Answer:
the third one...............
Answer:
a) see below
b) 40x20 meters
Step-by-step explanation:
Write down what you know:
- The area of the enclosure is length*width, so
![A = x \cdot y](https://tex.z-dn.net/?f=A%20%3D%20x%20%5Ccdot%20y)
- The length of the fencing is 80 meters, so
![2y + x = 80](https://tex.z-dn.net/?f=2y%20%2B%20x%20%3D%2080)
Now we have to combine these two equations above, and get rid of y in the process.
First rewrite the second as:
![y = 40 - \frac12 x](https://tex.z-dn.net/?f=y%20%3D%2040%20-%20%5Cfrac12%20x)
Then substitute for y in the first:
![A = x (40 - \frac12 x) = 40x - \frac12x^2](https://tex.z-dn.net/?f=A%20%3D%20x%20%2840%20-%20%5Cfrac12%20x%29%20%3D%2040x%20-%20%5Cfrac12x%5E2)
b) To maximize A, find the zero of the first derivative:
![A'(x) = 40 - x = 0 \implies x=40](https://tex.z-dn.net/?f=A%27%28x%29%20%3D%2040%20-%20x%20%3D%200%20%5Cimplies%20x%3D40)
So y = (80-40)/2 = 20 meters.
Enrico Fermi was an Italian–American physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and the "architect of the atomic bomb". He was one of very few physicists to excel in both theoretical physics and experimental physics.
Write the equation based on the problem
r stands for the price of a regular ticket, v stands for the price of a VIP ticket.
⇒ 69r + 40v = 12,601
⇒ 80r + 55v = 16,300
Solve the equation using elimination method.
I'm eliminating v, so I can find the r. We can eliminate v by changing the coefficient of first and second equation into the same number.
69r + 40v = 12,601 (multiply 11)
80r + 55v = 16,300 (multiply 8)
-----------------------------------------
759r + 440v = 138,611
640r + 440v = 130,400
------------------------------ - (substract)
119r = 8,211
r = 69
Subtitute 69 as r to one of the equation and find v
80r + 55v = 16,300
80(69) + 55v = 16,300
5,520 + 55v = 16,300
55v = 10,780
v = 196
So the price of a regular ticket is $69 and the price of a VIP ticket is $196
Find the difference
difference = 196 - 69
difference = 127
The difference is $127