Answer:
The Answer is 10 Miles.
Step-by-step explanation:
The jet is 52,800 feet high.
There are 5,280 feet in a mile.
Divide 52,800 by 5280 to find miles:
52800 / 5280 = 10 Miles.
Hope this Helps! Have an Awesome Day!! :-)
<span>(a) 2.09302406
(b) Lower limit of 95% confidence interval = 185.85
(a) To get the t-score, first determine the number of degrees of freedom you have. That's simply the number of samples minus 1, so in this case we have 19 degrees of freedom. Then calculate (1-0.95)/2 = 0.05/2 = 0.025 which is the size of the tail for the confidence interval you want. Finally, lookup in a T-Distribution Table for the 19 degrees of freedom and tail size. The value looked up will be 2.09302406.
(b) Once you have the t-score, to calculate your desired interval, calculate the following:
V = T*SD/sqrt(n)
where
V = Variance
T = T-score
SD = Standard deviation
n = number of samples
So let's plug in the values and calculate V
V = T*SD/sqrt(n)
V = 2.09302406*21.02/sqrt(20)
V = 2.09302406*21.02/4.472135955
V = 43.99536574/4.472135955
V = 9.837662849
Your 95% confidence interval is now the mean +/- V. So
lower limit = 195.69 - 9.84 = 185.85
upper limit = 195.69 + 9.84 = 205.53</span>
The first statement is false, the second statement is true :)
![\sum\limits_{k=1}^n\arcsin\left[\dfrac{\sqrt{k^2+2k}-\sqrt{k^2-1}}{k(k+1)}\right]=\\\\\\= \sum\limits_{k=1}^n\arcsin\left[\dfrac{\sqrt{k^2+2k}}{k(k+1)}-\dfrac{\sqrt{k^2-1}}{k(k+1)}\right]=\\\\\\= \sum\limits_{k=1}^n\arcsin\left[\dfrac{\sqrt{k^2+2k+1-1}}{k(k+1)}-\dfrac{\sqrt{k^2-1}}{k(k+1)}\right]=\\\\\\= \sum\limits_{k=1}^n\arcsin\left[\dfrac{\sqrt{(k+1)^2-1}}{k(k+1)}-\dfrac{\sqrt{k^2-1}}{k(k+1)}\right]=\\\\\\ ](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bk%3D1%7D%5En%5Carcsin%5Cleft%5B%5Cdfrac%7B%5Csqrt%7Bk%5E2%2B2k%7D-%5Csqrt%7Bk%5E2-1%7D%7D%7Bk%28k%2B1%29%7D%5Cright%5D%3D%5C%5C%5C%5C%5C%5C%3D%0A%5Csum%5Climits_%7Bk%3D1%7D%5En%5Carcsin%5Cleft%5B%5Cdfrac%7B%5Csqrt%7Bk%5E2%2B2k%7D%7D%7Bk%28k%2B1%29%7D-%5Cdfrac%7B%5Csqrt%7Bk%5E2-1%7D%7D%7Bk%28k%2B1%29%7D%5Cright%5D%3D%5C%5C%5C%5C%5C%5C%3D%0A%5Csum%5Climits_%7Bk%3D1%7D%5En%5Carcsin%5Cleft%5B%5Cdfrac%7B%5Csqrt%7Bk%5E2%2B2k%2B1-1%7D%7D%7Bk%28k%2B1%29%7D-%5Cdfrac%7B%5Csqrt%7Bk%5E2-1%7D%7D%7Bk%28k%2B1%29%7D%5Cright%5D%3D%5C%5C%5C%5C%5C%5C%3D%0A%5Csum%5Climits_%7Bk%3D1%7D%5En%5Carcsin%5Cleft%5B%5Cdfrac%7B%5Csqrt%7B%28k%2B1%29%5E2-1%7D%7D%7Bk%28k%2B1%29%7D-%5Cdfrac%7B%5Csqrt%7Bk%5E2-1%7D%7D%7Bk%28k%2B1%29%7D%5Cright%5D%3D%5C%5C%5C%5C%5C%5C%0A)
![=\sum\limits_{k=1}^n\arcsin\left[\dfrac{1}{k}\cdot\dfrac{\sqrt{(k+1)^2-1}}{\sqrt{(k+1)^2}}-\dfrac{1}{k+1}\cdot\dfrac{\sqrt{k^2-1}}{\sqrt{k^2}}\right]=\\\\\\= \sum\limits_{k=1}^n\arcsin\left[\dfrac{1}{k}\cdot\sqrt{\dfrac{(k+1)&^2-1}{(k+1)^2}}-\dfrac{1}{k+1}\cdot\sqrt{\dfrac{k^2-1}{k^2}}\right]=\\\\\\= \sum\limits_{k=1}^n\arcsin\left[\dfrac{1}{k}\cdot\sqrt{1-\dfrac{1}{(k+1)^2}}-\dfrac{1}{k+1}\cdot\sqrt{1-\dfrac{1}{k^2}}\right]=\\\\\\ ](https://tex.z-dn.net/?f=%3D%5Csum%5Climits_%7Bk%3D1%7D%5En%5Carcsin%5Cleft%5B%5Cdfrac%7B1%7D%7Bk%7D%5Ccdot%5Cdfrac%7B%5Csqrt%7B%28k%2B1%29%5E2-1%7D%7D%7B%5Csqrt%7B%28k%2B1%29%5E2%7D%7D-%5Cdfrac%7B1%7D%7Bk%2B1%7D%5Ccdot%5Cdfrac%7B%5Csqrt%7Bk%5E2-1%7D%7D%7B%5Csqrt%7Bk%5E2%7D%7D%5Cright%5D%3D%5C%5C%5C%5C%5C%5C%3D%0A%5Csum%5Climits_%7Bk%3D1%7D%5En%5Carcsin%5Cleft%5B%5Cdfrac%7B1%7D%7Bk%7D%5Ccdot%5Csqrt%7B%5Cdfrac%7B%28k%2B1%29%26%5E2-1%7D%7B%28k%2B1%29%5E2%7D%7D-%5Cdfrac%7B1%7D%7Bk%2B1%7D%5Ccdot%5Csqrt%7B%5Cdfrac%7Bk%5E2-1%7D%7Bk%5E2%7D%7D%5Cright%5D%3D%5C%5C%5C%5C%5C%5C%3D%0A%5Csum%5Climits_%7Bk%3D1%7D%5En%5Carcsin%5Cleft%5B%5Cdfrac%7B1%7D%7Bk%7D%5Ccdot%5Csqrt%7B1-%5Cdfrac%7B1%7D%7B%28k%2B1%29%5E2%7D%7D-%5Cdfrac%7B1%7D%7Bk%2B1%7D%5Ccdot%5Csqrt%7B1-%5Cdfrac%7B1%7D%7Bk%5E2%7D%7D%5Cright%5D%3D%5C%5C%5C%5C%5C%5C%0A)
![=\sum\limits_{k=1}^n\arcsin\left[\dfrac{1}{k}\cdot\sqrt{1-\left(\dfrac{1}{k+1}\right)^2}-\dfrac{1}{k+1}\cdot\sqrt{1-\left(\dfrac{1}{k}\right)^2}\right]=\\\\\\= \sum\limits_{k=1}^n\left[\arcsin\left(\dfrac{1}{k}\right)-\arcsin\left(\dfrac{1}{k+1}\right)\right]=\\\\\\](https://tex.z-dn.net/?f=%3D%5Csum%5Climits_%7Bk%3D1%7D%5En%5Carcsin%5Cleft%5B%5Cdfrac%7B1%7D%7Bk%7D%5Ccdot%5Csqrt%7B1-%5Cleft%28%5Cdfrac%7B1%7D%7Bk%2B1%7D%5Cright%29%5E2%7D-%5Cdfrac%7B1%7D%7Bk%2B1%7D%5Ccdot%5Csqrt%7B1-%5Cleft%28%5Cdfrac%7B1%7D%7Bk%7D%5Cright%29%5E2%7D%5Cright%5D%3D%5C%5C%5C%5C%5C%5C%3D%0A%5Csum%5Climits_%7Bk%3D1%7D%5En%5Cleft%5B%5Carcsin%5Cleft%28%5Cdfrac%7B1%7D%7Bk%7D%5Cright%29-%5Carcsin%5Cleft%28%5Cdfrac%7B1%7D%7Bk%2B1%7D%5Cright%29%5Cright%5D%3D%5C%5C%5C%5C%5C%5C)
![=\bigg[\arcsin(1)-\arcsin\left(\frac{1}{2}\right)\bigg]+\bigg[\arcsin\left(\frac{1}{2}\right)-\arcsin\left(\frac{1}{3}\right)\bigg]+\\\\\\+ \bigg[\arcsin\left(\frac{1}{3}\right)-\arcsin\left(\frac{1}{4}\right)\bigg]+\dots+ \bigg[\arcsin\left(\frac{1}{n}\right)-\arcsin\left(\frac{1}{n+1}\right)\bigg]=\\\\\\](https://tex.z-dn.net/?f=%3D%5Cbigg%5B%5Carcsin%281%29-%5Carcsin%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5Cbigg%5D%2B%5Cbigg%5B%5Carcsin%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29-%5Carcsin%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%5Cright%29%5Cbigg%5D%2B%5C%5C%5C%5C%5C%5C%2B%0A%5Cbigg%5B%5Carcsin%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%5Cright%29-%5Carcsin%5Cleft%28%5Cfrac%7B1%7D%7B4%7D%5Cright%29%5Cbigg%5D%2B%5Cdots%2B%0A%5Cbigg%5B%5Carcsin%5Cleft%28%5Cfrac%7B1%7D%7Bn%7D%5Cright%29-%5Carcsin%5Cleft%28%5Cfrac%7B1%7D%7Bn%2B1%7D%5Cright%29%5Cbigg%5D%3D%5C%5C%5C%5C%5C%5C)
![\sum\limits_{k=1}^n\arcsin\left[\dfrac{\sqrt{k^2+2k}-\sqrt{k^2-1}}{k(k+1)}\right]=\dfrac{\pi}{2}-\arcsin\left(\dfrac{1}{n+1}\right)}](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bk%3D1%7D%5En%5Carcsin%5Cleft%5B%5Cdfrac%7B%5Csqrt%7Bk%5E2%2B2k%7D-%5Csqrt%7Bk%5E2-1%7D%7D%7Bk%28k%2B1%29%7D%5Cright%5D%3D%5Cdfrac%7B%5Cpi%7D%7B2%7D-%5Carcsin%5Cleft%28%5Cdfrac%7B1%7D%7Bn%2B1%7D%5Cright%29%7D)
![\sum\limits_{k=1}^\infty\arcsin\left[\dfrac{\sqrt{k^2+2k}-\sqrt{k^2-1}}{k(k+1)}\right]=\\\\\\= \lim\limits_{n\to\infty}\sum\limits_{k=1}^n\arcsin\left[\dfrac{\sqrt{k^2+2k}-\sqrt{k^2-1}}{k(k+1)}\right]=\\\\\\= \lim\limits_{n\to\infty}\Bigg(\dfrac{\pi}{2}-\arcsin\left(\dfrac{1}{n+1}\right)\Bigg)=\dfrac{\pi}{2}-\lim\limits_{n\to\infty}\arcsin\left(\dfrac{1}{n+1}\right)=\\\\\\= \Bigg\{\dfrac{1}{n+1}\xrightarrow{n\to\infty}0\Bigg\}=\dfrac{\pi}{2}-\arcsin(0)=\dfrac{\pi}{2}-0=\dfrac{\pi}{2}](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bk%3D1%7D%5E%5Cinfty%5Carcsin%5Cleft%5B%5Cdfrac%7B%5Csqrt%7Bk%5E2%2B2k%7D-%5Csqrt%7Bk%5E2-1%7D%7D%7Bk%28k%2B1%29%7D%5Cright%5D%3D%5C%5C%5C%5C%5C%5C%3D%0A%5Clim%5Climits_%7Bn%5Cto%5Cinfty%7D%5Csum%5Climits_%7Bk%3D1%7D%5En%5Carcsin%5Cleft%5B%5Cdfrac%7B%5Csqrt%7Bk%5E2%2B2k%7D-%5Csqrt%7Bk%5E2-1%7D%7D%7Bk%28k%2B1%29%7D%5Cright%5D%3D%5C%5C%5C%5C%5C%5C%3D%0A%5Clim%5Climits_%7Bn%5Cto%5Cinfty%7D%5CBigg%28%5Cdfrac%7B%5Cpi%7D%7B2%7D-%5Carcsin%5Cleft%28%5Cdfrac%7B1%7D%7Bn%2B1%7D%5Cright%29%5CBigg%29%3D%5Cdfrac%7B%5Cpi%7D%7B2%7D-%5Clim%5Climits_%7Bn%5Cto%5Cinfty%7D%5Carcsin%5Cleft%28%5Cdfrac%7B1%7D%7Bn%2B1%7D%5Cright%29%3D%5C%5C%5C%5C%5C%5C%3D%0A%5CBigg%5C%7B%5Cdfrac%7B1%7D%7Bn%2B1%7D%5Cxrightarrow%7Bn%5Cto%5Cinfty%7D0%5CBigg%5C%7D%3D%5Cdfrac%7B%5Cpi%7D%7B2%7D-%5Carcsin%280%29%3D%5Cdfrac%7B%5Cpi%7D%7B2%7D-0%3D%5Cdfrac%7B%5Cpi%7D%7B2%7D)
![\sum\limits_{k=1}^\infty\arcsin\left[\dfrac{\sqrt{k^2+2k}-\sqrt{k^2-1}}{k(k+1)}\right]=\dfrac{\pi}{2}](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bk%3D1%7D%5E%5Cinfty%5Carcsin%5Cleft%5B%5Cdfrac%7B%5Csqrt%7Bk%5E2%2B2k%7D-%5Csqrt%7Bk%5E2-1%7D%7D%7Bk%28k%2B1%29%7D%5Cright%5D%3D%5Cdfrac%7B%5Cpi%7D%7B2%7D)
