Answer:
x=8.75
Step-by-step explanation:
The price x that maximizes profit is the maximum value of the function, and the maximum value of the function is located at a point where the first derivative of the function is equal to zero. The first derivative is:
![P(x) = - 2x^2+35x-99\\P'(x)=-2(2)x^{(2-1)}+35(1)-0\\P'(x)=-4x+35](https://tex.z-dn.net/?f=P%28x%29%20%3D%20-%202x%5E2%2B35x-99%5C%5CP%27%28x%29%3D-2%282%29x%5E%7B%282-1%29%7D%2B35%281%29-0%5C%5CP%27%28x%29%3D-4x%2B35)
Using P'(x)=0:
![0=-4x+35\\4x=35\\x=35/4\\x=8.75](https://tex.z-dn.net/?f=0%3D-4x%2B35%5C%5C4x%3D35%5C%5Cx%3D35%2F4%5C%5Cx%3D8.75)
The minimum value of the function is also at a point where the first derivative of the function is equal to zero. To differentiate if x=8. is a minimum or a maximum obtain the second derivative and evaluate it at x=8.75 if the value P''(x)>0 x is minimum and if P''(x)<0 x is a maximum.
![P'(x)=-4x+35\\P''(x)=-4(1)\\P''(x)=-4](https://tex.z-dn.net/?f=P%27%28x%29%3D-4x%2B35%5C%5CP%27%27%28x%29%3D-4%281%29%5C%5CP%27%27%28x%29%3D-4)
Evaluating at x=8.75:
![P''(8.75)=-4](https://tex.z-dn.net/?f=P%27%27%288.75%29%3D-4)
Therefore, x=8.75 is the maximum value of the function and it is the price that maximizes profit.
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➷ 250 - 210 = 40
40 - 15.89 = 24.11
It would be option A. $24.11
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Answer:
-3/5
Step-by-step explanation:
7 * -3/7 * 1/5
Rewritng
7/7 * -3/5 *1
Simplifying fractions
1 * -3/5 *1
-3/5
3.30
because if you have two of the same quantity then altogether means add so just add
Answer:
Solve for y in the second equation
Step-by-step explanation:
The other numbers in that equation are 9 and 3. If you divide them by three, they will not become a fraction.