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
I would say that the last one would be the most accurate.
Answer:
Step-by-step explanation:
<u>Use points on the graph:</u>
<u>Find the slope:</u>
<u>The y-intercept is known b = 7, so the equation is:</u>
Answer:
![2,25[-3 + x]](https://tex.z-dn.net/?f=2%2C25%5B-3%20%2B%20x%5D)
Step-by-step explanation:
The Greatest Common Divisor [GCD] is 2,25; you factor that out, leaving the remaining result inside the brackets.
I am joyous to assist you anytime.
<span>First we define Charlene's the average time, which is (8.4 + 8.6 + 8.3 + 8.5 + 8.7 + 8.5)/6 = 8.5. Normal time is 8.5/1.1 = 7.7. Charlene is faster than normal.</span>