IMSA
MI-4
Prob. Set #8
DUE: Fri.. Nov. 8
Fall 13
Give exact answers when possible. Otherwise, round to the nearest hundredth unless stated in the problem.
1)
At a party, a total of 1378 handshakes were exchanged. Assuming that each guest shook hands
with each o the others exactly once, find the number of guests at the party.
2)
Neal and Joe working together can do their
Snowflake project in 24 hours. If Neal
works alone for 8 hours and Joe then
finishes the job in 30 hours, how many
hours would it take each working alone to
do the Snowflake project?
1  3  ...  (2n  1)
2  4  ...  2n
3) NC Simplify:
4)
Finding distances between inaccessible points: In Pittsburgh, the Monongahela River joins with
the Allegheny River to form the Ohio River. Dr. Porzio wants to know the distance from P to Q,
on opposite sides of the Allegheny. He can move somewhat freely along the south bank. He
measures the following angles: PAQ = 43º18’, QAB = 48º32’, ABP = 38º43’, and
PBQ = 41º28’, He measures and finds AB=518 ft. [Answer to nearest foot.]
5)
How many positive integers, n, not exceeding 100, have the property that n is a multiple of 3 or
n is a multiple of 5? Explain/show thinking.
 4k  3k 
  5k 1 
k 1

6) NC Evaluate: a)
7)
8)
b)
1 2  3  2  3  4  3  4  5  ... 100 101102
Consider the triangle with sides of length 14 cm, 17 cm, and 21 cm.
a)
Find the measure of the largest angle in this triangle. (to nearest tenth of a degree)
b)
Find the area of this triangle. (to nearest tenth)
c)
Find the sum of the lengths of the altitudes of this triangle. (to nearest tenth)
Two trusses support a bridge. The
lower one is twice the length of the
upper one, and meets the bridge at an
angle of 12. What angle does the
upper truss meet the bridge? (nearest
tenth of a degree)
15°
12
Trusses
page 1
F13
IMSA
MI-4
Prob. Set #8
DUE: Fri.. Nov. 8
Fall 13
9)
Low tide occurred at 9:15 a.m. and high tide occurred exactly eight hours later. The height of the
water at high tide was 212 cm above that at low tide. If the low water mark is taken to be zero
and the height of the water follows a cosine curve, find a function that describes the height of the
water at time t given in hours past midnight.
10)
A 24 foot long flagpole is attached to the side of a building 18 feet from the top of the side of the
building. The flagpole forms an upward angle of 55 with the side of the building. A 20.3 foot
long wire runs from the end of the flagpole to the side of the building to help support the
flagpole. How far below the top of the side of the building is the wire attached? (nearest tenth of
a foot)
11)
The time required to fall from a height of h feet (or to rise to that height after a bounce) is
h
seconds. Now suppose that a ball, whose rebound ratio is 64 percent, is dropped from a
4
height of 16 feet. How much time passes before the ball strikes the ground for the sixth time?
(nearest tenth of a second)
12)
Determine the value(s) of m so that the lines with equations 5x + 3y = 7 and y = mx + 2 intersect
at an angle of 52.4. (nearest hundredth)
13)
x  t
The parametric form of the rectangular equation y  x 2 is 
. You can convince yourself of
2
y

t

this by removing the parameter t. Use a computer to graph and label the parametric form of this
parabola. You will attach it to your answer sheets after you do problem 14.
General Rotation Formula for Parametric Equations
The rotation of any parametric equations through an angle  is given by
 x  x 'cos  y 'sin 

 y  x 'sin   y 'cos
where x ' is the original equation for x and y ' the original equation for y.
 x '  cos
These formulas came from multiplying the rotation matrix R     
 y '  sin 
14)
 sin    x ' 
cos   y '

of the parametric equations you
4
graphed in problem #13. Plot and label this on the same grid as problem #13, and attach it to
your answer sheets.
Determine the parametric equations of the rotation of
page 2
F13