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DAWSON COLLEGE
MATHEMATICS DEPARTMENT
FINAL EXAMINATION
201-921-DW (Applied Maths) FALL 2008
DATE: December 15, 2008 TIME: 9.30 am-12.30 pm TEACHER: Andreea Panait
STUDENT NAME: _____________________________________
STUDENT I.D. #: _____________________________________
INSTRUCTIONS:
- Print your name and student I.D. number in the space provided.
- All questions are to be answered directly in the space provided on the examination paper. Show all the work neatly.
- Reverse side of pages may be used to complete a solution as long as it is clearly indicated on the paper (→), and/or for rough work.
- A scientific non-programmable calculator, without text storage or graphics capacity, is permitted.
- If necessary, you can consult an invigilator by raising your hand.
There are 17 questions. Please ensure that you have a complete examination before starting. This exam consists of 18 pages.
This examination paper must be returned intact.
Q. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 T
(1) Perform the operation and simplify:
(a) (3 points)
1
2
(^35)
3
2 − − −
−
y
x y
x
(b) ( 3 points) ( ) ( ) 2
1 2 2 1 x 2 x − 1 −^ + 2 x 2 x − 1
Solve the following equation for x :
x^2 − + x +^ = x −
x
Given the system of equations:
x z
x y z
x y z
(a) solve the system by using determinants;
From a point on the South Rim of the Grand Canyon, it is found that the angle of
elevation of a point on the North Rim is 1. 5 o. If the horizontal distance between the points is 22 km, how much higher is the point on the North Rim?
The floor of a sunroom is in the shape of a circular sector of arc length 16.0 m and diameter 9.50 m. What is the area of the floor?
(7) (10 points)
A naval cruiser on maneuvers travels 67 km at 34. 6 owest of north, then turns and
travels 44 km at (^13). 4 osouth of east, and finally turns to travel 89 km at (^25). 5 oeast of south. Find its displacement from its original position.
Given the function: ( ) (^)
cos 3
2 π f x x
(a) find the amplitude, the period, and the displacement;
(b) make a table and graph the function for one period.
(10) Prove the following identities:
(a) (5 points)
x x
x x csc 1 cos
csc cot
−
(b) (5 points)
tan 1 cos
cos (^22) (^2) x +^ x =
x
(12) Solve the following equations for x: (a) (4 points)
log x + log ( x + 2 ) = 1
(b) (4 points)
5 2 x +^1 =
Express as a sum or a difference of logarithms:
x
x^4 5
log
An element decays as: A = A 0 ekt , A is in grams and t is in years. If k =− 0. 056 then
what is the half-life of the element?
A 113 L sample of helium at 27 o C is cooled at constant pressure to − 78 o C. Calculate the new volume of the helium.
