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Mathematical Models 1 201- Fall 2009 Instructor: Bob DeJean
Final Examination
Please give numeric answers to 4 decimal places, except for accuracy/precision/significant digits questions.
1 mark questions
Calculate to the right accuracy:
=
- 3
Write 0.66 rads in degrees
Calculate e 2.1^ =
ln 0.0041 =
ln -12 =
The waves in my waterbed have an amplitude of 5 cm and a frequency of 0.08 Hz. What is their Angular Velocity?
2 mark questions
Write using simple logs
^ =
7 ln 7 3 x
x
Solve for x 5 (3 x+2) = 10 000
Find x : log x + log(x + 1) = log 90
A triangular sail, 4 m high and 1.5 m along the base, faces a wind machine some 20 m away. What solid angle (in steradians) does the sail make at the wind machine?
This diagram tries to show a 3-d box with a bump on one side. Some of its dimensions are marked. What is its Surface Area?
Solve for x and y: 3x – 2y = 26 4x + 5y = 27
Set up the determinants to find y, but don’t bother to work it out: 2x + 6y – 3z = 26 3x – 4y + 3z = - 4x + 5y + 6z = 7
3 mark questions
Find x:
The Town of Ste Anne’s is thinking of putting a park on a triangle of land with sides of 75m, 56m and 48m. What is the angle at the smallest corner of the land?
Sketch the graph of y = 12 sin(8t + π) Vertical Shift = Amplitude = Phase Shift = Period =
Solve for all possible values of X, an angle between 0 and 2π radians: 3 tan X + 4 = tan X
Calculate ( 3 + 5 j )( 2 − 11 j ) =
=
− j
j 2 3
12 5
Write 17 cis 40° in rectangular form.
Write 17 cis 40° in exponential form.
Calculate: (12 cis 45°) (3 cis 55°) =
(1.2 cis 15°)^5 =
Find the fourth roots of 81 cis 60°
A 50Ω resistor is in series with a 200 μFd capacitor. If a 60Hz current flows through them, what is their Impedance?
Find the slope of this curve at the point (1, 2): 7x + 5y = x^2 y + 15
What is the second derivative of 3 1
x
y?
4 mark question
Use the Limit Definition of Derivative to find the derivative of y = 5 x^2 − x + 4 Show all the steps.
Answers
0.017 (2 sig digs)
37.81°
-5. sfa
ln(7x + 3) – 7 ln x
9 only 0.0075 steradians 998.26 cm^2 x = 8 and y = -
y =
1.4765 m/s at 28.28° North of West infinity 6 Not continuous; circle breaks at -5 and 7
11.27 cm 39.76° sine wave with VS = 0 Amp = 12 PS = -0. Period = 0. 116.57° and 296.57°
61 – 23j
