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:
For 124 chirps per minute the temperature is 68 ºF.
For 68 chirps per minute the temperature is 54 ºF.
Step-by-step explanation:
Linear functions are those whose graph is a straight line. A linear function has the following form
b is the constant term or the y intercept. It is the value of the dependent variable when x = 0.
m is the coefficient of the independent variable. It is also known as the slope and gives the rate of change of the dependent variable.
We know that
- At 104 chirps per minute, the temperature is 63 ºF.
- At 176 chirps per minute, the temperature is 81 ºF.
This information can be converted to Cartesian coordinates (x, y). Where x = the number of chirps per minute and y = the temperature in ºF.
To find a linear function that let us find the outside temperature from how fast crickets chirp we must:
- Find the slope:
- Find the equation:
Solving for b
Therefore, the linear function is
Now, using this linear function we can know the temperature when we know the chirps per minute:
For 124 chirps per minute the temperature is:
For 68 chirps per minute the temperature is:
Answer:
1/5,3/10
Step-by-step explanation:
just look at the picture
