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- 1)Determine the open intervals on which the graph is concave upward or concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) y = 4x2 − x − 9 concave upward concave downward 2)Determine the open intervals on which the graph is concave upward or concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) g(x) = 21x2 − x3 concave upward concave downward8. The number of people, N, employed in a chain of cafes is related to thenumber of cafes, n, by the equation: N = 10n + 120(a) Illustrate this relation by plotting a graph of N against n for 0 ≤ n ≤ 20.(b) Hence, or otherwise, calculate the number of(i) employees when the company has 14 cafes;(ii) cafes when the company employs 190 people.(c) State the values of the slope and intercept of the graph and give aninterpretation.Determine the open intervals on which the graph is concave upward or concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) g(x) = 21x2 − x3 concave upward concave downward
- 11. Which graph represents the function f(x)=2sin(3θ)?A theater finds that there is a correlation between the number of ice cream flavors offered at its food stand and the number of tickets they sell for a show, which can be modeled by the function S(n) =-4n^2 + 192n + 5 where n is the number of ice cream flavors and S(n) is the number of tickets sold. What number of ice cream flavors should be available in order to maximize the number of tickets sold?Let K(t) be a measure of the knowledge you gain by studying for a test for t hours? Which do you think is larger K(8)-K(7) or K(3)-K(2)? Is the graph of K concave upward or downward? Why?
- Two students were playing the same game. The difference in points that each scored for the game can be modeled by the function y=5sinx+3sinxcosx. Within the interval 0<x<6, when is the difference in points the smallest? Group of answer choices 5.128 seconds 1.155 seconds 1.987 seconds 4.296 secondsTwo students were playing the same game. The difference in points that each scored for the game can be modeled by the function y=5sinx+3sinxcosx after x seconds. Within the interval 0<x<6, when does the function have a value of -1? Group of answer choices 3.146 seconds 3.592 seconds 5.682 seconds 5.128 seconds