Using only a simple calculator, find the values of \( k \) such that \( \operatorname{det}(M)=0 \), where \( M=\left[\begin{array}{ccc}-6 & k & 0 \\ 1 & 1 & k \\ 1 & 1 & 6\end{array}\right] \). As your answer, enter the SUM of the value(s) of \( k \) that satisfy this condition.

b. read none of magazine at all c. read exactly one of the magazines. 3. Use Mathematical induction to prove that \( x^{n}+y^{n} \) is divisible by \( x+y \) for odd natural number \( n \geq 1 \). 4. Solve the equation \( z^{6}+1=\sqrt{3} i \) where \( z \in c \).

b. read none of magazine at all c. read exactly one of the magazines. 3. Use Mathematical induction to prove that \( x^{n}+y^{n} \) is divisible by \( x+y \) for odd natural number \( n \geq 1 \). 4. Solve the equation \( z^{6}+1=\sqrt{3} i \) where \( z \in c \).

1.) Resolver la ecuación: \( \left|\frac{1}{\log _{x}(a)}\right|^{\log _{h}(x)}=b^{2 b} \)

av \( x>0, A=\sqrt{25 x^{2}}-\sqrt{4 x^{2}}-x \)

Perform the indicated operations, then simplify. \( \frac{5 y}{y+6}+\frac{7 y^{2}}{y^{2}-36}-\frac{4}{y-6} \) \( \frac{7 y^{2}+5 y-4}{y^{2}+2 y-36} \) \( \frac{12 y^{2}-34 y-24}{(y+6)(y-6)} \) \( \frac{12 y^{2}-34 y+24}{(y-6)(y+6)} \) \( \frac{7 y^{2}+5 y-4}{(y+6)(y-6)} \)