Find the domain and range of the following exponential function. \( y=-\log _{4}(x)+7 \) a) Record the vertical asymptote below. Be sure to record you answer as \( x=\# \). ing Record the domain below using interval notation. b) Record the range below using interval notation.

(16) \( g=x-c+y \), for \( x \)

Find the value of \( k \) that makes \( f(x) \) continuous at \( x=0 \) \[ f(x)=\left\{\begin{array}{ll}\frac{-5 x}{x^{2}-2 x} & \text { if } x \neq \\ k & \text { if } x=\end{array}\right. \] \( k=\square \)

Jika \( F(x)=\sin ^{2} 3 x \) maka \( \frac{d f}{d x} \cdots \)

Use the quadratic formula to solve the equation \( 2 x^{2}-3 x-5=0 \). \( \begin{array}{l}x=-5, x=2 \\ x=-1, x=\frac{5}{2} \\ x=-\frac{5}{2}, x=1 \\ x=-2, x=5\end{array} \)

November 6, 2024 at 8:54AM Solve the problem on a separate sheet of paper and submit the work to Grgdescope. SHOW ALL WORK using MatLab. 1. An experiment was conducted by having a group of children solve a puzzle. It was found that of those who had solved the puzzle on a given trial, 30\% could solve it on the next trial. And of those who couldn't solve the puzzle on a given trial, \( 60 \% \) could solve it on the next trail. At the present time, 80\% of the children solved the puzzle on the current trial, but 20\% did not. Assume that this process can be modeled as a Markov process. - Write the transition matrix. Label the columns and rows, using S for "able to solve" and NS for "not able to solve. - Write the initial distribution matrix. - What percent of the children will be able to solve the puzzle on the next trial (trial 1)? - What percent of the children will be able to solve the puzzle on trial 2? - After many trials, what percent of the children will fail to solve the puzzle on each trial?