Cemre G.

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Pre-Calculus

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Question:

Factor the following equation $$5x^2+11^x+2$$

Cemre G.

Answer:

$$5x + 11 + 2 $$ $$+5$$-------> $$+2$$ $$+1$$ -------> $$+1$$ Factor out 5 and 2 as (+5,+1) and (+2,+1). Make sure your signs are consistent. Then multiply the elements in the same row and sum those multiplications $$ 5*2 + 1*1 = 11$$ It gives the middle coefficient which is 11. Then answer is; $$ = (5x+2)(x+1)$$ Note: You could factor those out as (-5,-1) and (-2,-1). Then when you multiply them minuses will turn to plusses. $$(-5*-2)+(-1*-1) = + 10 + 1 = + 11$$

Artificial Intelligence

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Question:

What is the data structure of the frontier list ( list of successor nodes ) in breadth first search algorithm?

Cemre G.

Answer:

A "first in first out" queue

Physics

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Question:

An object of mass m and object of mass of 3m are released from the same height. Which one will have a higher velocity when they hit the ground? Ignore air friction and other dissipative effects.

Cemre G.

Answer:

From conservation of energy, initial gravitational potential energy will be equal to the kinetic energy when they hit the ground since dissipative effects are not present. Thus; $$mgh = 1/2*mv^2 $$ m's cancel out and we multiply each side by two to find velocity which is; $$ v = \sqrt{2gh} $$ It is clear that $$m$$'s will cancel out. As a result, it can be concluded that velocity is independent of the mass of the object, thus two of the object will have the same velocity when they hit the ground, regardless of their masses.

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