Answer:
Bell Curve
Step-by-step explanation:
Answer:
The values of x for which the model is 0 ≤ x ≤ 3
Step-by-step explanation:
The given function for the volume of the shipping box is given as follows;
V = 2·x³ - 19·x² + 39·x
The function will make sense when V ≥ 0, which is given as follows
When V = 0, x = 0
Which gives;
0 = 2·x³ - 19·x² + 39·x
0 = 2·x² - 19·x + 39
0 = x² - 9.5·x + 19.5
From an hint obtained by plotting the function, we have;
0 = (x - 3)·(x - 6.5)
We check for the local maximum as follows;
dV/dx = d(2·x³ - 19·x² + 39·x)/dx = 0
6·x² - 38·x + 39 = 0
x² - 19/3·x + 6.5 = 0
x = (19/3 ±√((19/3)² - 4 × 1 × 6.5))/2
∴ x = 1.288, or 5.045
At x = 1.288, we have;
V = 2·1.288³ - 19·1.288² + 39·1.288 ≈ 22.99
V ≈ 22.99 in.³
When x = 5.045, we have;
V = 2·5.045³ - 19·5.045² + 39·5.045≈ -30.023
Therefore;
V > 0 for 0 < x < 3 and V < 0 for 3 < x < 6.5
The values of x for which the model makes sense and V ≥ 0 is 0 ≤ x ≤ 3.
Step-by-step explanation:
let say he sold 5 bagels then he would sell 5 bagels
12-5=7 , b=7
replace in 12-5=7
b=12-s
now, this polynomial has roots of 3-i and 4i, namely 3 - i and 0 + 4i.
let's bear in mind that a complex root never comes all by her lonesome, her sibling is always with her, the conjugate, so if 3 - i is there, 3 + i is also coming along, likewise if 0 + 4i is there, her sibling 0 - 4i is also there.
![\bf \begin{cases} x=3-i\implies &x-3+i=0\\ x=3+i\implies &x-3-i=0\\ x=4i\implies &x-4i=0\\ x=-4i\implies &x+4i=0 \end{cases}\\\\[-0.35em] ~\dotfill\\\\ (x-3+i)(x-3-i)(x-4i)(x+4i)=\stackrel{y}{0} \\[2em] \underset{\textit{difference of squares}}{[(x-3)+i][(x-3)-i]}\underset{\textit{difference of squares}}{[x-4i][x+4i]}=0](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20x%3D3-i%5Cimplies%20%26x-3%2Bi%3D0%5C%5C%20x%3D3%2Bi%5Cimplies%20%26x-3-i%3D0%5C%5C%20x%3D4i%5Cimplies%20%26x-4i%3D0%5C%5C%20x%3D-4i%5Cimplies%20%26x%2B4i%3D0%20%5Cend%7Bcases%7D%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%28x-3%2Bi%29%28x-3-i%29%28x-4i%29%28x%2B4i%29%3D%5Cstackrel%7By%7D%7B0%7D%20%5C%5C%5B2em%5D%20%5Cunderset%7B%5Ctextit%7Bdifference%20of%20squares%7D%7D%7B%5B%28x-3%29%2Bi%5D%5B%28x-3%29-i%5D%7D%5Cunderset%7B%5Ctextit%7Bdifference%20of%20squares%7D%7D%7B%5Bx-4i%5D%5Bx%2B4i%5D%7D%3D0)
![\bf [(x-3)^2-i^2][x^2-(4i)^2]=y\implies [(x-3)^2-(-1)][x^2-(4^2i^2)]=0 \\[2em] [(x-3)^2-(-1)][x^2-(16(-1))]=0\implies [(x-3)^2+1][x^2+16]=0 \\[2em] [(x^2-6x+9)+1][x^2+16]=y\implies (x^2-6x+10)(x^2+16)=0 \\\\\\ x^4-6x^3+10x^2+16x^2-96x+160=0 \\\\\\ x^4-6x^3+26x^2-96x+160=0 \\\\\\ \stackrel{\textit{multiplying both sides by 4}}{4(x^4-6x^3+26x^2-96x+160)=4(0)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 4x^4-24x^3+104x^2-384x+640=y~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5B%28x-3%29%5E2-i%5E2%5D%5Bx%5E2-%284i%29%5E2%5D%3Dy%5Cimplies%20%5B%28x-3%29%5E2-%28-1%29%5D%5Bx%5E2-%284%5E2i%5E2%29%5D%3D0%20%5C%5C%5B2em%5D%20%5B%28x-3%29%5E2-%28-1%29%5D%5Bx%5E2-%2816%28-1%29%29%5D%3D0%5Cimplies%20%5B%28x-3%29%5E2%2B1%5D%5Bx%5E2%2B16%5D%3D0%20%5C%5C%5B2em%5D%20%5B%28x%5E2-6x%2B9%29%2B1%5D%5Bx%5E2%2B16%5D%3Dy%5Cimplies%20%28x%5E2-6x%2B10%29%28x%5E2%2B16%29%3D0%20%5C%5C%5C%5C%5C%5C%20x%5E4-6x%5E3%2B10x%5E2%2B16x%5E2-96x%2B160%3D0%20%5C%5C%5C%5C%5C%5C%20x%5E4-6x%5E3%2B26x%5E2-96x%2B160%3D0%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%204%7D%7D%7B4%28x%5E4-6x%5E3%2B26x%5E2-96x%2B160%29%3D4%280%29%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%204x%5E4-24x%5E3%2B104x%5E2-384x%2B640%3Dy~%5Chfill)
