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A publishing company estimates the revenue from the sale of a popular book by the rational function where x is the number of years since publication and R(x) is the total revenue in millions of dollars. Find the total revenue at the end of the second year.
15. Solve the equation by using the quadratic formula. (Enteryour answers as a comma-separated list.)
x2 ? 4x ? 4 = 0
(a) Give exact real answers.x = (b) Give answers rounded to two decimal places.x =
16. Use any method to find the exact real solution, if itexists. (Enter your answers as a comma-separated list. If there isno solution, enter NO SOLUTION.)
(w^2/6) - (w/3) - 4 =0
w=
17. Solve using quadratic methods. (Enter your answers as acomma-separated list.)
(x + 5)2 + 5(x + 5) + 4 = 0
x =
18. Consider the following equation.
y = (-1/22)x^2 +x
(a) Find the vertex of the graph of the equation.(x , y) = ( )(b) Determine if the vertex is a maximum or minimum point.
(c) Determine what value of x gives the optimal valueof the function.x = (d) Determine the optimal (maximum or minimum) value of thefunction.y =
20. The daily profit from the sale of a product is given byP = 14x ? 0.1x2 ? 50 dollars,where x is the number of units of production.
(a) What level of production maximizes profit?units(b) What is the maximum possible profit?$
21. If the supply function for a commodity is p =q2 + 14q + 49 and the demand functionis p = รขยย11q2 + 92q + 469,find the equilibrium quantity and equilibrium price.(q, p) = ( )
22. The supply and demand for a product are given by 2p? q = 80 and pq = 100 + 35q,respectively. Find the market equilibrium point.(q, p) = ( )
23. The total costs and total revenues for a company arerepresented by the equations shown below, where xrepresents the number of production units. Find the break-evenpoints. (Enter your answers as a comma-separated list.)
C(x) = 2100 + 20x +x2R(x) = 120x
x = units
24. If, in a monopoly market, the demand for a product isp = 130 ? 0.40x and the revenue function isR = px, where x is the number of unitssold, what price will maximize revenue? (Round your answer to thenearest cent.)$
28.