Well x stands for an unknown number. So lets say the value of x is 11 you would do 11=9 3x 11 and then multiply 33 x 2
It is 5 > the check thingy 18 because if you do 18 then put the check it is 4.242640687119285
hope i help pls give bristliest to me
Answer: = 1whole
Step-by-step explanation:
Answer:
![\left[\begin{array}{c}-\frac{8}{\sqrt{117} } \\\frac{7}{\sqrt{117} }\\\frac{2}{\sqrt{117} }\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-%5Cfrac%7B8%7D%7B%5Csqrt%7B117%7D%20%7D%20%5C%5C%5Cfrac%7B7%7D%7B%5Csqrt%7B117%7D%20%7D%5C%5C%5Cfrac%7B2%7D%7B%5Csqrt%7B117%7D%20%7D%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
We are required to find a unit vector in the direction of:
![\left[\begin{array}{c}-8\\7\\2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-8%5C%5C7%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
Unit Vector, ![\hat{a}=\dfrac{\overrightarrow{a}}{|\overrightarrow{a}|}](https://tex.z-dn.net/?f=%5Chat%7Ba%7D%3D%5Cdfrac%7B%5Coverrightarrow%7Ba%7D%7D%7B%7C%5Coverrightarrow%7Ba%7D%7C%7D)
The Modulus of
=![\sqrt{(-8)^2+7^2+(-2)^2}=\sqrt{117}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-8%29%5E2%2B7%5E2%2B%28-2%29%5E2%7D%3D%5Csqrt%7B117%7D)
Therefore, the unit vector of the matrix is given as:
![\left[\begin{array}{c}-\frac{8}{\sqrt{117} } \\\frac{7}{\sqrt{117} }\\\frac{2}{\sqrt{117} }\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-%5Cfrac%7B8%7D%7B%5Csqrt%7B117%7D%20%7D%20%5C%5C%5Cfrac%7B7%7D%7B%5Csqrt%7B117%7D%20%7D%5C%5C%5Cfrac%7B2%7D%7B%5Csqrt%7B117%7D%20%7D%5Cend%7Barray%7D%5Cright%5D)
Answer:
![7^{-1} \equiv 943 \,\,\, \text{mod 1320}](https://tex.z-dn.net/?f=7%5E%7B-1%7D%20%5Cequiv%20943%20%5C%2C%5C%2C%5C%2C%20%5Ctext%7Bmod%201320%7D)
Step-by-step explanation:
According to the information you are looking for the smallest integer n greater than 1 such that
![n^{-1} (\text{mod} \,\,\,\, 1320)](https://tex.z-dn.net/?f=n%5E%7B-1%7D%20%20%28%5Ctext%7Bmod%7D%20%5C%2C%5C%2C%5C%2C%5C%2C%201320%29)
is defined.
To begin with remember what a coprime means, two numbers are coprimes when their greatest common divisor is 1.
For example, 9,12 are NOT coprime because their greater common divisor is 3. But 5,6 are coprime because their greatest common divisor is 1.
Also what Euler's theorem. If "a,m" are coprimes then
![{\displaystyle a^{\phi(m)} \equiv 1](https://tex.z-dn.net/?f=%7B%5Cdisplaystyle%20a%5E%7B%5Cphi%28m%29%7D%20%20%5Cequiv%201)
Where
is the Euler's totient function. Remember that the totient function computes the number of coprimes less than
. Then
The Euler's theorem can also be applied for multiplicative inverses.
The smallest integer coprime to 1320, also
![\phi(1320) = 320](https://tex.z-dn.net/?f=%5Cphi%281320%29%20%20%3D%20320)
Then
![7^{-1} \equiv 7 ^{\phi(1320)-1} \,\,\, \text{mod 1320} \equiv 7^{320-1} \,\,\, \text{mod 1320} \\\equiv 7^{319} \,\,\, \text{mod 1320} \equiv 943 \,\,\, \text{mod 1320}](https://tex.z-dn.net/?f=7%5E%7B-1%7D%20%20%5Cequiv%207%20%5E%7B%5Cphi%281320%29-1%7D%20%20%5C%2C%5C%2C%5C%2C%20%5Ctext%7Bmod%201320%7D%20%20%5Cequiv%207%5E%7B320-1%7D%20%5C%2C%5C%2C%5C%2C%20%5Ctext%7Bmod%201320%7D%20%20%5C%5C%5Cequiv%207%5E%7B319%7D%20%5C%2C%5C%2C%5C%2C%20%5Ctext%7Bmod%201320%7D%20%20%5Cequiv%20943%20%5C%2C%5C%2C%5C%2C%20%5Ctext%7Bmod%201320%7D)