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Mathematical Models 1 201- Fall 2010 Final Examination Instructor: Bob DeJean
Except for accuracy/ significant digit questions, please answer to 4 decimal places.
1 mark questions
Calculate to the correct accuracy or significant digits: 2.4 x 10^4 + 7.41 x 10^3 =
Write ⡱ゕ⡳ in degrees.
Joel is floating in the Caribbean Sea, bobbing up and down some 20 cm every 35 seconds. What is his Amplitude?
What is his period?
Write his equation of motion? (keep things simple and assume it
is simple harmonic motion). (Each part is one mark)
2 mark questions
Bill’s ‘Vette is 7 m long. One end is firmly on pavement, but the other is on ice, so some of his friends pushed that end, turning it by some 150°. How far did the end move?
The buckle of Ryan’s belt is a rectangle of polished steel 9 cm by 8 cm. He stands 250 cm from the campfire warming himself. What solid angle does the buckle make with the fire?
Ravinder has designed a new sort of paper shredder. The design is quite sophisticated, depending on several lasers to reduce the paper to carbon dioxide. It looks like a garbage can 50 cm high, with a diameter of 24 cm. The top is concave, a hemisphere into which you do not put your hand if you are smart. What is the volume of Ravinder’s shredder?
Solve any way you like for x and y: 2x – 3y = 20 5x + 2y = 31
Write using simple logs: (^) =
y
log^1666 x^4
Write using one log: ln(x + 3) – ½ ln(x – 3) =
Solve for x in each case: 7 ( 3x + 1^ ) = 14 000 000
log ( 2x + 6) – log (x – 2) = log 4
Here’s the graph of a function. Are there any places where it is not continuous?
3 mark questions
Find x: 81° 73m 19m
X
Find angle X: 99° X 12cm 19cm
Sketch the graph of y = 12 + 4 sin(6x + 90°) Vertical shift is Amplitude is Phase Shift is Period is
Solve for angle X: 3 tan X – 5 = 6 (X is between 0 and 360°)
Find:
け→⦘^ lim
lim け→⡲
ᡶ⡰^ ㎘ 4ᡶ
2ᡶ⡰^ ㎘ 32 =
Find the derivatives: Simplify if it is easy. Y = 23x^3 – 333x^2 + 911
Y = 6x^2 sin(4x) + x
Y = 10(2x+3)^6
1 ㎗ sin ᡶ ᡶ
Find the derivatives y = tan x – sec 4x
Find the derivative, that is the 〱げ〱け, implicitly:
x^4 + y^4 = 3xy^3
Use the Limit Definition to find the derivative of y = 7x^2. Show your work.
amp = phase shift = -15° period = 60° wave ”ends” at 45° 74.74° or 254.74°
-1 + 6 j 1.1 + 1.7j 36cis69° 16 cis 300° 5 cis 50°, 5 cis 140°, 5 cis 230°, 5 cis 320° 10 cis -53.13° -41.61 + 90.93j 60 – 47.46j Ω
3 ¼ 69x^2 – 666x 12xsin(4x0+ 24x^2 cos(4x) + 1 4ᡶ⡱^ ㎗ 21ᡶ⡰ 䙦2ᡶ ㎗ ᡷ䙧⡰ 120 (2x + 3)^5
㐶
ᡶ 㑀^
ᡶ⡰^ 㑀
sec^2 x – 4sec(4x) tan(4x) ᡖᡷ ᡖᡶ =
3ᡷ⡱^ ㎘ 4ᡶ⡱
4ᡷ⡱^ ㎘ 9ᡶᡷ⡰
show all steps, from lim〵 →⡨
⡵䙦け⡸〵䙧ㄘ⡹⡵けㄘ 〵 to 14x
