A Cepheid star is a type of variable star, which means its brightness is not constant. The relationship between the brightness o
2 answers:
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Answer:
The solution proves that the equation has a non-trivial solution.
Step-by-step explanation:
We want to show that the equation has nontrivial solutions for which
Let be a set of non-zero numbers such that that
Because T is a linear solution:
=
=
=
=
= 0
This shows that are linearly independent with the mapping resulting in a non-trivial solution.
Answer:
Part 1: There are 4.7*10^21 ways to select 40 volunteers in subgroups of 10
Part 2: The research board can be chosen in 32760 ways
Step-by-step explanation:
Part 1:
The number of ways in which we can organized n elements into k groups with size n1, n2,...nk is calculate as:
So, in this case we can form 4 subgroups with 10 participants each one, replacing the values of:
- n by 40 participants
- k by 4 groups
- n1, n2, n3 and n4 by 10 participants of every subgroups
We get:
Part 2:
The number of ways in which we can choose k element for a group of n elements and the order in which they are chose matters is calculate with permutation as:
So in this case there are 4 offices in the research board, those are director, assistant director, quality control analyst and correspondent. Additionally this 4 offices are going to choose from a group of 5 doctors.
Therefore, replacing values of:
- n by 15 doctors
- k by 4 offices
We get: