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- continuous from attached image... ... to the graph of y2 - 3x + 2 = 0. (do not simplify or evaluate)On the interval -4 < x < -3, the function is… •maximum •minimum •increasing •decreasing •constantA rectangle is inscribed in the region bounded by the graph of y= e1-2x^2 and have one of its side lie on the x-axis. What are the dimensions of such a rectangle with the largest possible area?
- The population, P, of the city of Hazelton has grown according to the mathematical model P = 65,000(1.075)*, where t is the number of years since 2005. a) At what percentage is the population growing? b) If this trend continues, during which year will the population reach approx. 100,000?The total daily profit (in thousands of pesos) of a certain food company for the sale of x boxes of buko pie is given by the profit function P(x)=-0.001x^3+0.1x^2+3x-300 , where x is greater than or equal to 0 but less than or equal to 30. Determine the number of boxes of buko pie to be produced in order for the company to realize a maximum profit.A rectangle is inscribed in the region bounded by the graph of y= e1-2x^2 and have one of its side lies on the x-axis. What are the dimensions of such a rectangle with the largest possible area?
- Does x=3 belong to a local maximum or a local minimum? Does x=6 belong to a local maximum or a local minimum? Does x=0 belong to a local maximum or a local minimum?What are the conditions for a critical point of a function ƒ?The bar graph shows the number of fatal vehicle crashes per 100 million miles driven for drivers of various age groups.25-year-old drivers areinvolved in 4.1 fatal crashes per 100 million miles driven. Thus, when a group of 25-year-old Americans have driven a total of 100 million miles, approximately 4 have been in accidents in which someone died.The number of fatal vehicle crashes per 100 million miles, y, for drivers of age x can be modeled by the formulay = 0.013x2 - 1.19x + 28.24.Use the formula above and the bar graph.What age groups are expected to be involved in 10 fatal crashes per 100 million miles driven? How well does the formula model the trend in the actual data shown by the bar graph?
- sketch the graph, noting the transition points and asymptotic behavior. y = 3/2 x x3 + 1The success of a project depends on the effort level of a worker. In case of successthe revenues will be 400,000 TL whereas in case of no-success the revenues will be 0. The workercan provide a low effort level or a high effort level. The effort level cannot be observed by theprincipal. The worker requires an expected salary of 60,000 TL to provide the low effort leveland an expected salary of 80,000 TL to provide the high effort level. The success probabilitiesfor the project are 40% in case of low effort level and 80% in case of high effort level. Whatshould be the minimum bonus (that is awarded in addition to the base salary in case of success)and the base salary for the worker so that the worker has the incentives to provide the higheffort level?Suppose a man is 30 years old and would like to retire at age 60. Furthermore, he would like to have a retirement fund from which he can draw an income of $75,000 per year—- forever. How can he do it? Assume a constant APR of 6%. He can have a retirement fund from which he can draw $75,000 per year by having $? in his savings account when he retires.