How much pure acid should be mixed with 2 gallons of a \( 50 \% \) acid solution to get an \( 80 \% \) acid solution?

\( \sqrt { n ^ { 2 } - 1 } - ( n + 1 ) = \frac { ( n ^ { 2 } - 1 ) - ( n + 1 ) ^ { 2 } } { \sqrt { n ^ { 2 } - 1 } + ( n + 1 ) } = \frac { - 2 n - 2 } { \sqrt { n ^ { 2 } - 1 } + ( n + 1 ) } \rightarrow - 1 \)

268. Решите уравнение: \( \begin{array}{l}\text { a) }(y+2)\left(y^{2}-2 y+4\right)-y(y-3)(y+3)=44 \text {; } \\ \text { б) }(m-3)\left(m^{2}+3 m+9\right)-m(m+2)(m-2)=13 \\ \text { (B) }(3 a+1)\left(9 a^{2}-3 a+1\right)-3 a\left(9 a^{2}+4\right)=25 \text {; } \\ \text { (A) }(2 n-1)\left(4 n^{2}+2 n+1\right)-4 n\left(2 n^{2}-5\right)=21 \text {. }\end{array} \)

Вычислить следующие определители: а) \( \left|\begin{array}{cc}1 & -2 \\ -2 & 4\end{array}\right| \); б) \( \left|\begin{array}{ccc}1 & 2 & 0 \\ 0 & 0 & 3 \\ 5 & 0 & -1\end{array}\right| \), 2. Найти точку пересечения прямых \( l_{1}: 3 x-2 y=0 \) и \( l_{2}: y=-x+5 \). Построить прямые.

d) \( \begin{aligned} \frac{x}{2}-y & =\frac{5}{2} \\ 3 x+2 y & =-1(2)\end{aligned} \)

7. \( a, b \) ve \( c \) gerçel sayıları için \( a>0>b \cdot a \) \( b>c \) olduğuna göre, aşağıdakilerden hangisi kesinlil pozitiftir? \( \begin{array}{lll}\text { A) } a \cdot c & \text { B) } a \cdot b \cdot c & \text { C) } c \\ \text { D) } a+c & \text { E) } b^{2} \cdot c\end{array} \)