Prove that the divergence of a curl is always zero.

a) Give an example to show that the transitive closure of the symmetric closure of a relation is not necessarily the same as the symmetric closure of the transitive closure of this relation. b) Show, however, that the transitive closure of the symmetric closure of a relation must contain the symmetric closure of the transitive closure of this relation.

Lise overhears snippets of conversations between her classmates before the bell. Complete these sentences with the appropriate forms of the verbs.

Bea et Leo$\rule{1cm}{1pt}$ des tee-shirts. (vendre)

Suppose that the relation R is irreflexive. Is the relation R² necessarily irreflexive?

Find the zero of the function. $f(x)=0.25 x+0.5$

Suppose

$$A=\left[\begin{array}{cc} 3+2 i & 0 \\ -i & 2 \\ 1+i & 1-i \end{array}\right], \quad B=\left[\begin{array}{rr} -i & 2 \\ 0 & i \end{array}\right], \quad C=\left[\begin{array}{ccc} -1-i & 0 & -i \\ 3 & 2 i & -5 \end{array}\right]$$

Determine

$$A(B C)$$

The variable $z$ varies jointly with $x$ and $y$. Use the given values to write an equation relating $x, y$, and $z$. $x=8, y=4, z=16$

Show that the variance of the finite population $\left\{c_1, c_2, \ldots, c_N\right\}$ can be written as

$$\sigma^2=\frac{\sum_{i=1}^N c_i^2}{N}-\mu^2$$

Also, use this formula to recalculate the variance of the finite population of Exercise 16.

Vous avez été témoin des faits divers suivants. Votre partenaire va choisir un de ces faits et vous poser des questions comme:

• C'était quand?
• Qu'est-ce que tu faisais?
• Qu'est-ce que tu as vu?
• Ou étais-tu? $\quad$
• Qu'est-ce qui s'est passé?
• Qu'est-ce que tu as fait?

Répondez a ses questions en utilisant votre imagination.

Work the problem related to linear functions.

(a) Evaluate $f(-2)$ and $f(4)$.

(b) Graph $f$. How can the graph of $f$ be used to determine the zero of $f$?

(c ) Find the zero of $f$.

$$f(x)=x+0.5$$

Find the sum for each series.

$$\sum_{i=1}^4 i^i$$

Write given series in summation notation.

-2+4+(-6)+8+(-10)+12

Write the expression in the form $a+b i$. $(3-2 i)(4+5 i)$

Find a parametric representation. Circle in the plane z=1 with center (3, 2) and passing through the origin.