(a) A 75.0-kg man floats in freshwater with 3.00% of his volume above water when his lungs are empty, and 5.00% of his volume above water when his lungs are full. Calculate the volume of air he inhales-called his lung capacity-in liters. (b) Does this lung volume seem reasonable?

Find the eigenvalues and eigenvectors of A geometrically.

$$A = \left[ \begin{array} { l l } { \frac { 16 } { 25 } } & { \frac { 12 } { 25 } } \\ { \frac { 12 } { 25 } } & { \frac { 9 } { 25 } } \end{array} \right]$$

(projection onto the line through the origin with direction vector

$$\left[ \begin{array} { c } { \frac { 4 } { 5 } } \\ { \frac { 3 } { 5 } } \end{array} \right])$$

Approximate $f(x)=x^{2}$ on $[0, \pi]$ with a linear combination of the functions 1, $\cos (x), \cos (2 x), \cos (3 x)$, and $\cos(4x)$. Use $p(x)=1$ in the weighted inner product on this function space. Graph $f(x)$ and the approximating linear combination on the same set of axes. Hint: Calculate $f_S$, the orthogonal projection of f onto the subspace of $C[0, \pi]$ spanned by 1, $\sin(x), ... , \sin(5x).$

Murphy Co. is a high-end retailer of fine fashions for men. Murphy's inventory balance at the beginning of the year is $\$ 300,000$, and Murphy purchases $\$ 600,000$ of goods during the year. Its inventory balance at the end of the year is $\$ 250,000$. What is the cost of goods sold for the year?

Use projection matrices to find a fundamental matrix solution $\mathbf{x}(t)=e^{\mathbf{A} t}$ of each of the linear systems x' = Ax given in the following problem. $x_{1}^{\prime}=9 x_{1}+5 x_{2}, x_{2}^{\prime}=-6 x_{1}-2 x_{2} ; x_{1}(0)=1, x_{2}(0)=0$

Use a graphing calculator and the window indicated to graph the piecewise-defined function.

$$f(x)= \begin{cases}x-1 & \text { if } x \leq 3 \\ 2 & \text { if } x>3\end{cases}\quad$$

, window $[-4,6]$ by $[-2,4]$

Give structures for each of the following compounds. (a) $\mathrm{C}_3 \mathrm{H}_7 \mathrm{Br}: 81.03(3 \mathrm{H}, \mathrm{t}, J=7 \mathrm{~Hz}) ; \delta 1.88(2 \mathrm{H}$, sextet, $J=7 \mathrm{~Hz}), 83.40(2 \mathrm{H}, \mathrm{t}, J=7 \mathrm{~Hz})$ (b) $\mathrm{C}_2 \mathrm{H}_3 \mathrm{Cl}_3: 83.98(2 \mathrm{H}, \mathrm{d}, J=7 \mathrm{~Hz}) ; \delta 5.87(1 \mathrm{H}, \mathrm{t}, J=7 \mathrm{~Hz})$ (c) $\mathrm{C}_5 \mathrm{H}_8 \mathrm{Br}_4: 83.6$ (s; only resonance in the spectrum)

For the rectangular parallelepiped shown, develop an expression for the scalar projection ${F}_{B C}$ of F onto line BC. Point M is located at the centroid of the triangle ABC formed by "chopping off" the corner of the parallelepiped. Plot your expression over the range $0 \leq d \leq 3 b$, and determine the maximum value of ${F}_{B C}$ along with the corresponding value of d. See the table for the centroid location of a triangle.

Quelles sont vos habitudes quand vous partez en voyage? R$\'e$pondez aux questions avec un pronom compl$\'e$ment d’objet direct ou indirect.

La derni$\`e$re fois que vous $\^e$tes parti(e) en voyage...

Vous avez t$\'e$l$\'e$phon$\'e$ $\`a$ vos amis pendant le voyage?

Evaluate the function at each specified value of the independent variable and simplify.

$$f(x)= \begin{cases}4-5 x, & x \leq-2 \\ 0, & -2<x<2 \\ x^2+1, & x \geq 2\end{cases}$$

(b) $f(4)$

In this exercise, find the $x$-values (if any) at which $f$ is not continuous. Which of the discontinuities are removable?

$$f(x)= \begin{cases}10-3 e^{5-x}, & x>5 \\ 10-\frac{3}{5} x, & x \leq 5\end{cases}$$

When a star emitting electromagnetic radiation of frequency v moves with a speed s relative to an observer, the observer detects radiation of frequency $v_{emitting}=v f$ or v=v/f, where $f=\{(1-s / c)/(1+s / c)\}^{1 / 2}$ and c is the speed of light. (a) Three Fe l lines of the star HDE 271182, which belongs to the Large Magellanic Cloud, occur at 438.882 nm, 441.000 nm, and 442.020 nm. The same lines occur at 438.392 nm, 440.510 nm, and 441.510 nm in the spectrum of an Earth-bound iron arc. Decide whether HDE 271182 is receding from or approaching the Earth and estimate the star's radial speed with respect to the Earth. (b) What additional information would you need to calculate the radial velocity of HDE 271182 with respect to the Sun?

Use a graphing Utility to graph the function. Use the graph to determine any $x$-values at which the function is not continuous \

$$f(x)= \begin{cases}\dfrac{\cos x-1}{x}, & x<0 \\ 5 x, & x \geq 0\end{cases}$$

The $50,000 value represents the amount of money that was deposited to open Margaret's savings account. This value is known as the initial amount, or the principal, P. For a 5% interest rate, the value 1 + 0.05, or 1.05, represents the amount by which the current balance is multiplied to get the following year's balance. For any interest rate r, 1 + r is the annual growth factor. Write a function for Margaret's account balance at the annual interest rate of 4% with a principal of$50,000.