So we know that the formula for the area of a rectangle is

.
Now both the length and width of the rectangle increase at 3 km/s, therefore,
![A(t) = (3t+l)*(3t+w). Since the initial length = initial width = 4 km, then the initial area = 16 [tex]km^2](https://tex.z-dn.net/?f=A%28t%29%20%3D%20%283t%2Bl%29%2A%283t%2Bw%29.%20Since%20the%20initial%20length%20%3D%20initial%20width%20%3D%204%20km%2C%20then%20the%20initial%20area%20%3D%2016%20%5Btex%5Dkm%5E2)
. We want to know the time when the area is four times its original area, therefore, our new formula is:

. Plugging in our known
values we have:
![64 [km^2] = (3t + 4 [km])*(3t + 4 [km])](https://tex.z-dn.net/?f=64%20%5Bkm%5E2%5D%20%3D%20%283t%20%2B%204%20%5Bkm%5D%29%2A%283t%20%2B%204%20%5Bkm%5D%29)

The area is four times its original area after <span>\frac{4}{3} s[/tex]</span>.
140+500(10)
Multiply 500 times 10 which leaves you with 5000. Add 140 and the answer is 5140
Answer:
5 amperes will produce the maximum power of 300 watts.
Step-by-step explanation:
The general form of a quadratic function presents the function in the form

The vertex of a quadratic function is the highest or lowest point, also known as the maximum or minimum of a quadratic function.
We can define the vertex by doing the following:
- Identify a, b, and c
- Find, the x-coordinate of the vertex, by substituting a and b into

- Find, the y-coordinate of the vertex, by evaluating

We know that the power generated by an electrical circuit is modeled by

This function is a quadratic function.
To find the current that produce the maximum power you must
a = -12 and b = 120
- Find, the maximum current of the vertex, by substituting a and b into


- Find, the maximum-power, by evaluating


5 amperes will produce the maximum power of 300 watts.
We can check our work with the graph of the function
and see that the maximum is (5, 300).