Hello! This question is hard to answer because at some parts it cut the text off. Are you able to post a picture of the question?
Answer:
C. The greatest common factor was not factored out correctly from second group
Step-by-step explanation:
The following lines show the process of factorization by using common factor.
<u>Line 1:</u>
In line 1, the equation is given and is grouped from which common factors can be taken. This is completely fine.
![(3x^{2}+xy^{2}) +(-3xy-y^{3} )=0](https://tex.z-dn.net/?f=%283x%5E%7B2%7D%2Bxy%5E%7B2%7D%29%20%2B%28-3xy-y%5E%7B3%7D%20%29%3D0)
The only thing missing was equate to zero, but the options below talk about correct factors only, therefore this can't be considered as a mistake and can be ignored completely.
<u>Line 2:</u>
In line 2, the common terms are taken out from groups. The common term x is taken from group 1 which is fine. In second group the common term -y is taken out, which is fine but it was not factored out correctly. The correct factorization would have been:
![x(3x+y^{2}) -y(3x +y^{2} )=0](https://tex.z-dn.net/?f=x%283x%2By%5E%7B2%7D%29%20-y%283x%20%2By%5E%7B2%7D%20%29%3D0)
which is different from what is given in line 2.
Options:
A. The grouping is correct in line 1. So this option is does not hold.
B. Common factor was factored correctly from group 1. So this option does not hold.
C. Common factor was not factored correctly from group 2. So this option holds and is correct. Thus we choose this option as correct answer.
D. There is a mistake. So this option is also not correct.
<h3>
Answer: 0.1 units</h3>
===============================================
Work Shown:
0.001 = 1/1000
Apply the cube root to both parts of 1/1000 to get
![\sqrt[3]{1} = 1\\\\\sqrt[3]{1000} = 10](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B1%7D%20%3D%201%5C%5C%5C%5C%5Csqrt%5B3%5D%7B1000%7D%20%3D%2010)
So this means that, ![\left(\frac{1}{10}\right)^3 = \frac{1}{10}*\frac{1}{10}*\frac{1}{10} = \frac{1}{1000} = 0.001](https://tex.z-dn.net/?f=%5Cleft%28%5Cfrac%7B1%7D%7B10%7D%5Cright%29%5E3%20%3D%20%5Cfrac%7B1%7D%7B10%7D%2A%5Cfrac%7B1%7D%7B10%7D%2A%5Cfrac%7B1%7D%7B10%7D%20%3D%20%5Cfrac%7B1%7D%7B1000%7D%20%3D%200.001)
Having a side length of 1/10 = 0.1 unit leads to a volume of 0.001 cubic units.
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A shortcut alternative is to use your calculator to get
![(0.001)^{1/3} = 0.1](https://tex.z-dn.net/?f=%280.001%29%5E%7B1%2F3%7D%20%3D%200.1)
The exponent of 1/3 is the same as a cube root.
E^2x=(42-12)/3, that is easy
Then, the magic!
Ln(e^2x)=Ln[(42-12)/3]
2x.Ln(e)=Ln[(42-12)/3]. "Ln(e)=1"
X={Ln[(42-12)/3]}/2
Good luck!
M.