Use the construction in proof of the Chinese reminder theorem to find all solutions to the system of congruence:
1 answer:
Answer:
17,101,185, 269,.... is the solution.
i.e. x≡17 mod(84) is the solution
Step-by-step explanation:
Given that the system is
Considering from the last as 7 is big,
possible solutions would be 10,17,24,...
Since this should also be 1(mod4) we get this as 1,5,9,...17, ...
Together possible solutions would be 17, 45,73,121,....
Now consider I equation and then possible solutions are
5,8,11,14,17,20,23,26,29,...,47,....75, ....
Hence solution is 17.
Next number satisfying this would be 101, 185, ...
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Answer:
3.897
Step-by-step explanation:
equilateral triangles are also equiangular, meaning the have equal angles.
Triangle sum theory says that angles of a triangle add up to 180.
That means each angle is 60.
A = bh/2
You need the (h). The base of is 3. Perimeter = 9, so each side is 3
Draw a perpendicular line for the height. The line cuts the base in half (1.5)
Using trigonometry you can find the height.
tan 60° = h/1.5
h = height, 1.5 is half of 3, 60° is the base angle.
multiply each side by 1.5
1.5(tan 60°) = h
h=2.598
then substitute h into formula
A= <u>(2.598)(3) </u>
2
A = 3.897 rounded