I = sqrt(-1)
i^2 = -1
(-i)^2 = (-i)(-i) = i^2 = -1
(-i)^3 = (-i)(-i)(-i) = (-i)(i^2) = i
use these facts to find which equation is correct if x = -i
i bet on 2,3 or 4
Answer:
Step-by-step explanation:
If 3/4 of the lot was full and the lot holds 1000 vehicles, then there are 3/4(1000) in the lot. 3/4(1000) = 750. That means there are 750 vehicles in the lot. If 200 cars are in the lot, then 750 - 200 = 550 trucks.
i think it's t=0.2 Hope it helps:)
Answer:
m
Step-by-step explanation:
Let
Bas length of box=b
Height of box=h
Material used in constructing of box=36 square m
We have to find the height h and base length b of the box to maximize the volume of box.
Surface area of box=![2b^2+4bh](https://tex.z-dn.net/?f=2b%5E2%2B4bh)
![2b^2+4bh=36](https://tex.z-dn.net/?f=2b%5E2%2B4bh%3D36)
![b^2+2bh=18](https://tex.z-dn.net/?f=b%5E2%2B2bh%3D18)
![2bh=18-b^2](https://tex.z-dn.net/?f=2bh%3D18-b%5E2)
![h=\frac{18-b^2}{2b}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B18-b%5E2%7D%7B2b%7D)
Volume of box, V=![b^2h](https://tex.z-dn.net/?f=b%5E2h)
Substitute the values
![V=b^2\times \frac{18-b^2}{2b}](https://tex.z-dn.net/?f=V%3Db%5E2%5Ctimes%20%5Cfrac%7B18-b%5E2%7D%7B2b%7D)
![V=\frac{1}{2}(18b-b^3)](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B2%7D%2818b-b%5E3%29)
Differentiate w. r.t b
![\frac{dV}{db}=\frac{1}{2}(18-3b^2)](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdb%7D%3D%5Cfrac%7B1%7D%7B2%7D%2818-3b%5E2%29)
![\frac{dV}{db}=0](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdb%7D%3D0)
![\frac{1}{2}(18-3b^2)=0](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%2818-3b%5E2%29%3D0)
![\implies 18-3b^2=0](https://tex.z-dn.net/?f=%5Cimplies%2018-3b%5E2%3D0)
![\implies 3b^2=18](https://tex.z-dn.net/?f=%5Cimplies%203b%5E2%3D18)
![b^2=6](https://tex.z-dn.net/?f=b%5E2%3D6)
![b=\pm \sqrt{6}](https://tex.z-dn.net/?f=b%3D%5Cpm%20%5Csqrt%7B6%7D)
The negative value of b is not possible because length cannot be negative.
Again differentiate w.r.t b
![\frac{d^2V}{db^2}=-3b](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E2V%7D%7Bdb%5E2%7D%3D-3b)
At
![\frac{d^2V}{db^2}=-3\sqrt{6}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E2V%7D%7Bdb%5E2%7D%3D-3%5Csqrt%7B6%7D%3C0)
Hence, the volume of box is maximum at
.
![h=\frac{18-(\sqrt{6})^2}{2\sqrt{6}}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B18-%28%5Csqrt%7B6%7D%29%5E2%7D%7B2%5Csqrt%7B6%7D%7D)
![h=\frac{18-6}{2\sqrt{6}}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B18-6%7D%7B2%5Csqrt%7B6%7D%7D)
![h=\frac{12}{2\sqrt{6}}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B12%7D%7B2%5Csqrt%7B6%7D%7D)
![h=\sqrt{6}](https://tex.z-dn.net/?f=h%3D%5Csqrt%7B6%7D)
m
Answer:
f(3)=56, f(-4)=277
Step-by-step explanation:
f(x)=x^4-8x-11
f(3)=3^4-8(3)-11=3*3*3*3-24-11=9*3*3-35=27*3-25=81-25=56
f(-4)=(-4)^4-8(-4)-11=(-4)(-4)(-4)(-4)+32-11=(16)(16)+32-11=256+32-11=288-11=277