Answer:
![310\text{ feet and }210\text{ feet}](https://tex.z-dn.net/?f=310%5Ctext%7B%20feet%20and%20%7D210%5Ctext%7B%20feet%7D)
Step-by-step explanation:
GIVEN: A farmer has
of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is
.
TO FIND: Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions.
SOLUTION:
Let the length of rectangle be
and
perimeter of rectangular pen ![=2(x+y)=520\text{ feet}](https://tex.z-dn.net/?f=%3D2%28x%2By%29%3D520%5Ctext%7B%20feet%7D)
![x+y=260](https://tex.z-dn.net/?f=x%2By%3D260)
![y=260-x](https://tex.z-dn.net/?f=y%3D260-x)
area of rectangular pen ![=\text{length}\times\text{width}](https://tex.z-dn.net/?f=%3D%5Ctext%7Blength%7D%5Ctimes%5Ctext%7Bwidth%7D)
![=xy](https://tex.z-dn.net/?f=%3Dxy)
putting value of ![y](https://tex.z-dn.net/?f=y)
![=x(260-x)](https://tex.z-dn.net/?f=%3Dx%28260-x%29)
![=260x-x^2](https://tex.z-dn.net/?f=%3D260x-x%5E2)
to maximize ![\frac{d \text{(area)}}{dx}=0](https://tex.z-dn.net/?f=%5Cfrac%7Bd%20%5Ctext%7B%28area%29%7D%7D%7Bdx%7D%3D0)
![260-2x=0](https://tex.z-dn.net/?f=260-2x%3D0)
![x=130\text{ feet}](https://tex.z-dn.net/?f=x%3D130%5Ctext%7B%20feet%7D)
![y=390\text{ feet}](https://tex.z-dn.net/?f=y%3D390%5Ctext%7B%20feet%7D)
but the dimensions must be lesser or equal to than that of barn.
therefore maximum length rectangular pen ![=310\text{ feet}](https://tex.z-dn.net/?f=%3D310%5Ctext%7B%20feet%7D)
width of rectangular pen ![=210\text{ feet}](https://tex.z-dn.net/?f=%3D210%5Ctext%7B%20feet%7D)
Maximum area of rectangular pen ![=310\times210=65100\text{ feet}^2](https://tex.z-dn.net/?f=%3D310%5Ctimes210%3D65100%5Ctext%7B%20feet%7D%5E2)
Hence maximum area of rectangular pen is
and dimensions are ![310\text{ feet and }210\text{ feet}](https://tex.z-dn.net/?f=310%5Ctext%7B%20feet%20and%20%7D210%5Ctext%7B%20feet%7D)
10 2/3 inches=32/3 inches
8 3/4 inches= 35/4 inches
Find the common denominator, in this case, 12.
128/12 inches is Carla's plant
105/12 inches is Yolanda's plant.
128/12 > 105/12. Therefore, Carla's plant is taller than Yonlanda's
S=d/t
15 minutes = 0.25 hour
S=5/0.25
S= 20 miles per hour
"3 less than twice 'x' " . . . . that's (2x - 3)
" 2 more than the quantity (3 x) " . . . . . that's (3x + 2)
Their product is
(2x - 3) (3x + 2) .
If you want to expand it to a single expression, perform the multiplication,
and you have
6x² - 5x - 6 .
Answer:
-3 . -22 = 66 Explanation: There is no explanation, just putting this because of the 20 character minimum.