Answer:
40
Step-by-step explanation:
Calculator.
Answer:
74 gallons
Step-by-step explanation:
Volume of water to be added (in ft3) = π(2.0)
= 9.8175 ft3 (5 s.f)
Volume of water to be added (in gal) = 9.8175 (7.5)
= 74 gallons
Let x and y be the dimensions of the rectangle. If the perimeter is 40, we have
![2(x+y)=40 \iff x+y=20](https://tex.z-dn.net/?f=2%28x%2By%29%3D40%20%5Ciff%20x%2By%3D20)
We can expression one variable in terms of the others as
![x+y=20 \iff x=20-y](https://tex.z-dn.net/?f=x%2By%3D20%20%5Ciff%20x%3D20-y)
Since the area is the product of the dimensions, we have
![xy=(20-y)y=-y^2+20y](https://tex.z-dn.net/?f=xy%3D%2820-y%29y%3D-y%5E2%2B20y)
This is a parabola facing down, so it's vertex is the maximum:
![f(y)=-y^2+20y \implies f'(y)=-2y+20](https://tex.z-dn.net/?f=f%28y%29%3D-y%5E2%2B20y%20%5Cimplies%20f%27%28y%29%3D-2y%2B20)
So, the maximum is
![f'(y)=0 \iff -2y+20=0 \iff 2y=20 \iff y=10](https://tex.z-dn.net/?f=f%27%28y%29%3D0%20%5Ciff%20-2y%2B20%3D0%20%5Ciff%202y%3D20%20%5Ciff%20y%3D10)
And since we know that
, we have
as well.
This is actually a well known theorem: out of all the rectangles with given perimeter, the one with the greatest area is the square.
There is three terms in the expression "n2+6n-3".
In Algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs, or sometimes by divide.
You divide the top by the bottom. 8/18=.44