52 passengers, then a ticket costs $196.) If revenue is maximized, how many people would be on the plane?
2. Determine the point(s) on the curve y = x2 + 1 that are closest to (0, 2).
3. Let x and y be positive numbers whose sum is 50 (i.e., x + y = 50). What is the largest possible value of the product xy?
4. The number of bacteria N grows according to the formula N(t) = 6000t , where t 60+t2 is measured in weeks. What is the maximum size of the population, and when does this happen?
5. How fast does the water level drop when a cylindrical tank with a radius of 6 feet is drained at a rate of 3 ft3/min? (The volume V of a cylinder is V = πr2h, where r is the radius and h is the height of the cylinder.)
a person collects coins nickels dimes and quarters in a jar. at the end of the year they emptied the jar and found that
The demand function for a product is given by p= -0.01x^2 - 0.1x + 6 where p is unit price and x is the number in thousands.
Can we conclude that women are more careful on the job?
In a survey of 122 customers connected in a shopping mall, 82 consumers indicated that they buy brand A of a certain product, 71 buy brand B and 46 buy both brands. How many consumers participating in the survey buy only brand A?
Graph the function and determine its domain and range. Choose the correct graph of the function.
Calculate the line integral ∫c (2J→ + 3k→) dr→ where C is the y-axis from the origin to point (0,10, 0). Please show work, so that I may understand the solution process.
a new process for producing synthetic diamonds can be operated at a profitable level only if the average weight of the
A hollow cone is cut by a plane parallel to the base and the upper portion is removed. if the volume of the frustum obtained is 26/27 of volume of the cone. find at what height above the base the section is made, if height of the cone is 30cm
Each edge of the complete graph with 11 vertices is colored either red or blue. We then look at the graph consisting of all the red edges, and the graph consisting of all the blue edges. Prove that at least one of these two graphs is NOT planar..
Describe the asymptotic behavior of the solution as x aproches to infinity when the constants a, b , and k are varied.
within 5minutes of waking we forget half of our dreams within ten minutes we forget ninety percent. if we remember 3
Professor Ivy decides to compare her families' heights to the heights of her husband's family and is able to model this with the 2 normal curves below. Her family is the dotted line. His is the solid.Describe how Professor Ivy's family heights are ..
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