The Monk and the Mountain. A monk set out from a monastery in the valley at dawn. He walked all day up a winding path, stopping for lunch and taking a nap along the way. At dusk, he arrived at a temple on the mountaintop. The next day the monk made the return walk to the valley, leaving the temple at dawn, walking the same path for the entire day, and arriving at the monastery in the evening. Must there be at least one point along the path that the monk occupied at the same time of day on both the ascent and descent? (Source: The Act of Creation, Arthur Koestler)

A toll collector on a highway receives $2 for cars and$3 for buses. At the end of a 1-hour period, she collected $32. How many cars and buses passed through the toll booth during that period? List all possible solutions.

State the rounding rules for adding and subtracting measured numbers and for multiplying and dividing measured numbers. Give example using these rules.

A thin tube stretched across a street counts the number of pairs of wheels that pass over it. A car with two axles registers two counts. A light truck with three axles registers three counts. During a $1$-hour period, a Traffic counter registered $35$ counts. How many cars and light trucks passed over the traffic counter? List all possible solutions.

In paragraph $77$, the narrator says, “They carried the soldier’s greatest fear, which was the fear of blushing.” Why do you think the soldiers were more afraid to blush than to die?

If a function f represents a system that varies in time, the existence of $\lim _ { t \rightarrow \infty } f ( t )$ means that the system reaches a steady state (or equilibrium). For the following systems, determine whether a steady state exists and give the steady-state value. The population of a culture of tumor cells is given by $p ( t ) = \frac { 3500 t } { t + 1 }$.

Draw Conclusions

How do you think essays like "Freedom from Fear" can help bring about political change in places such as Myanmar?

ABSTAIN ; MONK::
$F$ repent: penitent
$G$ deny: refuse
$H$ stand: recliner
$J$ drink: water

Suppose you are designing a rectangular garden and you have $20$meters of fencing with which to enclose the garden.

a. Can you enclose a garden that is $7$ meters long and $3$ meters wide with the available fencing? What is the area of the garden?

b. Can you enclose a garden that is $8$ meters long and $2$ meters wide with the available fencing? What is the area of the garden?

c. By computing the area of other possible gardens that can be enclosed with $20$ meters of fencing, find or estimate the dimensions of the garden that has the most area.

You wish to fence in a rectangular garden in your $100 \times 90$ foot back yard, with one side of the garden against the house

a. Suppose you have 20 feet of available fencing for the garden. Find the dimensions of the garden that yields the largest possible area $A$ of the garden. b. Suppose that instead of 20 feet of fencing there are 80 feet of fencing. Find the area $A_1$ of the largest possible garden.

Summarize the strategic hints for problem solving given in this unit, and give an example of the meaning of each one.

Mathematics requires precision, so approximations should never be used. Decide whether the above statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.

A monk walks from a monastery gate to the top of a mountain to pray and returns to the monastery gate the next day. What is the monk's displacement? What is the relationship between the monk's displacement going from the monastery gate to the top of the mountain and the displacement going from the top of the mountain back to the gate?

Suppose a railroad rail is $1$ kilometer long and it expands on a hot day by $10$ centimeters in length. Approximately how high would the center of the rail rise above the ground?