© | Dror Bar-Natan: Classes: 2014-15: Math 475 - Problem Solving Seminar: | (7) |
Next: Blackboards for Thursday January 15
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**Next Quiz.** A subset of the problems here and problems
1.2.5-1.2.10 in Larson's.

**Note.** From next week and on, our TA Gaurav Patil will be
available in front of our classroom, MP 134, every Tuesday from 2:55PM
until the beginning of class, to answer questions regarding the marking of
quizes.

**Problem 1.** Cars $A$, $B$, $C$, and $D$ travel in the Sahara
Desert (an infinite boundless flat plane), each one at a constant speed and
direction (though these constants are not all the same). It is given that
cars $A$ and $B$ meet - namely, arrive to the same location at the same
time (and let's pretend that they simply continue driving through each
other without crashing). Likewise it is given that cars $A$ and $C$
meet, cars $A$ and $D$ meet, cars $B$ and $C$ meet, and cars $B$ and $D$
meet. Do cars $C$ and $D$ necessarily meet?

**Problem 2** (Larson's 1.2.2). A particle moving on a straight line
starts at rest and attains a velocity $v_0$ after traversing a distance
$s_0$. If the motion is such that the acceleration is never increasing,
find the maximum time for the transverse.

**Problem 3** (Larson's 1.2.3). If $a$ and $b$ are positive integers
with no common factor, show that

**Problem 4.** Prove

**Problem 5** (Larson's 1.2.5). Two poles, with heights $a$ and $b$,
are a distance $d$ apart (on level ground). A bird wishes to fly from the
top of the first pole to the top of the second pole, touching the ground in
between at some point $P$. Where should $P$ be located so that the bird
trajectory will be the shortest?

**Problem 6** (Larson's 7.1.14). In a convex quadrilateral, prove that
the sum of the lengths of the diagonal lies between the perimeter and half
the perimeter.

**Problem 7** (Larson's 7.4.19). Noting that the function
$f(x)=\sqrt{x}$ is concave, show that if $a,b,c$ are positive and satisfy
$c>a\cos^2\theta+b\sin^2\theta$, then
$\sqrt{c}>\sqrt{a}\cos^2\theta+\sqrt{b}\sin^2\theta$.

**Problem 8.** Use the back of this page to draw a figure of something
interesting. The best figures will be placed somewhere on this class' web
site.