Answer:
The maximum revenue is 16000 dollars (at p = 40)
Step-by-step explanation:
One way to find the maximum value is derivatives. The first derivative is used to find where the slope of function will be zero.
Given function is:
![R(p) = -10p^2+800p](https://tex.z-dn.net/?f=R%28p%29%20%3D%20-10p%5E2%2B800p)
Taking derivative wrt p
![\frac{d}{dp} (R(p) = \frac{d}{dp} (-10p^2+800p)\\R'(p) = -10 \frac{d}{dp} (p^2) +800 \ frac{d}{dp}(p)\\R'(p) = -10 (2p) +800(1)\\R'(p) = -20p+800\\](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdp%7D%20%28R%28p%29%20%3D%20%5Cfrac%7Bd%7D%7Bdp%7D%20%28-10p%5E2%2B800p%29%5C%5CR%27%28p%29%20%3D%20-10%20%5Cfrac%7Bd%7D%7Bdp%7D%20%28p%5E2%29%20%2B800%20%5C%20frac%7Bd%7D%7Bdp%7D%28p%29%5C%5CR%27%28p%29%20%3D%20-10%20%282p%29%20%2B800%281%29%5C%5CR%27%28p%29%20%3D%20-20p%2B800%5C%5C)
Now putting R'(p) = 0
![-20p+800 = 0\\-20p = -800\\\frac{-20p}{-20} = \frac{-800}{-20}\\p = 40](https://tex.z-dn.net/?f=-20p%2B800%20%3D%200%5C%5C-20p%20%3D%20-800%5C%5C%5Cfrac%7B-20p%7D%7B-20%7D%20%3D%20%5Cfrac%7B-800%7D%7B-20%7D%5C%5Cp%20%3D%2040)
As p is is positive and the second derivative is -20, the function will have maximum value at p = 40
Putting p=40 in function
![R(40) = -10(40)^2 +800(40)\\= -10(1600) + 32000\\=-16000+32000\\=16000](https://tex.z-dn.net/?f=R%2840%29%20%3D%20-10%2840%29%5E2%20%2B800%2840%29%5C%5C%3D%20-10%281600%29%20%2B%2032000%5C%5C%3D-16000%2B32000%5C%5C%3D16000)
The maximum revenue is 16000 dollars (at p = 40)
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I'm pretty sure it's 50°f because the original temperature is 37°f and after 8 minutes it was 42°f and 42 minus 37 is 5, 8 divided by 5 is 1.6 and then multiply that by 5 is 8 and 42 + 8=50°F
Answer:
5.1 days
Step-by-step explanation:
![3.4 \: miles = 1 \: day \\ 17.34 \: miles \: = x \: days](https://tex.z-dn.net/?f=3.4%20%5C%3A%20miles%20%3D%201%20%5C%3A%20day%20%5C%5C%2017.34%20%5C%3A%20miles%20%5C%3A%20%20%3D%20x%20%5C%3A%20days)
Cross Multiply
![3.4x = 17.34](https://tex.z-dn.net/?f=3.4x%20%3D%2017.34)
Divide both sides of the equation by 3.4
![\frac{3.4x}{3.4} = \frac{17.34}{3.4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3.4x%7D%7B3.4%7D%20%20%3D%20%20%5Cfrac%7B17.34%7D%7B3.4%7D%20)
![x = 5.1](https://tex.z-dn.net/?f=x%20%3D%205.1)