Answer:
Part A:
The vertex : x = - b / 2 a = - 28 : ( - 2 ) = 14
y = f ( 14 ) = - 14² + 28 · 14 - 192 = 196 + 392 - 192 = 4
The vertex is ( 14, 4 ). It means that the maximum hourly profit is $4, and that the shop should sell 14 sodas to reach the maximum.
Part B :
We will solve the quadratic equation:
x 1/2 = ( - 28 +/- sqrt ( 784 - 768 ) ) / ( - 2 )
x 1 = 12, x 2 = 16.
It means that if the shop must sell more than 12 and less then 16 sodas if they want to make a profit ( 13, 14, or 15 ). If they sell 12, or 16 they will brake even.
I think
The problem is using a right triangle, it means we can use the Pythagorean theorem in solving the problem. We have two possible measurements for the third side.
First length, when the third side is the hypotenuse:
x ² = 15² + 12²
x = 19.21
Second possible length, when the third leg is either an adjacent or base side:
15² = x² + 12²
x = 9
Therefore, the difference between the two possible answers are shown below:
Difference = 19.21 - 9 = 10.21
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Step-by-step explanation:
