Answer:
Step-by-step explanation:
This is something you learn in Geometry. Gotta love Geometry and all of its hundreds of rules for triangles and circles and all that good stuff!!
The rule for similar figures is
ratio of perimeter (one-to-one)-->area (square the one-to-one)-->volume (cube the one-to-one).
We are given area. You CANNOT CUBE THE AREA MEASURES TO GET TO THE VOLUME!! You have to find the one-to-one first and then go forward from there.
If the area is the one-to-one squared, then
The one-to-one is 3:2. To get to the volume now, cube those one-to-one values:
The function that the naval engineer uses related P (pressure) and d (depth of ocean).
<em>Is there any restriction on the domain ( d: depth of the ocean)? Yes!</em>
The domain would be from 0 (at sea level or 0 depth) until the depth of the ocean (which is not infinite). Hence, we can write:
Choice D is the correct one.
ANSWER: D
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)
Step two is the answer i hope that helps
X=8 I’m not that to sure but hope i helped!
