Answer:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Step-by-step explanation:
The area for a rectangle is given by the formula:

Where <em>w</em> is the width and <em>l</em> is the length.
We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.
First, differentiate the equation with respect to <em>t</em>, where <em>w</em> and <em>l</em> are both functions of <em>t: </em>
![\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BdA%7D%7Bdt%7D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5Bw%5Cell%5D)
By the Product Rule:

Since we know that dl/dt = 6 and that dw/dt = 5:

We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:

The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Hey there!
The answer to your question is 6.
To solve this equation when t = 1, we can simply plug t into the equation.
3 x 2(1)
3 x 2
5
Hope this helps your assignment! Have a great day! Good luck!
Answer:
John Muir
John Muir was an American naturalist born in Scotland on April 21, 1838. Step-by-step explanation:
No because then they would be different triangles. Congruent triangles are triangles that are the same
I hope I've helped!
Answer:
10
Step-by-step explanation:
The absolute value of 10 is 10. Algebraically speaking, the absolute value of a number x takes x and makes it positive.