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When a company produces and sells x thousand units per week, its total weekly profit is p thousand dollars, where upper p equals startfraction 800 x over 100 plus x squared endfraction . the production level at t weeks from the present is x equals 4 plus 2 t. find the marginal profit, startfraction dp over dx endfraction and the time rate of change of profit, startfraction dp over dt endfraction . how fast (with respect of time) are profits changing when tequals8?

Lillypad toys is a manufacturer of educational toys for children. six months ago, the company's research and development division came up with an idea for a unique touchscreen device that can be used to introduce children to a number of foreign languages. three months ago, the company produced a working prototype, and last month the company successfully launched its new device on the commercial market. what should lillypad's managers prepare for next? a. increased competition from imitators b. a prolonged period of uncontested success c. a sharp decline in demand for the product d. a difficult struggle to move from invention to innovation

Tara and her parents want to save at least $40,000 for college in 8 years. which statement describes the most effective savings plan for tara and her parents to meet their goal? tara and her parents should make deposits of $300 every month into a college savings account. tara and her parents should make deposits of $450 every month into a college savings account. tara and her parents should make deposits of $3,000 every year into a college savings account. tara and her parents should make deposits of $4,000 every year into a college savings account