Answer:
C_h = 0.166 nF
C_L = 0.153 nF
Explanation:
Given:
- Ideal frequency f_o = 500 KHz
- Bandwidth of frequency BW = 40 KHz
- The resistance identical to both low and high pass filter = 2 Kohms
Find:
Design a passive band-pass filter to do this by cascading a low and high pass filter.
Solution:
- First determine the cut-off frequencies f_c for each filter:
f_c,L for High pass filter:
f_c,L = f_o - BW/2 = 500 - 40/2
f_c,L = 480 KHz
f_c,h for Low pass filter:
f_c,h = f_o + BW/2 = 500 + 40/2
f_c,h = 520 KHz
- Now use the design formula for R-C circuit for each filter:
General design formula:
f_c = 1 /2*pi*R*C_i
C,h for High pass filter:
C_h = 1 /2*pi*R*f_c,L
C_h = 1 /2*pi*2000*480,000
C_h = 0.166 nF
C,L for Low pass filter:
C_L = 1 /2*pi*R*f_c,h
C_L = 1 /2*pi*2000*520,000
C_L = 0.153 nF
Answer:
C. The buoyant forces are equal on the objects since they have equal mass.
Explanation:
Correct option (C) The buoyant forces are equal on the objects since they have equal mass. For floating objects, the buoyant force equals the weight of the objects. Since each object has the same weight, they must have the same buoyant force to counteract that weight and make them float.
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.
