Answer:
Volume =
cubic centimeter
Step-by-step explanation:
Let the length of each side of the base of the box be A and the height of the box be H.
Area of material required to make the box is equal to is ![A^2 + 4*A*H.](https://tex.z-dn.net/?f=A%5E2%20%2B%204%2AA%2AH.)
Rearranging the above equation, we get -
![`H = \frac{(1900 - A^2)}{(4*A)}](https://tex.z-dn.net/?f=%60H%20%3D%20%5Cfrac%7B%281900%20-%20A%5E2%29%7D%7B%284%2AA%29%7D)
Volume of box is equal to product of base area of box and the height of the box -
![V = A*A* H](https://tex.z-dn.net/?f=V%20%3D%20A%2AA%2A%20H)
Substituting the given area we get -
![\frac{A^2*(1900 - A^2)}{4A} = \frac{(1900*A - A^3)}{4}](https://tex.z-dn.net/?f=%5Cfrac%7BA%5E2%2A%281900%20-%20A%5E2%29%7D%7B4A%7D%20%3D%20%5Cfrac%7B%281900%2AA%20-%20A%5E3%29%7D%7B4%7D)
For maximum volume
![\frac{dV}{dA} =0](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7BdA%7D%20%3D0)
![\frac{ 1900}{4} - \frac{3*A^2}{4} = 0](https://tex.z-dn.net/?f=%5Cfrac%7B%201900%7D%7B4%7D%20-%20%5Cfrac%7B3%2AA%5E2%7D%7B4%7D%20%3D%200)
![A^2 = \frac{1900}{3}](https://tex.z-dn.net/?f=A%5E2%20%3D%20%5Cfrac%7B1900%7D%7B3%7D)
Volume of the box
= ![\frac{\frac{1900}{3}*(1900 - \frac{1900}{3}) }{4 * \sqrt{\frac{1900}{3} } }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B1900%7D%7B3%7D%2A%281900%20-%20%5Cfrac%7B1900%7D%7B3%7D%29%20%7D%7B4%20%2A%20%5Csqrt%7B%5Cfrac%7B1900%7D%7B3%7D%20%7D%20%7D)
=
cubic centimeter
The answer is A. If you divide 3/8 which equals .375. Then you multiply .375 by 6 to get 2.25!
:D Hope this helps!
Answer:
12
Step-by-step explanation:
Answer:
![\left(g/f\right)\left(x\right)=\frac{x}{4}-\frac{1}{16}-\frac{79}{16\left(4x+1\right)}](https://tex.z-dn.net/?f=%5Cleft%28g%2Ff%5Cright%29%5Cleft%28x%5Cright%29%3D%5Cfrac%7Bx%7D%7B4%7D-%5Cfrac%7B1%7D%7B16%7D-%5Cfrac%7B79%7D%7B16%5Cleft%284x%2B1%5Cright%29%7D)
Step-by-step explanation:
![f(x)=4x+1](https://tex.z-dn.net/?f=f%28x%29%3D4x%2B1)
![g\left(x\right)=x^2\:-\:5](https://tex.z-dn.net/?f=g%5Cleft%28x%5Cright%29%3Dx%5E2%5C%3A-%5C%3A5)
As
(g/f)(x) = g(x) / f(x)
![=\:\frac{x^2\:-\:5}{4x+1}\:\:\:\:\:\:](https://tex.z-dn.net/?f=%3D%5C%3A%5Cfrac%7Bx%5E2%5C%3A-%5C%3A5%7D%7B4x%2B1%7D%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A)
![=\frac{x}{4}+\frac{-\frac{x}{4}-5}{4x+1}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%7D%7B4%7D%2B%5Cfrac%7B-%5Cfrac%7Bx%7D%7B4%7D-5%7D%7B4x%2B1%7D)
![=\frac{x}{4}-\frac{1}{16}+\frac{-\frac{79}{16}}{4x+1}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%7D%7B4%7D-%5Cfrac%7B1%7D%7B16%7D%2B%5Cfrac%7B-%5Cfrac%7B79%7D%7B16%7D%7D%7B4x%2B1%7D)
![=\frac{x}{4}-\frac{1}{16}-\frac{79}{16\left(4x+1\right)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%7D%7B4%7D-%5Cfrac%7B1%7D%7B16%7D-%5Cfrac%7B79%7D%7B16%5Cleft%284x%2B1%5Cright%29%7D)
Therefore,
![\left(g/f\right)\left(x\right)=\frac{x}{4}-\frac{1}{16}-\frac{79}{16\left(4x+1\right)}](https://tex.z-dn.net/?f=%5Cleft%28g%2Ff%5Cright%29%5Cleft%28x%5Cright%29%3D%5Cfrac%7Bx%7D%7B4%7D-%5Cfrac%7B1%7D%7B16%7D-%5Cfrac%7B79%7D%7B16%5Cleft%284x%2B1%5Cright%29%7D)
A+s=496
s=496-a
and we are also told that:
s=3a
Since s=s we can say:
3a=496-a add a to both sides
4a=496 divide both sides by 4
a=124
So 124 adult tickets were sold.