hopefully 16 is the answer
Answer:
Horizontal Asymptote: y=2
Vertical Asymptote: x=3
Step-by-step explanation:
One way: Look at graph
Look at for a horizontal or vertical line that both lines don't touch.
Second Way:
When you look for vertical asymptotes, you set the denominator equal to zero and solve.
For example, the second question has a denominator of x-3.
x-3=0
x=3 (This is the vertical asymptote)
When you look for horizontal asymptote, you do long division.
For example, the first question ![f(x)=\frac{2x}{x-3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B2x%7D%7Bx-3%7D)
The answer will be 2. 2 is the quotient. You only want quotient not remainder.
y=2.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The point of diminishing returns (x , y ) is (11, 21462)
Step-by-step explanation:
From the question we are told that
The function is ![R(x) = 10,000 -x^3 - 33x^2 + 800x , \ \ 0 \le x \le 20](https://tex.z-dn.net/?f=R%28x%29%20%3D%20%2010%2C000%20-x%5E3%20-%2033x%5E2%20%2B%20800x%20%2C%20%20%5C%20%5C%200%20%5Cle%20x%20%5Cle%2020)
Here R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in thousands of dollars).
Now differentiating R(x) we have
![R'(x) = -3x^2 +66x + 800](https://tex.z-dn.net/?f=R%27%28x%29%20%3D%20%20-3x%5E2%20%2B66x%20%2B%20800)
Finding the second derivative of R(x)
![R''(x) = -6x +66](https://tex.z-dn.net/?f=R%27%27%28x%29%20%3D%20%20-6x%20%2B66)
at inflection point ![R''(x) = 0](https://tex.z-dn.net/?f=R%27%27%28x%29%20%3D%20%200)
So ![-6x +66 = 0](https://tex.z-dn.net/?f=-6x%20%20%2B66%20%20%3D%200)
=> ![x= 11](https://tex.z-dn.net/?f=x%3D%20%2011)
substituting value of x into R(x)
![R(x) = 10,000 -(11)^3 - 33(11)^2 + 800(11) ,](https://tex.z-dn.net/?f=R%28x%29%20%3D%20%2010%2C000%20-%2811%29%5E3%20-%2033%2811%29%5E2%20%2B%20800%2811%29%20%2C)
![R(x) = 21462](https://tex.z-dn.net/?f=R%28x%29%20%3D%2021462)
Now the point of diminishing returns (x , y ) i.e (x , R(x) ) is
(11, 21462)
Answer:
I'm sorry if I'm wrong but I'm pretty sure it is D) 6
Step-by-step explanation:
the ones who ate five or six had to eat four pieces before that
and there's 3 little x's for 4, 2 for 5, and 1 for 6
my second guess is 3 if you know for certain that your teacher wouldn't do that sort of thing