2009 Excellence in Mathematics Contest
Team Project Level I
(Precalculus or higher)
School Name:
Group Members:
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
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Reference Sheet
Formulas and Facts
You may need to use some of the following formulas and facts in working through this project.
You may not need to use every formula or each fact.
d
x1 ) 2 ( y2
( x2
b2
2a
b
x
1
2
h(t )
r
4ac
x
y
gt 2 h0
where
is in radians
y ab
F
x
Gm1m2
r2
1 mile = 5280 feet = 1609
meters
cos
v xt
1
2
v yt
F
sin
a
gt
mv 2
r
sin
b
a
1
2
t
a2
vy
gt 2 (v0 sin A)t h0
A
0
x
r
b2 c2 2bc cos
sin
c
1
2
ab sin
L
1 ae bt
where c 0 and b 0
P(t )
n
where n is the length of the half-life
vx
1
2
h(t )
2
u(t ) T (u0 T )ekt where k
T (t )
y a( x h)2 k
y
r
sin
a 2 b2 c2
2bc
cos
ax2 bx c
y
sin
cos
tan
s
y1 ) 2
v0 cos
v0 sin
gt
2
Gravity = 9.8 m/sec² = 32 ft/sec²
References:
www.collegeboard.com
2
v v0 at
N
N 0e
kt
1 hr = 60 mins = 3600 sec
SUDDEN IMPACT: THE SUSPECTS
Summary of the Crime
Dudley “Fingers” Mousehand, chief programmer for Macrohard Corporation and alleged corporate
spy for Pear Computing, fell to his death on August 11, 2009, from one of the balconies at the
Macrohard Corporate Center in Bluemond, WA.
The Suspects
Gil Bates
CEO of Macrohard Corporation and software king-pin. Lives in a waterfront mansion on
Puget Sound. Threatened to “eliminate” Mousehand after discovering trade secrets were
being leaked to Pear Computing.
Debra Downtime
Anarchy activist and renegade author of deadly computer viruses. Low-level programmer
on Macrohard’s Operating System Door 99™ and long-time lover of Tim Witt. In recent
months, however, she had shown a romantic interest in Dudley Mousehand although they
frequently and violently quarreled.
Tim Witt
Head of DIM Computing, a lead publisher of antivirus software. Long-time lover of Debra
Downtime: however, in recent months he’d been losing ground to Dudley Mousehand. He
and Mousehand had engaged in a brief skirmish at a Macrohard reception.
Nick Smythe
Former security guard at Macrohard Corporation. Discovered secret Pear Computing
documents while searching Mousehand’s suitcase during a spot security check. Informed
his daughter, an advertising executive at Pear Computing. Mousehand was fired shortly
thereafter. Mousehand had threatened to “squash Smythe like a fly” after being fired from
Pear Computing. Smythe departed early the afternoon of Mousehand’s death.
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SUDDEN IMPACT: FALLING BODY
Summary of the Crime
Dudley “Fingers” Mousehand, chief programmer for Macrohard Corporation and alleged corporate
spy for Pear Computing, fell to his death on August 11, 2009, from one of the balconies at the
Macrohard Corporate Center in Bluemond, WA.
New Information
Chief Investigator, Sally Sleuth has come to you for technical assistance. The coroner has released
his preliminary report. Based on the damage to Mousehand’s body, it appears that he struck the
ground at a speed between 125 – 150 ft/sec. The acceleration of a falling body due to gravity
(neglecting air resistance) is 32 feet per second per second. (Note: a negative acceleration
indicates a falling body and a positive acceleration indicates a rising body.)
Your Mission, Should You Choose To Accept It
1. If Mousehand’s initial velocity at the moment of the fall was 0 feet per second, develop a
function that gives his instantaneous velocity t seconds after falling.
2. Develop a function that gives the vertical distance that Mousehand has traveled after t
seconds have elapsed.
3. Determine how long Mousehand had been falling when he struck the ground.
4. Determine the approximate distance Mousehand had fallen when he struck the ground.
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SUDDEN IMPACT: IMPACT VELOCITY
Summary of the Crime
Dudley “Fingers” Mousehand, chief programmer for Macrohard Corporation and alleged corporate
spy for Pear Computing, fell to his death on August 11, 2009, from one of the balconies at the
Macrohard Corporate Center in Bluemond, WA.
New Information
Chief Investigator, Sally Sleuth, has again come to you for technical assistance. Detectives have
determined that although Gil Bates had been tied up in meetings until 2:30 pm, he was in his office
at the purported time of the alleged crime. Debra Downtime alleges she was in her office as well
but detectives have been unable to substantiate her claim. Both Bates and Downtime claim to have
been alone. Bates’ office is 346 feet above the ground, Mousehand’s office is 306 feet above the
ground, and Downtimes’ office is 266 feet above the ground. Outdoor security cameras captured
images of Mousehand as he fell. Image analysis indicated that he was at 206 feet at 15:22.02 and
110 feet at 15:22.03.
Your Mission, Should You Choose To Accept It
1. Determine from which office he fell
2. Calculate his velocity at impact. Does this substantiate the coroner’s report that the velocity
of impact was between 125 and 150 ft/sec?
3. Determine whether your results have cleared any of the murder suspects.
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SUDDEN IMPACT: AGE OF ART
Summary of the Crime
Dudley “Fingers” Mousehand, chief programmer for Macrohard Corporation and alleged corporate
spy for Pear Computing, fell to his death on August 11, 2009, from one of the balconies at the
Macrohard Corporate Center in Bluemond, WA.
New Information
Chief Investigator, Sally Sleuth, has again come to you for technical assistance. Detectives have
discovered that the famous Van Gogh painting, Starry Night, has been stolen. The painting, which
had been loaned to Mousehand by The Museum of Modern Art in return for a $750,000
contribution, vanished from his office on the day of his death.
A search of Tim Witt’s condominium turned up a painting that appears to be the stolen art work.
Witt claims that the painting is a replica, not the original. He said he purchased the work as a gift
for Downtime and had intended to give it to her during the 3 pm ribbon-cutting ceremony for his
new building, DIM Towers, on the day of the crime. However, Downtime stood him up.
Witt presented detectives with a hand-written sales receipt from a Seattle art dealer date/time
stamped: 08/11/09 13:52:46. The dealer says he sold a Starry Night replica to Witt sometime in
the afternoon of August 11, 2009, but refused to disclose any other details. Due to his extensive
criminal history, the dealer’s credibility is questionable.
Scientific analysis of the painting revealed that it contains 99.2% of its original carbon-14 (half-life
5730 years). The original painting was completed in June 1889.
Your Mission, Should You Choose To Accept It
1. Determine if the painting in Witt’s possession is an original or a replica.
2. Determine whether your results have cleared any of the murder suspects.
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SUDDEN IMPACT: ART AUCTION
Summary of the Crime
Dudley “Fingers” Mousehand, chief programmer for Macrohard Corporation and alleged corporate
spy for Pear Computing, fell to his death on August 11, 2009, from one of the balconies at the
Macrohard Corporate Center in Bluemond, WA.
New Information
Detectives believe that one of the murder suspects has the stolen Van Gogh painting, Starry Night,
and will attempt to sell it on the black market. The periodic underground art auction is to be held in
Pikes Place Market tomorrow night at 11 pm.
In an interview with detectives, Nick Smythe’s daughter reluctantly revealed that her father had
incurred a $400,000 gambling debt. Mobsters have given him 31 days from today to pay off the
debt. Furthermore, he depleted his life savings paying for his late wife’s cancer treatments and has
been living month to month on his income from Macrohard.
Detectives speculate that if Smythe is the thief (and possible killer) he will attempt to raise money
by selling the painting. Black market financial experts estimate that the painting will generate
between $300,000 and $500,000. They told Sleuth that the amount of revenue, R, the painting
should generate is proportional to the difference between 1 and the reciprocal of the fourth root of
the number of auction attendees, A. A painting of similar quality sold at last month’s auction for
$375,000. There were 256 people in attendance.
Your Mission, Should You Choose To Accept It
1. Determine the minimum auction attendance necessary to generate $400,000.
2. Find the instantaneous rate of change of the revenue with respect to the number of auction
attendees and explain what it would mean in the context of this situation. Determine the
instantaneous rate of change for a specific number of auction attendees and explain
(including the use of correct units) what this value means.
3. Find lim R ( A) and lim R( A) and explain what each means in the context of the situation.
A
0
A
Your explanations should include graphs, tables, symbols and/or words.
4. Determine whether your results have cleared any of the murder suspects.
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SUDDEN IMPACT: TIME OF DEATH
Summary of the Crime
Dudley “Fingers” Mousehand, chief programmer for Macrohard Corporation and alleged corporate
spy for Pear Computing, fell to his death on August 11, 2009, from one of the balconies at the
Macrohard Corporate Center in Bluemond, WA.
New Information
The coroner’s office has informed Sally Sleuth that Mousehand did not die as a result of the injuries
sustained by the fall. He was already dead. Mousehand had sustained 29 bee stings on the chest
and gone into anaphylactic shock and died of cardiac arrest. Blood tests further revealed that he
was heavily sedated at the time. Detectives discovered traces of Valium in a wineglass left on the
floor of his office.
Detectives have confiscated the computers of Downtime, Mousehand, and Smythe. Mousehand
sent the following e-mail to Downtime at 2:01 pm. She had not yet read it when her computer was
confiscated.
My love,
Am looking forward to our rendezvous this afternoon. Will meet you
at Ivar’s instead of Pier 51 on the waterfront at 4 pm. Thought we
might catch an early movie after dinner.
Am still angry with Smythe for getting me fired. Think I’ll call him
into my office and give him a piece of my mind. I’d love to toss him
out of my life.
BTW, my computer has been acting up. Might be a virus. When you
get a chance, come have a look.
Yours Truly,
Fingers
Smythe returned from a going away luncheon for one of his subordinates at 2:05 pm. He received
the following e-mail from Mousehand at 2:07 pm.
Mr. Smythe:
I am concerned with the security situation in my office. Even though
my Van Gogh painting is encased in glass, I do not feel secure. Meet
me in my office at 3 pm to discuss security.
Mr. Mousehand
Mousehand’s computer was inoperable due to irreparable damage caused by a computer virus so
detectives were unable to extract any additional information from it.
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Smythe reported to Mousehand’s office as directed at 3 pm and claims that when he entered the
office he found Mousehand lying on the floor. He says he immediately felt light headed and passed
out. When he regained consciousness, he discovered that the body of Mousehand had vanished. He
claims he got spooked and fled to his daughter’s office at Pear Computing.
Many of the investigative team believe Smythe is the killer; however, Sleuth believes that
Downtime is the culprit. Unfortunately, she has been unable to come up with any evidence to clear
Smythe; however, the coroner just released some information that she thinks you may be able to use
to vindicate him. At 4:22 pm, Mousehand’s body temperature was 93.4 F and 5:22 pm it was
91.6 F. The temperature inside of Mousehand’s office and outside the Macrohard Corporate Center
from 1 – 6 pm was 68 F.
Your Mission, Should You Choose To Accept It
1. Determine the time of death of Mousehand. Assume his temperature at the time of death
was 98.6 F.
2. Determine whether your results have cleared any of the murder suspects.
3. Who killed Dudley “Finger” Mousehand?
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