<span>we are asked to determine the integral tan^(-1)(8 x) dx. we use the inverse property of trigonometric equation in integral calculus such that the answer is </span><span>integral tan^(-1)(8 x) dx. = </span>x tan^(-1)(8 x)-1/16 log(64 x^2+1)+ C where C is a constant.
Answer:
1/3 kilometer in one minute
Step-by-step explanation:
8/24=1/3
Answer:
when n=7, x=2, ![p=\frac{1}{2}](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B1%7D%7B2%7D)
Step-by-step explanation:
Given : Information n=7, x=2, ![p=\frac{1}{2}](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B1%7D%7B2%7D)
To find : Evaluate ![C(n,x)\ p^x\ q^{n-x}](https://tex.z-dn.net/?f=C%28n%2Cx%29%5C%20p%5Ex%5C%20q%5E%7Bn-x%7D)
Solution :
The formula given is a binomial distribution,
can be written as ![^nC_x\ p^x\ q^{n-x}](https://tex.z-dn.net/?f=%5EnC_x%5C%20p%5Ex%5C%20q%5E%7Bn-x%7D)
Here, n=7 x=2 and ![p=\frac{1}{2}](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B1%7D%7B2%7D)
![q=1-p=1-\frac{1}{2}=\frac{1}{2}](https://tex.z-dn.net/?f=q%3D1-p%3D1-%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D)
Substitute all values in the formula,
![=^7C_2\ (\frac{1}{2})^2\ (\frac{1}{2})^{7-2}](https://tex.z-dn.net/?f=%3D%5E7C_2%5C%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E2%5C%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B7-2%7D)
![=\frac{7!}{2!(7-2)!}\ (\frac{1}{2})^2\ (\frac{1}{2})^{5}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B7%21%7D%7B2%21%287-2%29%21%7D%5C%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E2%5C%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B5%7D)
![=\frac{7!}{2!5!}\ (\frac{1}{2})^{2+5}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B7%21%7D%7B2%215%21%7D%5C%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B2%2B5%7D)
![=\frac{7\times 6\times 5!}{2\times 5!}\ (\frac{1}{2})^{7}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B7%5Ctimes%206%5Ctimes%205%21%7D%7B2%5Ctimes%205%21%7D%5C%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B7%7D)
![=21\times\frac{1}{128}](https://tex.z-dn.net/?f=%3D21%5Ctimes%5Cfrac%7B1%7D%7B128%7D)
![=\frac{21}{128}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B21%7D%7B128%7D)
Therefore,
when n=7, x=2, ![p=\frac{1}{2}](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B1%7D%7B2%7D)
Just work backwards.
342.5/ 34.25 = 10