Asquare with side x is changing with time where x(t)=3t+1. what is rate of change of the area of the square when t=2 seconds.

Rate of change of the area of the square is 42 units at t = 2.

Step-by-step explanation:

We note that the area of the square is given by: but we aim to find . But we can use the chain rule to pull out that dA/dt. Doing so gives us:

Now, (by the power rule and

But since we have "x" and not "t", we want to find what x is when t = 2. Substituting t = 2 gives us x(2) = 3(2) + 1 = 7.

So, finally, we see that:

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: