Answer:
T(x) = 180x³ - 630x² + 1090x + 200
Step-by-step explanation:
- The number of TVs produced can be modeled by M(x) = 3x² - 11x + 20 , where x is number of years since 2000
- The average revenue per TV(in dollars) can be modeled by R(x) = 60x + 10
- The total revenue is the product of the revenue per TV and the number of TV
Total revenue = M(x) . R(x)
∵ M(x) = 3x² - 11x + 20
∵ R(x) = 60x + 10
∴ Total revenue = (3x² - 11x + 20)(60x + 10)
∵ T(x) can be used to model Mr. Renzo's total revenue
∴ T(x) = (3x² - 11x + 20)(60x + 10)
Let us multiply each term in the 1st bracket by each term in the 2nd bracket, then add the like terms
(3x² - 11x + 20)(60x + 10) = 3x²(60x) + 3x²(10) + (-11x)(60x) + (-11x)(10) + 20(60x) + 20(10)
(3x² - 11x + 20)(60x + 10) = 180x³ + 30x² + (-660x²) + (-110x) + 1200x + 200
Remember (-)(+) = (-)
(3x² - 11x + 20)(60x + 10) = 180x³ + 30x² - 660x² - 110x + 1200x + 200
Add like terms
(3x² - 11x + 20)(60x + 10) = 180x³ + (30x² - 660x²) + (-110x + 1200x) + 200
(3x² - 11x + 20)(60x + 10) = 180x³ - 630x² + 1090x + 200
∵ (3x² - 11x + 20)(60x + 10) = 180x³ - 630x² + 1090x + 200
∵ T(x) = (3x² - 11x + 20)(60x + 10)
∴ T(x) = 180x³ - 630x² + 1090x + 200
