Well the line is straight so it will always have the same slope no matter what points you use but to solve it mathematically you do change in y/change in x
(3.5-(-1))/(4-(-5))
4.5/9 = 0.5
So the slope is 0.5
Now pick 2 random points on the line
(-3,0) and (5,4)
Now do the same thing for these 2 points
(4-0)/5-(-3)
4/8 = 0.5
So no matter what points the slope is always 0.5
So, if we define a straight line<span> to be the one that a particle takes when no forces are on it, or better yet that an object with no forces on it takes the quickest, and hence</span>shortest<span> route </span>between two points<span>, then walla, the </span>shortest distance between two points<span> is the geodesic; in Euclidean space, a </span>straight line<span> as</span>
Hello.
Have a beautiful and joyful day ahead
Thanks for points..
Answer:
80cm^2/s
Step-by-step explanation:
This is a related rates problem where we are considering the rate at which the area of a square changes with respect to time.
So lets consider the area of a square:
A = s^2 (where s represents the length of one side of the square)
Related rates problem deal with functions of time so if we take the area and side length as a function of time and then differentiate implicitly we get:

The problem states that the side of a square is increasing at a rate off 8cm/s so we can conclude that ds/dt = 8cm/s leaving us with:

Now, to solve for s we have to consider the other value given. If the area of the square is initially 25cm^2 we can plug this into our formula for area to solve for the side length.
25 = s^2
s = +/- 5 (since side lengths are only positive we only consider +5)
s = 5
Now we can plug this back in for s:

Therefore, the rate at which the area of the square is increasing is 80cm^2 per second.