Answer:
nine hundred thirty-eight one hundred twenty thousandths
Step-by-step explanation:
The simplified expression of (-11/2x+30)-2(-11/4x-5/2) is 35
<h3>How to simplify the expression?</h3>
The expression is given as:
(-11/2x+30)-2(-11/4x-5/2)
Expand the bracket
-11/2x + 30 + 11/2x + 5
Collect the like terms
11/2x -11/2x + 30 + 5
Evaluate the like terms
35
Hence, the simplified expression of (-11/2x+30)-2(-11/4x-5/2) is 35
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Tom--------------
>10 sq ft per minute
Tim-------------------
>3.5*10=35 sq ft per minute
Both painters (10+35)=45
sq ft per minute
let's assume a cubic unit crate----------> V1=1*1*1=1 feet3
<span>the total surface of the cube is S1=6*(1*1)=6 </span>sq
ft
if the volume of the cube increases twice
V2=2 feet3 ------------------- > 2=x*x*x------------- >x=2^(1/3)
And the S2=6*(2^(1/3)*<span> 2</span>^(1/3)=9.5244 sq ft
V2/V1=9.5244/6=1.5874
Therefore
If Tim and Tom-----------------------
> take 1 day----------- > to paint a crate V1
For the crate V2------------- > take 1.5874 days
assuming an 8-hour work day
0.5874*8=4.70 hr-------------- > 4 h 42 min
The answer is 1 day 4h 42 min
Answer:
Remember, a basis for the row space of a matrix A is the set of rows different of zero of the echelon form of A.
We need to find the echelon form of the matrix augmented matrix of the system A2x=b2
![B=\left[\begin{array}{cccc}1&2&3&1\\4&5&6&1\\7&8&9&1\\3&2&4&1\\6&5&4&1\\9&8&7&1\end{array}\right]](https://tex.z-dn.net/?f=B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%262%263%261%5C%5C4%265%266%261%5C%5C7%268%269%261%5C%5C3%262%264%261%5C%5C6%265%264%261%5C%5C9%268%267%261%5Cend%7Barray%7D%5Cright%5D)
We apply row operations:
1.
- To row 2 we subtract row 1, 4 times.
- To row 3 we subtract row 1, 7 times.
- To row 4 we subtract row 1, 3 times.
- To row 5 we subtract row 1, 6 times.
- To row 6 we subtract row 1, 9 times.
We obtain the matrix
![\left[\begin{array}{cccc}1&2&3&1\\0&-3&-6&-3\\0&-6&-12&-6\\0&-4&-5&-2\\0&-7&-14&-5\\0&-10&-20&-8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%262%263%261%5C%5C0%26-3%26-6%26-3%5C%5C0%26-6%26-12%26-6%5C%5C0%26-4%26-5%26-2%5C%5C0%26-7%26-14%26-5%5C%5C0%26-10%26-20%26-8%5Cend%7Barray%7D%5Cright%5D)
2.
- We subtract row two twice to row three of the previous matrix.
- we subtract 4/3 from row two to row 4.
- we subtract 7/3 from row two to row 5.
- we subtract 10/3 from row two to row 6.
We obtain the matrix
![\left[\begin{array}{cccc}1&2&3&1\\0&-3&-6&-3\\0&0&0&0\\0&0&3&2\\0&0&0&2\\0&0&0&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%262%263%261%5C%5C0%26-3%26-6%26-3%5C%5C0%260%260%260%5C%5C0%260%263%262%5C%5C0%260%260%262%5C%5C0%260%260%262%5Cend%7Barray%7D%5Cright%5D)
3.
we exchange rows three and four of the previous matrix and obtain the echelon form of the augmented matrix.
![\left[\begin{array}{cccc}1&2&3&1\\0&-3&-6&-3\\0&0&3&2\\0&0&0&0\\0&0&0&2\\0&0&0&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%262%263%261%5C%5C0%26-3%26-6%26-3%5C%5C0%260%263%262%5C%5C0%260%260%260%5C%5C0%260%260%262%5C%5C0%260%260%262%5Cend%7Barray%7D%5Cright%5D)
Since the only nonzero rows of the augmented matrix of the coefficient matrix are the first three, then the set
![\{\left[\begin{array}{c}1\\2\\3\end{array}\right],\left[\begin{array}{c}0\\-3\\-6\end{array}\right],\left[\begin{array}{c}0\\0\\3\end{array}\right] \}](https://tex.z-dn.net/?f=%5C%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C2%5C%5C3%5Cend%7Barray%7D%5Cright%5D%2C%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C-3%5C%5C-6%5Cend%7Barray%7D%5Cright%5D%2C%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C3%5Cend%7Barray%7D%5Cright%5D%20%5C%7D)
is a basis for Row (A2)
Now, observe that the last two rows of the echelon form of the augmented matrix have the last coordinate different of zero. Then, the system is inconsistent. This means that the system has no solutions.
Answer:
a) Frequency remains constant
b) Wavelength remains constant
c) speed of the wave remains constant
d) Intensity decreases
e) amplitude of its electric field decreases
Explanation:
a) Frequency can be defined as the number of crests that pass a fixed point in the medium in unit time. It is the source of the wave that will determine the frequency. If the small source is changed to a bigger and faster one then the frequency will change. In our case, there is no change of source of wave, so the frequency remains constant.
b) The speed of of the wave is directly proportional to the wavelength. If we double the speed, the wavelength also doubles. Since the speed has not been doubled in our case, the wavelength will remain constant.
c) As indicated in b) since the wavelength is proportional to speed and it has not changed in our case, then the speed remains constant.
d) The intensity of a wave decreases as it moves further away from the source.
e) The intensity is related to the amplitude. Since the intensity decreases, the amplitude also decreases.
