The answer is 2.20
You get this by doing 13.2÷6=2.2
Hope it helps
Lets see whether the river is going against the boat or with it
speed=distance/time
22 miles per 1.5 hour
speed=22/1.5=14.66666 mile per hour
50mph>14.6666666mph
ok it slowed down, so it it going agains the current
boatspeed-currentspeed=realspeed
realspeed=14.666666mph
boatspeed=50mph
50-curretn speed=14.66666666666666
50 both sides
-currentspeed=-35.33333333333333
multiply -1
currentspeed=35.33333333333333mph
the current is 35 and 1/3mph agains the boat
Answer:
SLOPE = -5
Step-by-step explanation:
Because that's what x is.
Answer: 41. A) 0 42. B) 1/12 43. B) 16
<u>Step-by-step explanation:</u>
The pattern is: multiply the bottom row and subtract the top number.
Sample: 3 x 2 - 5 = 1
5 x 3 - 6 = 9
2 x 1 - 1 = 1
41) 7 x 13 - x = 91
91 - x = 91
x = 0
42) 1/2 x 1/2 - 1/6 = x
1/4 - 1/6 = x
3/12 - 2/12 = x
1/12 = x
Check the fractions. I had to guess what the denominators are because the image is blurry.
43) 8 x 3 - 8 - x
24 - 8 = x
16 = 0
Answer:
![\displaystyle \large \boxed{ \lim_{x \rightarrow +\infty} {x\left(\sqrt{x^2-1}-x\right)}=-\dfrac{1}{2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%20%5Cboxed%7B%20%5Clim_%7Bx%20%5Crightarrow%20%2B%5Cinfty%7D%20%7Bx%5Cleft%28%5Csqrt%7Bx%5E2-1%7D-x%5Cright%29%7D%3D-%5Cdfrac%7B1%7D%7B2%7D%7D)
Step-by-step explanation:
Hello, please consider the following.
![\sqrt{(x^2-1)}-x\\\\=\sqrt{x^2(1-\dfrac{1}{x^2})}-x\\\\=x\left( \sqrt{1-\frac{1}{x^2}}-1\right)](https://tex.z-dn.net/?f=%5Csqrt%7B%28x%5E2-1%29%7D-x%5C%5C%5C%5C%3D%5Csqrt%7Bx%5E2%281-%5Cdfrac%7B1%7D%7Bx%5E2%7D%29%7D-x%5C%5C%5C%5C%3Dx%5Cleft%28%20%5Csqrt%7B1-%5Cfrac%7B1%7D%7Bx%5E2%7D%7D-1%5Cright%29)
For x close to 0, we can write
![\sqrt{1+x}=1+\dfrac{1}{2}x-\dfrac{1}{8}x^2+o(x^2)\\\\\ \text{x tends to } +\infty \text{ means }\dfrac{1}{x} \text{ tends to 0}\\\\\text{So, when }\dfrac{1}{x}\text{ is close to 0, we can write.}\\\\\sqrt{1-\dfrac{1}{x^2}}=1-\dfrac{1}{2}\dfrac{1}{x^2}-\dfrac{1}{8}\dfrac{1}{x^4}+o(\dfrac{1}{x^4})](https://tex.z-dn.net/?f=%5Csqrt%7B1%2Bx%7D%3D1%2B%5Cdfrac%7B1%7D%7B2%7Dx-%5Cdfrac%7B1%7D%7B8%7Dx%5E2%2Bo%28x%5E2%29%5C%5C%5C%5C%5C%20%5Ctext%7Bx%20tends%20to%20%7D%20%2B%5Cinfty%20%5Ctext%7B%20means%20%7D%5Cdfrac%7B1%7D%7Bx%7D%20%5Ctext%7B%20tends%20to%200%7D%5C%5C%5C%5C%5Ctext%7BSo%2C%20when%20%7D%5Cdfrac%7B1%7D%7Bx%7D%5Ctext%7B%20%20is%20close%20to%200%2C%20we%20can%20write.%7D%5C%5C%5C%5C%5Csqrt%7B1-%5Cdfrac%7B1%7D%7Bx%5E2%7D%7D%3D1-%5Cdfrac%7B1%7D%7B2%7D%5Cdfrac%7B1%7D%7Bx%5E2%7D-%5Cdfrac%7B1%7D%7B8%7D%5Cdfrac%7B1%7D%7Bx%5E4%7D%2Bo%28%5Cdfrac%7B1%7D%7Bx%5E4%7D%29)
So,
![x\left( \sqrt{1-\frac{1}{x^2}}-1\right)\\\\=x(1-\dfrac{1}{2}\dfrac{1}{x^2}+o(\dfrac{1}{x^2})-1)\\\\=-\dfrac{1}{2x}+o(\dfrac{1}{x})](https://tex.z-dn.net/?f=x%5Cleft%28%20%5Csqrt%7B1-%5Cfrac%7B1%7D%7Bx%5E2%7D%7D-1%5Cright%29%5C%5C%5C%5C%3Dx%281-%5Cdfrac%7B1%7D%7B2%7D%5Cdfrac%7B1%7D%7Bx%5E2%7D%2Bo%28%5Cdfrac%7B1%7D%7Bx%5E2%7D%29-1%29%5C%5C%5C%5C%3D-%5Cdfrac%7B1%7D%7B2x%7D%2Bo%28%5Cdfrac%7B1%7D%7Bx%7D%29)
It means that
![\displaystyle \lim_{x \rightarrow +\infty} {x\left(\sqrt{x^2-1}-x\right)}\\\\=\lim_{x \rightarrow +\infty} {-\dfrac{x}{2x}}=-\dfrac{1}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Crightarrow%20%2B%5Cinfty%7D%20%7Bx%5Cleft%28%5Csqrt%7Bx%5E2-1%7D-x%5Cright%29%7D%5C%5C%5C%5C%3D%5Clim_%7Bx%20%5Crightarrow%20%2B%5Cinfty%7D%20%7B-%5Cdfrac%7Bx%7D%7B2x%7D%7D%3D-%5Cdfrac%7B1%7D%7B2%7D)
Thank you