The circumference follows the formula
C= 2 (pi)R
R is the radius which is half the diameter when we put this into the equation we get
C = 2 (pi)(4.5)
C=28.274334
Answer:
A.
Step-by-step explanation:
As shown in the question we can interpret the following:
![x_{1} = -2\\y_{1} = 1\\x_{2} = 5\\y_{2} = -4](https://tex.z-dn.net/?f=x_%7B1%7D%20%20%3D%20-2%5C%5Cy_%7B1%7D%20%3D%201%5C%5Cx_%7B2%7D%20%3D%205%5C%5Cy_%7B2%7D%20%3D%20-4)
Now all we have to do is plug these values into the equation, and so we find that A. is the correct answer.
Answer:
190.4
Step-by-step explanation:
Solve the following system:
{2 y - 3 x - 8 = 3 y + 4 x - 1 | (AB=DE)
4 y + 10 x + 3 = -2 y - 17 x + 9 | (BC=EF)
x = -16/5, y = 77/5
DF=AC=-27x+5y+27=190.4
There you go, have a great day
Answer:
The statement that correctly uses limits to determine the end behavior of f(x) is;
so the end behavior of the function is that as x → ±∞, f(x) → 0
Step-by-step explanation:
The given function is presented here as follows;
![f(x) = \dfrac{7 \cdot x^2+ x + 1}{x^4 + 1}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cdfrac%7B7%20%5Ccdot%20x%5E2%2B%20x%20%2B%201%7D%7Bx%5E4%20%2B%201%7D)
The limit of the function is presented as follows;
![\lim\limits_{x \to \pm \infty} \dfrac{7 \cdot x^2+ x + 1}{x^4 + 1}](https://tex.z-dn.net/?f=%5Clim%5Climits_%7Bx%20%5Cto%20%5Cpm%20%5Cinfty%7D%20%20%20%5Cdfrac%7B7%20%5Ccdot%20x%5E2%2B%20x%20%2B%201%7D%7Bx%5E4%20%2B%201%7D)
Dividing the terms by x², we have;
![\lim\limits_{x \to \pm \infty} \dfrac{\dfrac{7 \cdot x^2}{x^2} + \dfrac{x}{x^2} + \dfrac{1}{x^2} }{\dfrac{x^4}{x^2} +\dfrac{1}{x^2} }= \lim\limits_{x \to \pm \infty} \dfrac{7 + \dfrac{1}{x} + \dfrac{1}{x^2} }{x^2 +\dfrac{1}{x^2} }](https://tex.z-dn.net/?f=%5Clim%5Climits_%7Bx%20%5Cto%20%5Cpm%20%5Cinfty%7D%20%20%20%5Cdfrac%7B%5Cdfrac%7B7%20%5Ccdot%20x%5E2%7D%7Bx%5E2%7D%20%2B%20%5Cdfrac%7Bx%7D%7Bx%5E2%7D%20%20%2B%20%5Cdfrac%7B1%7D%7Bx%5E2%7D%20%7D%7B%5Cdfrac%7Bx%5E4%7D%7Bx%5E2%7D%20%2B%5Cdfrac%7B1%7D%7Bx%5E2%7D%20%20%7D%3D%20%5Clim%5Climits_%7Bx%20%5Cto%20%5Cpm%20%5Cinfty%7D%20%20%20%5Cdfrac%7B7%20%2B%20%5Cdfrac%7B1%7D%7Bx%7D%20%20%2B%20%5Cdfrac%7B1%7D%7Bx%5E2%7D%20%7D%7Bx%5E2%20%2B%5Cdfrac%7B1%7D%7Bx%5E2%7D%20%20%7D)
As 'x' tends to ±∞, we have;
![\lim\limits_{x \to \pm \infty} \dfrac{7 + \dfrac{1}{x} + \dfrac{1}{x^2} }{x^2 +\dfrac{1}{x^2} } = \lim\limits_{x \to \pm \infty} \dfrac{7 + 0 + 0 }{x^2 +0 } = \lim\limits_{x \to \pm \infty} \dfrac{7 }{x^2 }](https://tex.z-dn.net/?f=%5Clim%5Climits_%7Bx%20%5Cto%20%5Cpm%20%5Cinfty%7D%20%20%20%5Cdfrac%7B7%20%2B%20%5Cdfrac%7B1%7D%7Bx%7D%20%20%2B%20%5Cdfrac%7B1%7D%7Bx%5E2%7D%20%7D%7Bx%5E2%20%2B%5Cdfrac%7B1%7D%7Bx%5E2%7D%20%20%7D%20%3D%20%20%5Clim%5Climits_%7Bx%20%5Cto%20%5Cpm%20%5Cinfty%7D%20%20%5Cdfrac%7B7%20%2B%200%20%20%2B%200%20%7D%7Bx%5E2%20%2B0%20%20%7D%20%3D%20%20%5Clim%5Climits_%7Bx%20%5Cto%20%5Cpm%20%5Cinfty%7D%20%20%5Cdfrac%7B7%20%20%7D%7Bx%5E2%20%20%7D)
However, we have that the end behavior of 7/x² as 'x' tends to ±∞ is 7/x² tends to 0;
Therefore, we have;
![f(x) \rightarrow 0 \ as \lim\limits_{x \to \pm \infty} \dfrac{7 }{x^2 }](https://tex.z-dn.net/?f=f%28x%29%20%5Crightarrow%200%20%5C%20as%20%20%5Clim%5Climits_%7Bx%20%5Cto%20%5Cpm%20%5Cinfty%7D%20%20%5Cdfrac%7B7%20%20%7D%7Bx%5E2%20%20%7D)
The statement that correctly uses limits to determine the end behavior of f(x) is therefor given as follows;
so the end behavior of the function is that as x → ±∞, f(x) → 0.