A permutation on the set {1, . . . , k} is a one-to-one, onto function on this set. When p is a permutation, p^t means the composition of p with itself t times. Let PERM-POWER = {(p, q, t)| p = q^t where p and q are permutations on {1, . . . , k} and t is a binary integer}. Show that PERM-POWER ∈ P.

Idon’t understand the double8 coding problem. it is java

For positive constants a and b, the force between two atoms in a molecule is given f(r) = −a r2 + b r3 , where r > 0 is the distance between the atoms. note: a and b are upper case letters. (a) find f '(r) = (b) find the critical point for f(r). r = (c) find f ''(r) = (d) find the value of r so that f ''(r) = 0.

4. does the kernel phenotype distribution support the idea that the cob is the result of a dihybrid cross? what information supports your answer? if a dihybrid cross (i.e. f1 to f2 of standard mendelian crosses) is not indicated what conditions might contribute to this finding.