Assume that when adults with smartphones are randomly​

Perform the indicated operation with complex numbers. (Simplify your answe completely.)
${\displaystyle (4-8i)(9+7i)}$

How to solve $\mathbf{\text{x}}\text{'}\text{'}\left(t\right)=\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]\mathbf{\text{x}}\left(t\right)$
What I'm thinking is to consider the first order version
$\mathbf{\text{x}}\text{'}\left(t\right)=\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]\mathbf{\text{x}}\left(t\right)$
which I know how to solve, the solution is
$\mathbf{\text{x}}\left(t\right)=\mathbf{\text{c}}\left[\begin{array}{c}{e}^{-t}\\ e^{-t}\end{array}\right]$
How do I use this to solve the second-order equation?

${\displaystyle {\log }_3\left(\frac{x^9{y}^8}{7}\right)}$
A) ${\displaystyle 9{\log }_3\left(x\right)+8{\log }_3\left(y\right)-{\log }_3\left(7\right)}$
B) ${\displaystyle 9{\log }_3\left(x\right)-8{\log }_3\left(y\right)-{\log }_3\left(7\right)}$
C) $\left(9{\log }_3\right(x\left)\right)\left(8{\log }_3\right(y\left)\right)-{\log }_3\left(7\right)$
D) ${\displaystyle 9{\log }_3\left(x\right)+8{\log }_3\left(y\right)-{\log }_3\left(7\right)}$

(ad≥ + 2ycost = coser?t

 Let f be the function from R to R defined by f(x) = x2 •

 Find

 a) f-1 ({1}).

 b) f-1 ({x \ 0 < x < I }).

 c) f-1 ({x \ x > 4}).

Let ${\displaystyle a_1,b_1}$ be two real numbers such that ${\displaystyle 0<a_1<b_1}$. For ${\displaystyle n\ge 1}$, we define ${\displaystyle a_{n+1}={\left(a_n{b}_n\right)}^{\frac{1}{2}}}$ and $b_{n+1}=\frac{(a_n+b_n)}{2}$
a) Prove that the sequence ${\displaystyle \left\{a_n\right\}n\in N}$ is monotonically increasing and that the sequence ${\displaystyle \left\{b_n\right\}n\in N}$ is monotonically decreasing.
b) Show that the sequences ${\displaystyle \left\{a_n\right\}}$ and ${\displaystyle \left\{b_n\right\}}$ are bounded.
c) Deduce that the two sequences converge and prove that they converge to the same limit.

Find the 51st term of the arithmetic sequence $29,9,-11,\mathrm{.}\mathrm{.}\mathrm{.}$29,9,−11,...