세 점 \( O, A, B \) 에 대하여 \( \overrightarrow{O A}=\vec{a}, \overrightarrow{O B}=\vec{b} \) 라 하자. 선분 \( A B \) 를 \( 2: 3 \) 으 로 내분하는 점을 \( P \), 외분하는 점을 \( Q \) 라 할 때, 벡터 \( \overrightarrow{P Q} \) 를 \( \vec{a}, \vec{b} \) 로 나타내면 \( \frac{1}{5}(x \vec{a}+y \vec{b}) \) 이다. \( x \) 는?

두 평면벡터 \( \vec{a}=(12,-1), \vec{b}=(4,-6) \) 의 내적을 구하여라.

3. The volume, \( V \), of a cylinder with radius \( r \) and height \( h \) can be found using this equation. Which of the following equations has been correctly rearranged to solve for \( r \) ?

D. Which function \( A \) represents the area of the \( n \)th square, where \( n \) represents the total number of inscribed squares? \( A(n)=(64+n)\left(\frac{1}{2}\right)^{n} \) \( A(n)=64 n\left(\frac{1}{2}\right)^{n}-n \) \( A(n)=64 n\left(\frac{1}{2}\right)^{n}+n \) \( A(n)=64\left(\frac{1}{2}\right)^{n} \)

6) A line can only be used as a justification step once in a proof, such that if Line \( \# 1 \) is used with a modus ponens, it cannot be used for any subsequent steps of the proof.

If \( G H=80, H F=60, G F=75, K I=30 \), and \( J I=37.5 \), find the perimeter of \( \triangle I J K \). Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.