Zheng

Let $\mathcal{G}$ be the graph of the parametric equations \begin{align*} x &= \cos(4t),\\ y &= \sin(6t). \end{align*}What is the length of the smallest interval $I$ such that the graph of these equations for all $t\in I$ produces the entire graph $\mathc...

(a) Suppose $x$ and $y$ are points on the unit circle such that the line through $x$ and $y$ intersects the real axis. Show that if $z$ is the point where this line intersects the real axis, then $z = \dfrac{x+y}{xy+1}$. (b) Let $Q_1 Q_2 \dotsb Q_{18}$ be...

The vector $\begin{pmatrix} k \\ 2 \end{pmatrix}$ is orthogonal to the vector $\begin{pmatrix} 3 \\ 5 \end{pmatrix}$. Find $k$. I thought the answer should be 10/4/

Latex: The vector $\begin{pmatrix} k \\ 2 \end{pmatrix}$ is orthogonal to the vector $\begin{pmatrix} 3 \\ 5 \end{pmatrix}$. Find $k$. Regular: The vector <k, 2>, is orthogonal to the vector <3, 5>. Find k. I can't seem to figure it out, I thought k would...

Compute the distance between the parallel lines given by \[\begin{pmatrix} 1 \\ 4 \end{pmatrix} + t \begin{pmatrix} 4 \\ 3 \end{pmatrix}\] and \[\begin{pmatrix} -5 \\ 6 \end{pmatrix} + s \begin{pmatrix} 4 \\ 3 \end{pmatrix}.\]

Find the $2 \times 2$ matrix $\bold{A}$ such that \[\bold{A} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2 \end{pmatrix}\] and \[\bold{A} \begin{pmatrix} 0 \\ 1 \end{pmatrix} = \begin{pmatrix} -7 \\ 4 \end{pmatrix}.\]

That answer keeps on coming as wrong, I had gotten that answer earlier. I am not sure what is wrong :(

Thanks!

I do not know how to solve this, I am struggling, any help would be appreciated!

I don't know what you are talking about, but the two real roots must be 3/4, and 9.

My bad! Thanks for the help! I was able to figure out the latex problem accordingly :)