# Tutor profile: Fahim I.

## Questions

### Subject: SAT II Mathematics Level 2

Find the determinant of the following matrix: [ 4 5 ] [ 6 9 ]

Determinant of the matrix = a*d - b*c = 4*9 - 6*5 = 36-30 = 6.

### Subject: Java Programming

Assume you have a binary search tree, write a method that will give you the largest value in the BST.

public BinaryNode<T> getMax(){ BinaryNode<T> currentNode = root; while(currentNode.getRight() != null){ currentNode = currentNode.getRight(); } return currentNode; }

### Subject: Calculus

I am more experienced in topics in AP Calculus A/B. A hollow cylinder with a radius of 3 meters is being filled up with water at 2 m^3 per minute. How fast is the height increasing?

This is a related rates problem as my teacher would call it. First, we need to take the volume formula for a cylinder: V = PI*r^2*h. We take the derivative of this formula with respect to time and we get dV/dt = PI*r^2*dh/dt Notice how the value of 'r^2' is not affected by the derivative since as the water keeps on flowing into the cylinder it doesn't change the radius. So for this problem, we can treat the radius as a constant factor (this wouldn't be the case if we were filling a sphere up, for example). Now we take this derivative and plug in what we know we get dV/dt = 2; r = 3; dh/dt = ?. So we need to find out dh/dt. So we can plug our values into the equation dV/dt = PI*r^2*dh/dt and get 2 = PI*9*dh/dt which means dh/dt = 2/(9*PI) meters per minute. dh/dt means the change in height with respect to time, which is a fancy way of saying that that's our answer.

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