Answer:
5
Step-by-step explanation:
given that x and y are proportional, they can be expressed as y = rx, where r is the proportionality constant. Thus, we can solve for r by doing y/x in any given point.
![\frac{8}{1.6} = \frac{15}{3} = \frac{22}{4.4} = 5](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B1.6%7D%20%3D%20%5Cfrac%7B15%7D%7B3%7D%20%20%3D%20%5Cfrac%7B22%7D%7B4.4%7D%20%3D%205)
The first option is correct. See an explanation below.
Assuming you mean
![\lim_{x \to 4} \frac{\sqrt{x+5}-3}{4-x}](https://tex.z-dn.net/?f=%20%5Clim_%7Bx%20%5Cto%204%7D%20%5Cfrac%7B%5Csqrt%7Bx%2B5%7D-3%7D%7B4-x%7D)
that means as x approaches 4
if we sub 0 for x we get
0/0
and intermitent form
use l'hopital's rule
so
take the derivitive of the top and bottom seperatly
l'hopitals rule is something like
if
![\lim_{x \to n} \frac{f(x)}{g(x)}](https://tex.z-dn.net/?f=%20%5Clim_%7Bx%20%5Cto%20n%7D%20%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D)
results in 0/0 or -∞/∞ or∞/∞ then keep doing it until f(n)/g(n) gives a form that isn't intermitent
so
take derivitive of top and bottom
![\dfrac{\frac{1}{2\sqrt{x+5}}}{-1}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%2B5%7D%7D%7D%7B-1%7D)
now, if we subsitute 4 for x we get
![\dfrac{\frac{1}{2\sqrt{4+5}}}{-1}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cfrac%7B1%7D%7B2%5Csqrt%7B4%2B5%7D%7D%7D%7B-1%7D)
=
![\dfrac{\frac{1}{2\sqrt{9}}}{-1}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cfrac%7B1%7D%7B2%5Csqrt%7B9%7D%7D%7D%7B-1%7D)
=
![\dfrac{\frac{1}{2(3)}}{-1}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cfrac%7B1%7D%7B2%283%29%7D%7D%7B-1%7D)
=
![\dfrac{\frac{1}{6}}{-1}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cfrac%7B1%7D%7B6%7D%7D%7B-1%7D)
=
Yea i gusse is this a question????????????????????????????????????????????????????????????..............................................................
*see attachment showing the line graph
Answer:
2
Step-by-step explanation:
The red line represents the line for women, while the blue line represents the line for men.
Age 45 is the middle of 40 and 45 on the x-axis.
The average number of awakenings during the night for 45 -year-old men ≈ 5
The average number of awakenings during the night for 45 -year-old women = 3
The difference = 5 - 3 = 2 times during the night.