A periscope consists of two flat mirrors and is used for viewing objects when an obstacle impedes direct viewing. Suppose Curious George is looking through a periscope, in which the two flat mirrors are separated by a distance $L=0.400 \mathrm{~m}$, at the Man in the Yellow Hat, whose hat is at $d_0=3.00 \mathrm{~m}$ from the upper mirror. What is the distance $D$ of the final image of the yellow hat from the lower mirror?

A periscope consists of two flat mirrors and is used for viewing objects when an obstacle impedes direct viewing. Suppose that Curious George is looking through a periscope at the Man in the Yellow Hat, whose hat is at $d_0=3.00 \mathrm{~m}$ from the upper mirror, and suppose that the two flat mirrors are separated by a distance $L=0.400 \mathrm{~m}$. What is the distance $D$ of the final image of the yellow hat from the lower mirror?

(a) How many normal modes of vibration are there for the following molecules: (i) $\mathrm{H}_{2} \mathrm{O},$ (ii) $\mathrm{H}_{2} \mathrm{O}_{2},$ (iii) $\mathrm{C}_{2} \mathrm{H}_{4} ?$ (b) How many normal modes of vibration are there for the following molecules: (i) $\mathrm{C}_{4} \mathrm{H}_{4},$ (ii) $\mathrm{C}_{4} \mathrm{H}_{3} \mathrm{C H}_{2},$ (iii) $\mathrm{HC}\equiv\mathrm{C}-\mathrm{C} \equiv \mathrm{C}-\mathrm{H}?$

State whether each function is

(i) a polynomial (state its degree),

(ii) a power function, or

(iii) a rational function.

(a) $y=\frac{x-6}{x+6}$

(b) $y=1.3 t^3-8.52 t^5$

(c) $y=x^{-1}$

(d) $y=x^{10}$

Find constants $a, b, c, m, n$ so that the integral is in one of the following forms from a table of integrals. Give the form (i)–(iii) you use.

(i)$\quad \displaystyle \int \frac{dx}{ax^{2}+bx+c}$

(ii)$\quad \displaystyle \int \frac{mx+n}{ax^{2}+bx+c}\ dx$

(iii)$\quad \displaystyle \int \frac{dx}{(ax^{2}+bx+c)^{n}},\;n>0$

$$\displaystyle \int \frac{dx}{(x^{2}-5x+6)^{3}(x^{2}-4x+4)^{2}(x^{2}-6x+9)^{2}}$$

(a) Assume that air consists of $\mathrm{N}_{2},$ molecules with a collision diameter of 395 pm. Calculate (i) the mean speed of the molecules, (ii) the mean free path, (iii) the collision frequency in air at 1.0 atm and $25^{\circ} \mathrm{C}.$ (b) The best laboratory vacuum pump can generate a vacuum of about I nTorr. At $25^{\circ} \mathrm{C}$ and assuming that air consists of $\mathrm{N}_{2}$ molecules with a collision diameter of 395 pm, calculate at this pressure (i) the mean speed of the molecules, (ii) the mean free path, (iii) the collision frequency in the gas.

You will notice that each movie review begins with some basic facts. Read the following fact excerpt from your textbook reading. Then answer the question below.

Mad Max: Furia en la carretera

Australia, 2015-Clasificación: R-Director: George Mller,-I Actores: Tom

Hardy. Charlize Theron, Nicholas Hoult, Hugh Keays-Byrne

What is the second part of the title of the movie? ____________

Four words have been omitted. Complete each of the other column

Using the given information determine (a) sin (s+t),tan (s+t), and $(c)$ the quadrant of s+t. $\cos s=-\frac{8}{17}$ and $\cos t=-\frac{3}{5}$, s and t in quadrant III

Find the values of the given parameter for which the equation has

i two distinct real roots

ii one real repeated root

iii no real roors.

$\quad(2 s+1) x^2=s(3 x-1)$

(a) Use Euler's method to estimate B(1), given that $\frac{d B}{d t}=0.05 B$ and $B = 1000$ when $t = 0$. Take:

(i) $\Delta t = 1$ and 1 step

(ii) $\Delta t = 0.5$ and 2 steps

(iii) $\Delta t = 0.25$ and 4 steps

(b) Suppose B is the balance in a bank account earning interest. Explain why the result of your calculation in part (i) is equivalent to compounding the interest once a year instead of continuously.

(c) Interpret the result of your calculations in parts (ii) and (iii) in terms of compound interest.

You will notice that each movie review begins with some basic facts. Read the following fact excerpt from your textbook reading. Then answer the question below.

Mad Max: Furia en la carretera

Australia, 2015-Clasificación: R-Director: George Mller,-I Actores: Tom

Hardy. Charlize Theron, Nicholas Hoult, Hugh Keays-Byrne

In what year was the movie made? ____________

Four words have been omitted. Complete each of the other column

Step i: A ball rolls from the origin on a one-dimensional coordinate axis and stops at $(x=30 \mathrm{~m})$.
Step ii: It next rolls from $(x=30 \mathrm{~m})$ to $(x=-30 \mathrm{~m})$.
Step iii: Finally, it rolls from $(x=-30 \mathrm{~m})$ to $(x=0 \mathrm{~m})$.
a. What is the ball's displacement during Step i?
b. What is the ball's displacement during Step ii?
c. What is the ball's displacement during Step iii?
d. What is the total of the three displacements?
e. Generalize about the displacement of any round trip (one that begins and ends at the same position).