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minersaysay22
16.10.2019 •
Mathematics
The function f(x) = −x^2 + 48x − 432 models the profit, in dollars, a game developer makes for selling a new game, where x is the number of games sold and f(x) is the amount of profit.
part a: determine the vertex. what does this calculation mean in the context of the problem? (5 points)
part b: determine the x-intercepts. what do these values mean in the context of the problem?
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Ответ:
Part A
Find the zeros:
−x^2 + 48x − 432 = 0
x^2 - 48x + 432 = 0
Factor
(x - 36 ) (x - 12 )=0
Two solutions: x = 36 and x = 12
The vertex is in x = (36 +12 )/ 2 = 24
f(24) = -(24)^2 + 48(24) − 432 = 144
The vertex is (24, 144).
Given that the coefficient of x^2 is negative, the parabole opens downward, that mean that the vertex is a maximum value.
In the context of the problem that means that the maximum profit is 144 and is obtainded when the number of games sold is 24.
Part B.
The x-intercepts are the values of x when y=0. Which we calculated above.
They are x = 24 and x = 36.
Those values are the number of games for which the profit is zero.
Ответ:
5/16
Step-by-step explanation:
you can't split 5 in half, so you need to multiply the fraction to make it so you can split it in half. Multiply the equation by 2
5/8 * 2=10/16
now you can divide it by two to get 5/16
Hope this helps!