PUZZLER
For thousands of years the spinning
Earth provided a natural standard for our
measurements of time. However, since
1972 we have added more than 20 leap
seconds to our clocks to keep them
synchronized to the Earth. Why are such
adjustments needed?
P U Z Z L E R
One of the most popular early bicycles
was the penny farthing, introduced in
1870. The bicycle was so named because
the size relationship of its two wheels
was about the same as the size relationship of the penny and the farthing, two
Englis
P U Z Z L E R
Airbags have saved countless lives by
reducing the forces exerted on vehicle
occupants during collisions. How can
airbags change the force needed to
bring a person from a high speed to a
complete stop? Why are they usually
safer than seat be
Math 11 Fall 2010 Final Exam
Tuesday, December 7, 2010
Instructor (circle one):
Barnett
Van Erp
PRINT NAME:
Instructions: This is a closed book, closed notes exam. You have three hours, do all 11 problems.
There are 100 points total, and points for each p
MATH 201 - Final Exam
January 12, 2011 (180 minutes)
1. Rewrite each of the double integrals below in the form specied. (If
necessary, break into several integrals.)
x2
2
f dydx: change the order of integration to
a)
dxdy.
0
0
2
/2
f drd: change to rectan
Math 11 Fall 2007 Practice Problems Here are some problems on the material we covered since the second midterm. This collection of problems is not intended to mimic the nal in length, content, or diculty. The nal exam will concentrate on material covered
MATH 201 - Final Exam
January 13, 2010 (180 minutes)
1. Let S be the set of points P in 3-space such that the distance of P from the point (1, 1, 1) is
the same as the distance of P from the plane z = 3.
a) Write down an equation of S.
b) Sketch S and des
MATH 201 - Final Exam
January 12, 2011 (180 minutes)
1. Rewrite each of the double integrals below in the form specied. (If
necessary, break into several integrals.)
x2
2
a)
b)
0
0
/2
2
0
f dydx: change the order of integration to
f drd: change to rectang
Here are some problems to keep you awake at night. As usual these are not necessarily representative of the problems on the nal, but should give you a decent review of the new material. You are on your own for the old material. 1. Consider two vector elds
2.2
This is the Nearest One Head
361
PUZZLER
This one-bottle wine holder is an interesting example of a mechanical system that seems to defy gravity. The system (holder plus bottle) is balanced when its center of gravity is directly over the lowest suppor
P U Z Z L E R
Chum salmon climbing a ladder in the
McNeil River in Alaska. Why are sh ladders like this often built around dams? Do
the ladders reduce the amount of work
that the sh must do to get past the dam?
(Daniel J. Cox/Tony Stone Images)
c h a p t
P U Z Z L E R
The Spirit of Akron is an airship that is
more than 60 m long. When it is parked
at an airport, one person can easily support it overhead using a single hand.
Nonetheless, it is impossible for even a
very strong adult to move the ship
abrupt
P U Z Z L E R
This airplane is used by NASA for astronaut training. When it ies along a certain curved path, anything inside the
plane that is not strapped down begins to
oat. What causes this strange effect?
(NASA)
web
For more information on microgravit
2.2
423
This is the Nearest One Head
P U Z Z L E R
More than 300 years ago, Isaac Newton
realized that the same gravitational force
that causes apples to fall to the Earth
also holds the Moon in its orbit. In recent
years, scientists have used the Hubble
P U Z Z L E R
In a moment the arresting cable will be
pulled taut, and the 140-mi/h landing of
this F/A-18 Hornet on the aircraft carrier
USS Nimitz will be brought to a sudden
conclusion. The pilot cuts power to the
engine, and the plane is stopped in le