What is the distance between (-5, -6) and (-3,-8)?
1 answer:
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Use Hooke's law to find the spring constant. If it takes 8N to stretch the spring by 0.1m, then
I'm going to assume the spring is fixed to a ceiling, and that any stretching in the downward direction counts as movement in the positive direction. The spring's motion is then modeled by
where
is the position of the spring's free end as it moves up and down. Solving this is easy enough: the characteristic solution will be
Given that the spring is stretched to a length of 1m (a difference of 0.25m from its natural length), and is released with no external pushing or pulling, we have the two initial conditions
and 
.
So the spring's motion is dictated by the function
I'm going to assume the spring is fixed to a ceiling, and that any stretching in the downward direction counts as movement in the positive direction. The spring's motion is then modeled by
where
Given that the spring is stretched to a length of 1m (a difference of 0.25m from its natural length), and is released with no external pushing or pulling, we have the two initial conditions
So the spring's motion is dictated by the function
The correct answers are:
- The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true.
- The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.
Further explanation:
Given equations are:
2x-y = -5
x+3y = 22
We have to check whether the given statements are true or not. In order to find that we have to put the points in the equations
Putting the point in 2x-y = -5
Putting the point in x+3y=22
The point satisfies the first equation but doesn't satisfy the second. So,
1. The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true.
This statement is true as the point satisfies the first equation
2. The ordered pair (7, 19) is a solution to the second equation because it makes the second equation true.
This Statement is false.
3. The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.
This statement is true.
4. The ordered pair (7, 19) is a solution to the system because it makes both equations true.
This statement is false as the ordered pair doesn't satisfy both equations.
Keywords: Solution of system of equations, linear equations
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