Answer:
Thus, the coffee shop is willing to supply 6 pounds per week at a price of $4 per pound.
Step-by-step explanation:
We are given the following information in the question:
The marginal price per pound (in dollars) is given by:
![p'(x) = \displaystyle\frac{208}{(x+7)^2}](https://tex.z-dn.net/?f=p%27%28x%29%20%3D%20%5Cdisplaystyle%5Cfrac%7B208%7D%7B%28x%2B7%29%5E2%7D)
where x is the supply in pounds.
![P(x) = \displaystyle\int p'(x)~dx =\displaystyle\int\displaystyle\frac{208}{(x+7)^2}~dx\\\\P(x) = \frac{-208}{(x+7)} + c\\\\\text{where c is the constant of integration.}](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%5Cdisplaystyle%5Cint%20p%27%28x%29~dx%20%3D%5Cdisplaystyle%5Cint%5Cdisplaystyle%5Cfrac%7B208%7D%7B%28x%2B7%29%5E2%7D~dx%5C%5C%5C%5CP%28x%29%20%3D%20%5Cfrac%7B-208%7D%7B%28x%2B7%29%7D%20%2B%20c%5C%5C%5C%5C%5Ctext%7Bwhere%20c%20is%20the%20constant%20of%20integration.%7D)
The coffee shop is willing to supply 9 pounds per week at a price of $7 per pound.
Thus, we are given that
P(9) = 7
Putting the values, we get,
![P(x) = \displaystyle\frac{-208}{(x+7)} + c\\\\P(9) = 7\\\\\displaystyle\frac{-208}{(9+7)} + c = 7\\\\c = 7 + \frac{208}{16} = 20](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%5Cdisplaystyle%5Cfrac%7B-208%7D%7B%28x%2B7%29%7D%20%2B%20c%5C%5C%5C%5CP%289%29%20%3D%207%5C%5C%5C%5C%5Cdisplaystyle%5Cfrac%7B-208%7D%7B%289%2B7%29%7D%20%2B%20c%20%3D%207%5C%5C%5C%5Cc%20%3D%207%20%2B%20%5Cfrac%7B208%7D%7B16%7D%20%3D%2020)
![P(x) = \displaystyle\frac{-208}{(x+7)} + 20](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%5Cdisplaystyle%5Cfrac%7B-208%7D%7B%28x%2B7%29%7D%20%2B%2020)
Now, we have to find how many pounds it would be willing to supply at a price of $4 per pound.
P(x) = 4
![P(x) = \displaystyle\frac{-208}{(x+7)} + 20 = 4\\\\\frac{-208}{x+7} = -16\\\\x + 7 = 13\\x = 6](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%5Cdisplaystyle%5Cfrac%7B-208%7D%7B%28x%2B7%29%7D%20%2B%2020%20%3D%204%5C%5C%5C%5C%5Cfrac%7B-208%7D%7Bx%2B7%7D%20%3D%20-16%5C%5C%5C%5Cx%20%2B%207%20%3D%2013%5C%5Cx%20%3D%206)
Thus, the coffee shop is willing to supply 6 pounds per week at a price of $4 per pound.
It’s 5/7 5/8 I did the math
Answer:
hmmmm. probably 2? I think it's two
Answer:
384
Step-by-step explanation:
24 bouquets * 16 flowers = 384 flowers
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