# Tutor profile: Dilnur Y.

## Questions

### Subject: SAT

if 2x-y=4, what is the value of 9^x/3^y?

9^x/3^y = (3^2x)/(3^y) = 3^(2x-y) We know that 2x-y=4, so: 3^(2x-y) = 3^4 = 81

### Subject: Number Theory

How can we compute the number of divisors of number n? Explain your answer step by step, and give an example.

First, we will have to get its prime factorization. Let's say it looks like this: n = (p1^a1) * (p2^a2)......* (pk^ak), where p1, p2....pk are relatively prime. Then, we should be able to see that, n divides every variation of its prime divisor's degree. In other words, a1 can be 0, 1, ....ak, and n will still divide each and every variation of the new number. This is true for a2,.....ak. Now, we are going to dive into the world of Combinatorics. There are (ai+1) variations of ai, starting from zero up until ai. To put it into perspective, we can get (ai+1) new divisors by changing the pi's degree from 0 until ai, where 1 <= i <= k. We use the multiplication principle to get the total number of divisors of n. So, the total number of divisors of n is (a1+1)*(a2+1).......(ak+1). Example: n=12. 1) primer factorization 12= (2^2)*3 2) Degrees a1=2, a2=1 3) Number of divisors is: (a1+1)*(a2+1) = (2+1)*(1+1) = 6 Indeed, 12 has six divisors: 1, 2, 3, 4, 6, 12

### Subject: C++ Programming

class Record{ public: Record(string date); }; class Book: public Record{ public: Book(string date, string title); // } In Java, we can access the superclass constructor of class Book with a keyword 'super'. In constructor Book, for instance, in Java, we could just say: Book(string date, string title){ super(date); } How can we achieve something similar in C++?

C++ does not let us access superclass methods with keywords, such as 'super'. Nonetheless, in C++, we can access the superclass by calling it by name, followed by two colons. So, we would access Record's constructor as such: Book(string date, string title){ Record::Record(date); }

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