An 80.0-kg skydiver jumps out of a balloon at an altitude of 1 000 m and opens his parachute at an altitude of 200 m. (a) Assuming the total retarding force on the skydiver is constant at 50.0 N with the parachute closed and constant at 3 600 N with the parachute open, find the speed of the skydiver when he lands on the ground. (b) Do you think the skydiver will be injured? Explain. (c) At what height should the parachute be opened so that the final speed of the skydiver when he hits the ground is 5.00 m/s? (d) How realistic is the assumption that the total retarding force is constant? Explain.

Let $\mathcal{B}=\{b_1,b_2,b_3\}$, where

$$\begin{equation*}b_1=\begin{bmatrix}2\\1\\-1\end{bmatrix},b_2=\begin{bmatrix}-1\\-1\\1\end{bmatrix},\text{ and } b_3=\begin{bmatrix}-1\\-2\\1\end{bmatrix}.\end{equation*}$$

(a) Show that $\mathcal{B}$ is a basis for $R^3$. (b) Determine the matrix $A=[[e_1]_B\text{ }[e_2]_B\text{ }[e_3]_B]$. (c) What is the relationship between $A$ and $B=[b_1\text{ }b_2\text{ }b_3]$.

Using complete sentences, first tell if these items are in your classroom. Then tell how many of each there are.

Des ordinateurs?

Using complete sentences, first tell if these items are in your classroom. Then tell how many of each there are.

Des pasters?

Compute the scalar triple product $\mathbf{u} \cdot(\mathbf{v} \times \mathbf{w})$. u=(3, -1, 6), v=(2, 4, 3), w=(5, -1, 2).

Show that in terms of mole fractions of gases and total gas pressure the equilibrium constant expression for

$$\mathrm{N}_2(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_3(\mathrm{~g})$$

is

$$K_p=\frac{\left(x_{\mathrm{NH}_3}\right)^2}{\left(x_{\mathrm{N}_2}\right)\left(x_{\mathrm{H}_2}\right)^2} \times \frac{1}{\left(P_{\text {tot }}\right)^2}$$

For the three perpetrators in Exercise $5.64$, determine the number of possibilities in which

b. exactly two of the three persons are convicted.

Un voyage. Qu'est-ce que ces personnes ont fait dans le sud de la France? Faites des phrases completes au passé composé.

MODELE: nous / choisir / huitres

Nous avons choisi des huitres.

Thibaut/perdre / porte-monnaie (wallet)

Simplify.

$$\left(8 x^4 y^{-3}\right)\left(\dfrac{1}{2} x^{-5} y^2\right)$$

Un voyage. Qu'est-ce que ces personnes ont fait dans le sud de la France? Faites des phrases completes au passé composé.

MODELE: nous / choisir / huitres

Nous avons choisi des huitres.

Sylvie / finir / bouteille de vin

Le docteur Girard donne des conseils $\`{a}$ ses patients. Compl$\`{e}$te la phrase avec le subjonctif des verbes entre parenth$\`{e}$ses.

II fiut que j' $\rule{1cm}{0.2pt}$ (attendre) les résultats de votre examen,

Suppose that A has the singular value decomposition

$$A=\left[\begin{array}{rrrr}{\frac{1}{2}} & {\frac{1}{2}} & {\frac{1}{2}} & {\frac{1}{2}} \\ {\frac{1}{2}} & {-\frac{1}{2}} & {-\frac{1}{2}} & {\frac{1}{2}} \\ {\frac{1}{2}} & {-\frac{1}{2}} & {\frac{1}{2}} & {-\frac{1}{2}} \\ {\frac{1}{2}} & {\frac{1}{2}} & {-\frac{1}{2}} & {-\frac{1}{2}}\end{array}\right]\left[\begin{array}{rrr}{24} & {0} & {0} \\ {0} & {12} & {0} \\ {0} & {0} & {0} \\ {0} & {0} & {0}\end{array}\right]\left[\begin{array}{rrr}{\frac{2}{3}} & {-\frac{1}{3}} & {\frac{2}{3}} \\ {\frac{2}{3}} & {\frac{2}{3}} & {-\frac{1}{3}} \\ {-\frac{1}{3}} & {\frac{2}{3}} & {\frac{2}{3}}\end{array}\right]$$

(a) Find orthonormal bases for the four fundamental spaces of A. (b) Find the reduced singular value decomposition of A.

In this exercise, find the area of the intersection of the circles r=sin $\theta$ and r=$\sqrt{3} \cos \theta$.

Write the partial fraction decomposition of each rational expression. $\frac{x-4}{x^{2}(x-1)}$