Archimedes principle states
that
F1 / A1 = F2 / A2
F2 = (A2 / A1) * F1
Also, formula for the force is
F = mg. Formula for the area of the cylinder is A = πr^2, therefore we get
F2 = (πr2^2 / πr1^2) * mg
Since the diameter of the
cylinders are 2 cm and 24 cm, r1 = 12 and r2 = 1.
Substituting the values to the
derived equation, we get
F2 = (π 1^2 / π 12^2) * 2400 * 9.8
F2 = 163.3333 N
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Answer:
The consecutive charge configuration has a more intense field than alternating
Explanation:
In each corner we place a different account there are only two different settings, see attached.
In the case of alternating charging (+ - + -) see diagram 1, the electric field in the center is canceled in pairs, resulting in a zero field
In the case of consecutive loads (+ + - -) in this case we have a result between the two charges, therefore the total field is
E = 2 k q / ra2 a cos 45
The consecutive charge configuration has a more intense field than alternating
Answer: Hence, ( 30,20 ) will not maximize the profit as it lies inside the solution region.
Explanation:
Answer:
A. False
B. False
C. True
D. True
E. True
F. True
Explanation:
A. The equation Ax=b is referred to as a matrix equation and not vector equation.
B. If the augmented matrix [ A b ] has a pivot position in every row then equation Ax=b may or may not be consistent. It is inconsistent if [A b] has a pivot in the last column b and it is consistent if the matrix A has a pivot in every row.
C. In the product of Ax also called the dot product the first entry is a sum of products. For example the the product of Ax where A has [a11 a12 a13] in the first entry of each column and the corresponding entries in x are [x1 x2 x3] then the first entry in the product is the sum of products i.e. a11x1 + a12x2 +a13x3
D. If the columns of mxn matrix A span R^m, this states that every possible vector b in R^m is a linear combination of the columns which makes the equation consistent. So the equation Ax=b has at least one solution for each b in R^m.
E. It is stated that a vector equation x1a1 + x2a2 + x3a3 + ... + xnan = b has the same solution set as that of the linear system with augmented matrix [a1 a2 ... an b]. So the solution set of linear system whose augmented matrix is [a1 a2 a3 b] is the same as solution set of Ax=b if A=[a1 a2 a3] and b can be produced by linear combination of a1 a2 a3 iff the solution of linear system corresponding to [a1 a2 a3 b] takes place.
F. It is true because lets say b is a vector in R^m which is not in the span of the columns. b cannot be obtained for some x which belongs to R^m as b = Ax. So Ax=b is inconsistent for some b in R^m and has no solution.
