The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
Let the area be y .
Area = (base) × (height)
Base = 2x
Height = h
Let the area of the rectangular pens be y .
∴ y = 2xh
Perimeter of all the fencing = 4x+3h
∴ 4x+3h = 120
now we solve for h
3h = 120-4x
h = 40 - 4/3 x
Now we will substitute this value in the above first equation:
y = 2xh
or, y = 2x (40 - 4/3 x)
or, y = 80x - 8/3 x²
Now for the maximum area we have to find the first order differentiation of y
now,
dy /dx = 80 - 16/3 x
At dy/dx = 0 we get the value of x for which y is maximum.
80 - 16/3 x = 0
or, - 16/3 x = -80
or, x = 15 feet
Hence height = 40 - 4/3 x = 40 - 20 = 20feet
Maximum area = 2xh = 2×15×40 = 1200 square feet
The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
Disclaimer : The missing figure for the question is attached below.
To learn more about area visit:
brainly.com/question/27531272
#SPJ4
Well it would be (x+3)(x+3)
using the FOIL method you end up with:
x^2 + 6x + 9
:D
(820*7)-(480*7)=? This is how to solve the equation
Answer:
Zach earns $10 and for the pair of boots Zach earns $15
Step-by-step explanation:
Let be x the number of pairs of shoes
Let be y the number of pairs of boots
Then we can establish the following system of equations with the data of the statement:

We subtract the second equation from the first equation to eliminate the variable y and solve for x, just like this:

For y replacing in the first equation the value of x and solving for y:

So for the pair of shoes Zach earns $10 and for the pair of boots Zach earns $15
Please mark be as brainliest if you found this helpful. please