Answer:
vapor fraction = 0.4 and 0.08
Explanation:
At reasonably high temperatures, a mixture will exist in the form of a sub cooled liquid. Between these extremes, the mixture exists in a two phrase region where it is a vapor liquid equilibrium. From a vapor-liquid phase diagram, a mixture of 40% A, 39% B, and 21% C separates to give the vapor compositions of 0.4 and 0.08.
Determine whether w is in the span of the given vectors v1; v2; : : : vn
. If your answer is yes, write w as a linear combination of the vectors v1; v2; : : : vn and enter the coefficients as entries of the matrix as instructed is given below
Explanation:
1.Vector to be in the span means means that it contain every element of said vector space it spans. So if a set of vectors A spans the vector space B, you can use linear combinations of the vectors in A to generate any vector in B because every vector in B is within the span of the vectors in A.
2.And thus v3 is in Span{v1, v2}. On the other hand, IF all solutions have c3 = 0, then for the same reason we may never write v3 as a sum of v1, v2 with weights. Thus, v3 is NOT in Span{v1, v2}.
3.In the theory of vector spaces, a set of vectors is said to be linearly dependent if at least one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be linearly independent.
4.Given a set of vectors, you can determine if they are linearly independent by writing the vectors as the columns of the matrix A, and solving Ax = 0. If there are any non-zero solutions, then the vectors are linearly dependent. If the only solution is x = 0, then they are linearly independent.
Step 1:
Start by setting it up with the divisor 8 on the left side and the dividend 27 on the right side like this:
8 ⟌ 2 7
Step 2:
The divisor (8) goes into the first digit of the dividend (2), 0 time(s). Therefore, put 0 on top:
0
8 ⟌ 2 7
Step 3:
Multiply the divisor by the result in the previous step (8 x 0 = 0) and write that answer below the dividend.
0
8 ⟌ 2 7
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (2 - 0 = 2) and write the answer below.
0
8 ⟌ 2 7
- 0
2
Step 5:
Move down the 2nd digit of the dividend (7) like this:
0
8 ⟌ 2 7
- 0
2 7
Step 6:
The divisor (8) goes into the bottom number (27), 3 time(s). Therefore, put 3 on top:
0 3
8 ⟌ 2 7
- 0
2 7
Step 7:
Multiply the divisor by the result in the previous step (8 x 3 = 24) and write that answer at the bottom:
0 3
8 ⟌ 2 7
- 0
2 7
2 4
Step 8:
Subtract the result in the previous step from the number written above it. (27 - 24 = 3) and write the answer at the bottom.
0 3
8 ⟌ 2 7
- 0
2 7
- 2 4
3
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 27 divided by 8 calculated using Long Division is:
3
Answer:
In engineering design, failure is expected. It helps you find the best solutions before implementing them in the “real world”. Having a prototype fail is a GOOD thing, because that means you have learned something new about the problem and potential solutions.
Explanation:
