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)
Answer:
for second and third letters, we again have 26 combinations available and thus 26×26×26=17576 combinations for letters. But digits are from 0 to 9 i.e. 10 combinations for each place and tolal 10×10=100 combinations. Hence for LLLDD , we have 1,757,600 combinations available for license plates.
Step-by-step explanation:
There are 7 6ths in 1 1/6
Each of those slots would have 1/6 wrote in them I believe
Let me know if I'm correct :)
You would multiply 100894 by 23451 to get 2366065194 than add 4 to get 2366065198
Answer:
x will be 120 degrees
Step-by-step explanation:
I will loves easy questions!