In the following exercise, describe and sketch the graph of the level surface f(x, y, z) = c at the given value of c.

$$f(x, y, z)=x^2-y+z^2, \quad c=2$$

A figure is graphed on coordinate plane the coordinates of its vertices are P(3, -5), Q(6, -1), R(4, 5), S(-2.5, 4), T(-5, -0.5) and the coordinates of its image are P'(8,-10), Q'(11, -6), R'(9, 0), S'(2.5, -1), T'(0, -5.5).

What translation maps PQRST onto P'Q'R'S'T' ?

Find the value of n such that the expression is a perfect square trinomial.

$$p^{2}-6 p+n$$

Find the indicated matrices using a calculator.

$$A=\begin{bmatrix} 6 & -3 \\ 4 & -5 \end{bmatrix}$$

$$B=\begin{bmatrix} 3 & 12 \\ -9 & -6 \end{bmatrix}$$

$$C=\begin{bmatrix} -1 & 4 & -7 \\ 2 & -6 & 11 \end{bmatrix}$$

$$D=\begin{bmatrix} 7 & 9 & -6 \\ -4 & 0 & 8 \end{bmatrix}$$

$$A - B - 2C$$

Consider the following parametric equations. Describe the curve.

$$x = t ^ { 3 } - 1$$

, y=5t+1;

$$- 3 \leq t \leq 3$$

Use the points A(-1,2,4),B(0,6,-3), and C(2,-4,1). Write parametric equations for the line through C and the midpoint of AB.

If n is a perfect number, prove that $\sum_{d \mid n} l / d=2$.

¿Qué hiciste el viernes pasado? ¿Qué hicieron tus amigos?

Compute $A-B^T$ if

$$\begin{equation*}A=\begin{bmatrix}3&&-1&&2&&4\\1&&5&&-6&&-2\end{bmatrix},B=\begin{bmatrix}-4&&0\\ 2&&5\\ -1&&-3\\ 0&&2 \end{bmatrix}\end{equation*}$$

Write parametric equations for the given curve for the given definitions of $x$:

$$y=-4 x+1$$

a. $x=t$ b. $x=\frac{t}{2}$ c. $x=-4 t$

Graph each interval and write the interval in set-builder notation.

$$(-1, \infty)$$

The 2016 U.S. presidential election was unusual in several ways. First, the candidate who won the most electoral votes, Donald Trump, did not win the most popular votes. Second, several minor-party candidates received enough votes to possibly affect the outcome. The official results showed that Hillary Clinton received 48.04% of the popular vote, Donald Trump received 45.95%, Gary Johnson got 3.28%, and Jill Stein won 1.06%. After the election, there was much discussion about the polls, which had indicated that Clinton would win. Suppose you had taken a Simple Random Sample of 1000 voters in an exit poll and asked them for whom they had voted.

In 95% of such polls, your sample proportion of voters for Trump should be between what two values?

Find a set of parametric equations to represent the graph of the given rectangular equation using the parameters (a) t = x and (b) t = 2 - x. $y=x^{3}-x^{2}$

For this exercise, let

$$\begin{array}{ll} \mathbf{A}=\left[\begin{array}{ll} 1 & 2 \\ 4 & 3 \end{array}\right], & \mathbf{B}=\left[\begin{array}{rr} -3 & 5 \\ 2 & -1 \end{array}\right], \\ \mathbf{C}=\left[\begin{array}{rr} 1 & -1 \\ -1 & 1 \end{array}\right], & \mathbf{D}=\left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right], \\ \mathbf{E}=\left[\begin{array}{ll} 1 & 3 \\ 2 & 6 \end{array}\right], & \mathrm{F}=\left[\begin{array}{rr} 3 & 3 \\ -1 & -1 \end{array}\right], \\ \mathbf{0}=\left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right], & \mathrm{I}=\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right] . \end{array}$$

Find the following. $\\$$$$\mathrm{E}+0$