The demand equation illustrates the price of an item and how it relates to the demand of the item.
- The slope of the demand function is -1/2
- The equation of the demand function is:

- The price that maximizes her revenue is: Ghc 85
From the question, we have:


The number of plates (x) decreases by 10, while the price (y) increases by 5. The table of value is:

The slope (m) is calculated using:

So, we have:



The equation of the demand is as follows:
The initial number of plates (300) decreases by 10 is represented as: (300 - 10x).
Similarly, the initial price (20) increases by 5 is represented as: (20 + 5x).
So, the demand equation is:

Open the brackets to calculate the maximum revenue


Equate to 0

Differentiate with respect to x

Collect like terms

Divide by 100

So, the price at maximum revenue is:



In conclusion:
- The slope of the demand function is -1/2
- The equation of the demand function is:

- The price that maximizes her revenue is: Ghc 85
Read more about demand equations at:
brainly.com/question/21586143
Answer: 84 mm is MAYBE the answer.
so hmmm seemingly the graphs meet at -2 and +2 and 0, let's check

so f(x) = g(x) at those points, so let's take the integral of the top - bottom functions for both intervals, namely f(x) - g(x) from -2 to 0 and g(x) - f(x) from 0 to +2.
![\stackrel{f(x)}{2x^3-x^2-5x}~~ - ~~[\stackrel{g(x)}{-x^2+3x}]\implies 2x^3-x^2-5x+x^2-3x \\\\\\ 2x^3-8x\implies 2(x^3-4x)\implies \displaystyle 2\int\limits_{-2}^{0} (x^3-4x)dx \implies 2\left[ \cfrac{x^4}{4}-2x^2 \right]_{-2}^{0}\implies \boxed{8} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cstackrel%7Bf%28x%29%7D%7B2x%5E3-x%5E2-5x%7D~~%20-%20~~%5B%5Cstackrel%7Bg%28x%29%7D%7B-x%5E2%2B3x%7D%5D%5Cimplies%202x%5E3-x%5E2-5x%2Bx%5E2-3x%20%5C%5C%5C%5C%5C%5C%202x%5E3-8x%5Cimplies%202%28x%5E3-4x%29%5Cimplies%20%5Cdisplaystyle%202%5Cint%5Climits_%7B-2%7D%5E%7B0%7D%20%28x%5E3-4x%29dx%20%5Cimplies%202%5Cleft%5B%20%5Ccfrac%7Bx%5E4%7D%7B4%7D-2x%5E2%20%5Cright%5D_%7B-2%7D%5E%7B0%7D%5Cimplies%20%5Cboxed%7B8%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\stackrel{g(x)}{-x^2+3x}~~ - ~~[\stackrel{f(x)}{2x^3-x^2-5x}]\implies -x^2+3x-2x^3+x^2+5x \\\\\\ -2x^3+8x\implies 2(-x^3+4x) \\\\\\ \displaystyle 2\int\limits_{0}^{2} (-x^3+4x)dx \implies 2\left[ -\cfrac{x^4}{4}+2x^2 \right]_{0}^{2}\implies \boxed{8} ~\hfill \boxed{\stackrel{\textit{total area}}{8~~ + ~~8~~ = ~~16}}](https://tex.z-dn.net/?f=%5Cstackrel%7Bg%28x%29%7D%7B-x%5E2%2B3x%7D~~%20-%20~~%5B%5Cstackrel%7Bf%28x%29%7D%7B2x%5E3-x%5E2-5x%7D%5D%5Cimplies%20-x%5E2%2B3x-2x%5E3%2Bx%5E2%2B5x%20%5C%5C%5C%5C%5C%5C%20-2x%5E3%2B8x%5Cimplies%202%28-x%5E3%2B4x%29%20%5C%5C%5C%5C%5C%5C%20%5Cdisplaystyle%202%5Cint%5Climits_%7B0%7D%5E%7B2%7D%20%28-x%5E3%2B4x%29dx%20%5Cimplies%202%5Cleft%5B%20-%5Ccfrac%7Bx%5E4%7D%7B4%7D%2B2x%5E2%20%5Cright%5D_%7B0%7D%5E%7B2%7D%5Cimplies%20%5Cboxed%7B8%7D%20~%5Chfill%20%5Cboxed%7B%5Cstackrel%7B%5Ctextit%7Btotal%20area%7D%7D%7B8~~%20%2B%20~~8~~%20%3D%20~~16%7D%7D)
Answer:
y = (1/3)x + 4
Step-by-step explanation:
Two points on this line are (0, 4) and (3, 5).
As we move from the first point to the second, x increases by 3 and y increases by 1. Thus, the slope, m, of the line is m = rise / run = 1/3.
Use the slope-intercept equation: y = mx + b.
If we use the data from the point (0, 4), we get:
4 = (1/3)(0) + b, so that b = 4. The desired equation is y = (1/3)x + 4.
<span>y-2>1/2(x-2) can be expanded as follows: y - 2 > (1/2)x - 1
Mult. all terms by 2 to remove the fractions:
2y - 4 > x - 2
Add 4 to both sides: 2y > x + 2
Div. both sides by 2: y > (1/2)x + 1 (answer)</span>