After paying 4 tolls, Tony will have 4×$1.25 = $5.00 less change in his car. At that point, he will have $1 in change. The appropriate choice is
graph of line going through (0, 6) and (4,1)
Hello,
I would love to answer but there is no screenshot to see!
Engineering and computer game designer. geometry can be applicable in many careers.
A cardinal number of a set is the number of elemenents it contains. Therefore the cardinal number of A is equal to 5.
Answer:
![2 ft^3](https://tex.z-dn.net/?f=2%20ft%5E3)
Step-by-step explanation:
We are given that
Side of square shaped piece= 3ft
Let square of side x cut from each corner of square piece cardboard.
Length of box=![3-2x](https://tex.z-dn.net/?f=3-2x)
Breadth of box=![3-2x](https://tex.z-dn.net/?f=3-2x)
Height of box= x
We have to find the largest volume of box.
Volume of box is given by
![V=x(3-2x)^2](https://tex.z-dn.net/?f=V%3Dx%283-2x%29%5E2)
![V=(4x^3-12x^2+9x)](https://tex.z-dn.net/?f=V%3D%284x%5E3-12x%5E2%2B9x%29)
Differentiate w.r.t x
![\frac{dV}{dx}=12x^2-24x+9](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdx%7D%3D12x%5E2-24x%2B9)
Substitute ![\frac{dV}{dx}=0](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdx%7D%3D0)
![12x^2-24x+9=0](https://tex.z-dn.net/?f=12x%5E2-24x%2B9%3D0)
![4x^2-8x+3=0](https://tex.z-dn.net/?f=4x%5E2-8x%2B3%3D0)
![(2x-1)(2x-3)=0](https://tex.z-dn.net/?f=%282x-1%29%282x-3%29%3D0)
![2x-1=0\implies x=\frac{1}{2}](https://tex.z-dn.net/?f=2x-1%3D0%5Cimplies%20x%3D%5Cfrac%7B1%7D%7B2%7D)
![2x-3=0\implies x=\frac{3}{2}](https://tex.z-dn.net/?f=2x-3%3D0%5Cimplies%20x%3D%5Cfrac%7B3%7D%7B2%7D)
![x=\frac{1}{2}, x=\frac{3}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B2%7D%2C%20x%3D%5Cfrac%7B3%7D%7B2%7D)
Again differentiate w.r.t x
![\frac{d^2V}{dx^2}=24x-24](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E2V%7D%7Bdx%5E2%7D%3D24x-24)
Substitute ![x=\frac{1}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B2%7D)
![\frac{d^2V}{dx^2}=12-24=-12](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E2V%7D%7Bdx%5E2%7D%3D12-24%3D-12%3C0)
Substitute ![x=\frac{3}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B3%7D%7B2%7D)
![\frac{d^2V}{dx^2}=36-24=12>0](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E2V%7D%7Bdx%5E2%7D%3D36-24%3D12%3E0)
Therefore,
at ![x=\frac{1}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B2%7D)
Hence, the volume is maximum at ![x=\frac{1}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B2%7D)
Substitute the value
then we get
![V=\frac{1}{2}(3-1)^2=2 ft^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B2%7D%283-1%29%5E2%3D2%20ft%5E3)