Convert a fraction to simplest form
1 answer:
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Answer:
Step-by-step explanation:
we want to figure out the general term of the following recurrence relation
we are given a linear homogeneous recurrence relation which degree is 2. In order to find the general term ,we need to make it a characteristic equation i.e
the steps for solving a linear homogeneous recurrence relation are as follows:
- Create the characteristic equation by moving every term to the left-hand side, set equal to zero.
- Solve the polynomial by factoring or the quadratic formula.
- Determine the form for each solution: distinct roots, repeated roots, or complex roots.
- Use initial conditions to find coefficients using systems of equations or matrices.
Step-1:Create the characteristic equation
Step-2:Solve the polynomial by factoring
factor the quadratic:
solve for x:
Step-3:Determine the form for each solution
since we've two distinct roots,we'd utilize the following formula:
so substitute the roots we got:
Step-4:Use initial conditions to find coefficients using systems of equations
create the system of equation:
solve the system of equation which yields:
finally substitute:
and we're done!
Answer:
16 students can sit around a cluster of 7 square table.
Step-by-step explanation:
Consider the provided information.
We need to find how many students can sit around a cluster of 7 square table.
The tables in a classroom have square tops.
Four students can comfortably sit at each table with ample working space.
If we put the tables together in cluster it will look as shown in figure.
From the pattern we can observe that:
Number of square table in each cluster Total number of students
1 4
2 6
3 8
4 10
5 12
6 14
7 16
Hence, 16 students can sit around a cluster of 7 square table.
