Answer:
Step-by-step explanation:
hello,
i advice you check the question again if it is GF(
) or GF(24). i believe the question should rather be in this form;
multiplication in GF(
): Compute A(x)B(x) mod P(x) =
+
+1, where A(x)=
+1, and B(x)=
.
i will solve the above question and i believe with this you will be able to solve any related problem.
A(x)B(x)=![(x^{2} +1) (x^{3}+x+1) mod (x^{4}+x+1 ) = (x^{5} +x^{3}+x^{2} ) + (x^{3}+x+1 ) mod (x^{4} + x+1 )](https://tex.z-dn.net/?f=%28x%5E%7B2%7D%20%2B1%29%20%28x%5E%7B3%7D%2Bx%2B1%29%20mod%20%28x%5E%7B4%7D%2Bx%2B1%20%20%29%20%3D%20%28x%5E%7B5%7D%20%2Bx%5E%7B3%7D%2Bx%5E%7B2%7D%20%20%29%20%2B%20%28x%5E%7B3%7D%2Bx%2B1%20%20%29%20mod%20%28x%5E%7B4%7D%20%2B%20x%2B1%20%29)
= ![x^{5}+2x^{3} +x^{2} + x + 1 mod(x^{4}+x+1 )](https://tex.z-dn.net/?f=x%5E%7B5%7D%2B2x%5E%7B3%7D%20%2Bx%5E%7B2%7D%20%20%2B%20x%20%2B%201%20mod%28x%5E%7B4%7D%2Bx%2B1%20%20%29)
=![2x^{2} +1](https://tex.z-dn.net/?f=2x%5E%7B2%7D%20%2B1)
please note that the division by the modulus above we used
![\frac{x^{5}+2x^{3}+x^{2} +1 }{x^{4}+x+1}= x+\frac{2x^{3} +1}{x^{4}+x+1}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B5%7D%2B2x%5E%7B3%7D%2Bx%5E%7B2%7D%20%2B1%20%20%7D%7Bx%5E%7B4%7D%2Bx%2B1%7D%3D%20x%2B%5Cfrac%7B2x%5E%7B3%7D%20%2B1%7D%7Bx%5E%7B4%7D%2Bx%2B1%7D)
Answer:
8.54
Step-by-step explanation:
formula:
![d=\sqrt{(x2-x1)^2 + (y2-y1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x2-x1%29%5E2%20%2B%20%28y2-y1%29%5E2%7D)
![d=\sqrt{(-4 - (-7))^2 + (0-(-8))^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-4%20-%20%28-7%29%29%5E2%20%2B%20%280-%28-8%29%29%5E2%7D)
![d=\sqrt{3^2 + 8^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B3%5E2%20%2B%208%5E2%7D)
![d=\sqrt{9 + 64}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B9%20%2B%2064%7D)
![d=\sqrt{73}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B73%7D)
d= 8.54
Answer:
Theres a lot of numbers you can choose from 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96,
Step-by-step explanation:
Answer:
<4 = 22
Step-by-step explanation:
<4 = x
x + 158 = 180
x = 22