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.
Answer:
cross multiply and they should equal the same
Step-by-step explanation:
Answer:
Using 5.25 cups of flour would make 3 batches of cookies. He made 180 cookies.
Step-by-step explanation:
To see how many batches you make all you do is take the 5.25 and divide it by 1.75 because thats how much it takes to make 1. When you divide it you get 3. If there are 5 dozen in each batch thats 60 cookies because 1 dozen is 12. Then,since he made 3 batches you multiply the 60 by 3 and you get 180.
Hope this helps!
Answer:
x ≈ 83.533
y = 9105.13
Step-by-step explanation:
Step 1: Substitution
109x = 79x + 2506
30x = 2506
x = 83.533
Step 2: Plug <em>x</em> in
y = 109(83.533)
y = 9105.13
Graphically: