im not sure how to explain it, but i know its b
Width=w
length=(40-2w)/2=20-w
A=w(40-w)
A=40w-w²
A'=40-2w=0
2w=40
w=20
20x20 is the size of the pen having the greatest area. this tells us the largest rectangle for a given perimeter is a square
Answer:
A. ![g'(3)=-\frac{1}{2}](https://tex.z-dn.net/?f=g%27%283%29%3D-%5Cfrac%7B1%7D%7B2%7D)
Step-by-step explanation:
We have been given that f be a differentiable function such that
,
,
, and
. The function g is differentiable and
for all x.
We know that when one function is inverse of other function, so:
![g(f(x))=x](https://tex.z-dn.net/?f=g%28f%28x%29%29%3Dx)
Upon taking derivative of both sides of our equation, we will get:
![g'(f(x))*f'(x) =1](https://tex.z-dn.net/?f=g%27%28f%28x%29%29%2Af%27%28x%29%20%3D1)
![g'(f(x))=\frac{1}{f'(x)}](https://tex.z-dn.net/?f=g%27%28f%28x%29%29%3D%5Cfrac%7B1%7D%7Bf%27%28x%29%7D)
Plugging
into our equation, we will get:
![g'(f(6))=\frac{1}{f'(6)}](https://tex.z-dn.net/?f=g%27%28f%286%29%29%3D%5Cfrac%7B1%7D%7Bf%27%286%29%7D)
Since
, then
.
![g'(3)=\frac{1}{f'(6)}](https://tex.z-dn.net/?f=g%27%283%29%3D%5Cfrac%7B1%7D%7Bf%27%286%29%7D)
Since we have been given that
, so we will get:
![g'(3)=\frac{1}{-2}](https://tex.z-dn.net/?f=g%27%283%29%3D%5Cfrac%7B1%7D%7B-2%7D)
![g'(3)=-\frac{1}{2}](https://tex.z-dn.net/?f=g%27%283%29%3D-%5Cfrac%7B1%7D%7B2%7D)
Therefore,
and option A is the correct choice.
Answer:
the answer is x=5 for a fact
Step-by-step explanation:
They are in agreement. All of the expressions provided are equivalent. Chris says that 14.6 percent of the world's oranges are grown in Florida. Then, Mary Beth says that 292 out of 2000 oranges are grown in Florida. If we compare the two, 292 is actually 14.6 percent of 2000. So they are saying the same thing. Allison says that 0.146 of the oranges are grown in Florida. 0.146 is actually 14.6 percent as a decimal, so if we change it back into a percent, she is saying that 14.6 percent of oranges are grown in Florida. Sound familiar? They are all in agreement.<span />