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)
14.4 rounds to about 14 as a percentage that is 14%
Answer:
D
Step-by-step explanation:
![\frac{f(x)}{g(x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D)
=
Factor out 2 on the numerator and 2x on the denominator.
= ![\frac{2(x+2)}{2x(x+2)}](https://tex.z-dn.net/?f=%5Cfrac%7B2%28x%2B2%29%7D%7B2x%28x%2B2%29%7D)
Cancel the factor (x + 2) on the numerator/ denominator
=
← cancel the 2 on numerator/ denominator
=
: x ≠ 0
Answer:
A. Multiply 3x−3y=1 by 2, and multiply −2x+4y=2 by 3.
Step-by-step explanation:
Given
![3x - 3y = 1](https://tex.z-dn.net/?f=3x%20-%203y%20%3D%201)
![-2x+ 4y = 2](https://tex.z-dn.net/?f=-2x%2B%204y%20%3D%202)
Required
A good first step
A good first step is to eliminate x and this is done as follows:
Multiply
by 2 (gotten from coefficient of x in the second equation)
Multiply
by 3 (gotten from coefficient of x in the first equation)
This gives:
![6x - 6y = 2](https://tex.z-dn.net/?f=6x%20-%206y%20%3D%202)
![-6x + 12y = 6](https://tex.z-dn.net/?f=-6x%20%2B%2012y%20%3D%206)
Add both equations
![6x - 6x - 6y + 12y = 2 + 6](https://tex.z-dn.net/?f=6x%20-%206x%20-%206y%20%2B%2012y%20%3D%202%20%2B%206)
![6y = 8](https://tex.z-dn.net/?f=6y%20%3D%208)
![y = \frac{4}{3}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B4%7D%7B3%7D)
<em>Hence (a), is true</em>
Answer:
C 5/4 s
Step-by-step explanation: