For this case we have that by definition, the area of a rectangle is given by:
![A = w * l](https://tex.z-dn.net/?f=A%20%3D%20w%20%2A%20l)
Where:
w: Is the width of the rectangle
l: is the length of the rectangle
According to the data of the statement we have:
![A = 81-x ^ 2\\w = 9-x](https://tex.z-dn.net/?f=A%20%3D%2081-x%20%5E%202%5C%5Cw%20%3D%209-x)
So, the length is given by:
![l = \frac {A} {w}\\l = \frac {81-x ^ 2} {9-x}](https://tex.z-dn.net/?f=l%20%3D%20%5Cfrac%20%7BA%7D%20%7Bw%7D%5C%5Cl%20%3D%20%5Cfrac%20%7B81-x%20%5E%202%7D%20%7B9-x%7D)
We factor the numerator:
![l = \frac {(9 + x) (9-x)} {9-x}](https://tex.z-dn.net/?f=l%20%3D%20%5Cfrac%20%7B%289%20%2B%20x%29%20%289-x%29%7D%20%7B9-x%7D)
We simplify:
![l = 9 + x](https://tex.z-dn.net/?f=l%20%3D%209%20%2B%20x)
So, the length is ![9 + x](https://tex.z-dn.net/?f=9%20%2B%20x)
Answer:
![9 + x](https://tex.z-dn.net/?f=9%20%2B%20x)
Answer:36!
Step-by-step explanation:
If four coordinates are given then:-
- Find length of the sides using distance formula
![\boxed{\sf \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Csf%20%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D%7D)
- Now break down into two triangles .
- Use herons formula and find areas of the triangles .add them and get the area
8x + 114x + 3
8x + 114x = 122x
112x + 3
the derivitive is just the slope
minimum happens when the derivitive goes from negative to positive, imagine a slope of the function, the minimum is where the slope goes from neative to positive, and to get there, it has to pass through 0
max happens when the derivitive goes from positive to negative
increaseing is when the derivitive is positive
so, based on what you said, the slope of f(x) is 0 at x=-3, x=1 and x=2 since those are where the derivitive is 0 (derivitive is just the slope)
A and B are wrong because the derivitive isn't 0 at those points
C is correct because increasing means that the derivitive is positive, and so therefo since the only hoirontal place in between 1 and 2 is 1.5, it must remain positive throughout and not dip down, C is right
D is wrong then
answer is C