# ENT 300 set 1

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1. 1. y=sin(x), x can be _____, but without units is always _____.
2. 2. pi radians is ____ degrees
180
3. The unit of sin(x) is
none
4. ____is unitless because it is defined as arc length/radius
5. y=A*sin(x), A is
amplitude
6. y=A*sin(w*t), t is _____ and w is _____.
time in seconds, frequency in radians/second
7. y=A*sin(w*t), w is
2*pi*f
8. y=A*sin(2*pi*f*t), f is frequency
cycles/second or Hertz
9. y=A*sin( t * 2 * pi / T ), T is ______ measured in ______.
cycles/second or Hertz
10. y=A*sin(2*pi*f*t), f is
1/T
11. y=A*sin(w*t + theta), theta is _____, measured in ______.
phase shift (or angle), degrees or radians
12. y=A*sin(w*t + theta) + B, B is _____ shift, measured with same unit as ______.
vertical, A
13. cos(x) = sin(x _____)
+pi/2
14. sin(x) = cos(x _____)
-pi/2
15. Time of 123 ms is _____ seconds
0.123
16. Time of 123456 us is _____ seconds
0.123456
17. Any angle given without units is ALWAYS
18. If an angle has units of degrees, then the degree unit ____ be written, because radians will be assumed otherwise.
must
19. The derivative of a contant is
not defined
20. The derivative of a function that has a constant value is
another function whose constant value is zero
21. Derivative operator is a _______ operator
slope
22. All of the following are equivalent. The best way to verbalize _____ is derivative of y with respect to x.
dy(x)/dx
23. All of the following are equivalent. The best way to verbalize _____ is derivative with respect to x of y
(d/dx)y(x)
24. All of the following are equivalent. The best way to verbalize _____ is y-prime of x.
y'(x)
25. The best way to verbalize _____ is y-prime.
y'
26. y' and y'(x) and (d/dx)y(x) and dy(x)/dx and dy/dx all mean the same thing
true
27. The value of y at x=x1 is
• y(x1)
• y'(x1)
• dy/dx | x=x1
• (d/dx)y(x) | x=x1
28. The independent variable in y(x) is
x
29. The dependent variable in y(x) is
y
30. h'(x) = g(x) and h(x)=x^n. g(x)=
n*x^(n-1)
31. h'(x) = g(x) and h(x)=sin(x), g(x)=
cos(x)
32. h'(x) = g(x) and h(x)=cos(x), g(x)=
-sin(x)
33. e=2.718 and e^1 and exp(1) all mean the same thing
true
34. h'(x) = g(x) and h(x)=exp(x), g(x)=
h'(x) + g'(x)
35. (d/dx)( a*h(x) + b*g(x) ) =
a*h'(x) + b*g'(x)
36. (d/dx)( h(x) / g(x) ) =
(h'*g - h*g') / g^2
37. y(x) = M*x + B. The slope of the line normal to y(x) is
-1/M
38. The square root of -1 is
the symbol i (usually and in calculators) or the symbol j (in electrical engineering)
39. i*i is
-1
40. i^3 is
-i
41. i^4 is
1
42. A complex number is
like a 2D vector
43. Complex numbers
are frequently used in electrical engineering
44. The number (3+i4) is an example of a _______ number in rectangular form.
complex
45. The real part of 3+i4 is
3
46. The imaginary part of 3+4i is
4
47. The magnitude of 3+i4 is
5
48. The angle of 3+i4 is
53.13 DEG
49. The sum of 3 and 4i is
3+4i
50. The magnitude of the sum of 3 and i4 is
5
51. The angle (radians) of the sum of 3 and i4 is
0.9273
52. exp(1)=e^(1) is known as Euler's number and is
2.71828
53. exp(i*pi)*1=e^(i*pi)*1 is a complex number in polar form and is the same as
-1
54. exp(-i*pi)*2=e^(-i*pi)*2 is a complex number in polar form and is also
-2
55. exp(-i*pi/2)*3=e^(-i*pi/2)*3 is a complex number in polar form and is also
-3i
56. The sum of 3 and 4i is
• exp(0.927i)*5
• 5*exp(0.927i)
• both of these
57. The sum of 3 and i4 has an angle of
• both of these
• 53.13 degrees
58. Complex numbers can be
• all of these
• multiplied and divided
• raised to powers
• placed in matrices
59. exp(i*z) is the same as
cos(z)+i*sin(z), which is know as Euler's formula
60. sin(z), cos(z), tan(z), ln(z), log(z) are defined when z is a complex number
TRUE
61. AC voltage of 5*exp(i53.13 deg) has an amplitude of
5 volts
62. AC voltage of 5*exp(0.927i) has an phase of
63. Euler's identity (e^(i*pi)+1=0) contains all the special numbers: 0, 1, e, i, and pi, and has been called the most profound equation in all of mathematics.
true
64. Some say that Euler's identity (e^(i*pi)+1=0) is so mysterious that it can hardly be comprehended.
true
65. Engineering technology students know that Euler's identity (e^(i*pi)+1=0) is easy to understand, because e^(i*pi) is a complex number in polar form and is equal to -1.
true
66. A vector that has a length of one is called a ______ vector.
unit
67. vector = [1.2, 3.4, 5.6], where 1.2 is called the _____ component
first
68. The dot product of two 3D vectors is
69. a scalar (not a vector), which is the same as a number
70. The dot product is useful for calculating the angle between two vectors:
(2D or 3D)
71. The dot product of two vectors A and B is defined as dotP(A,B)=
norm(A) * norm(B) * cos(theta)
72. The length of a 3D vector A=[a,b,c] is norm(A)=
sqrt(a*a + b*b + c*c)
73. The magnitude of the cross product of two vectors A and B is
norm(A)*norm(B)*sin(theta)
74. The cross product of two 3D vectors is
a 3D vector
75. The cross product of two 3D vectors is useful
in 3D torque problems
76. A 3D vector with components a,b, and c can be stored into a row vector as
[a,b,c]
77. A 3D vector with components a,b, and c can stored into a column vector as
[a;b;c]
78. The dot-product operation is commutative which means dotP(a,b) = dotP(b,a)
true
79. The cross-product operation is commutative which means crossP(a,b) = crossP(b,a)
false
80. Regarding a,b,c in crossP(a,b) = c,
all are 3D vectors
81. In crossP(a,b) = c
c is perpendicular to both a and b
82. acos( dotP(a,b) / ( norm(a) * norm(b) ) ) sto-> nn(a,b) is a TI-89 function that computes the
angle between vectors a and b
83. The formula for calculating torque is
R cross F = crossP(R,F)
84. In calculating torque about point-O by crossP(R,F), R
a vector from point-O to any point on the line of action of force-F
85. In calculating torque-T about point-O by T=crossP(R,F), the direction of T
perpendicular to both R and F and is given by the right-hand rule
86. x/norm(x) sto--> uu(x) is a TI-89 function. Then typing: uu(A) will calculate the ______ of vector-A
unit vector in the direction
87. The augment function in the TI-89
combines two vectors into a matrix
88. g-inverse multiplied by the weight vector in Video H300475 at 2:19 is an error, because [0;0;100]
is the negative of the weight vector
89. The number of radians in 180 degrees is
pi
90. The number of degrees in one radian is approximately
57
91. The angle measured in radians is
92. the arc length divided by the radius
93. The dimension of a radian is
dimensionless
94. The number of gradians in 360 degrees is
400
95. Angles are measured relative to the
positive x axis
96. Positive angles "go" _______ from the ________.
counterclockwise, x-axis
97. A vector with an angle of pi/2 radians point along the _____ axis
+y
98. A vector with an angle of pi radians point along the _____ axis
-x
99. A vector with an angle of negative-pi radians point along the _____ axis
-x
100. A vector with an angle of negative-pi/2 radians point along the _____ axis
-y
101. The maximum airplane angle is _____ degrees
90
102. Airplane angles are measured from
North or South
103. An airplane angle of ____ is the same as 100 degrees.
104. N10W or 10 degrees NW
105. Airplane angles are
always positive
106. TI-89 angles are measured
positive when counterclockwise from x-axis
107. The matrix method in solving simulaneously linear equations is most efficient because
the unknown variables, x and y, are not entered into the calculator
108. ToB=torque in Newton-meters (Nm) about point-o due to force-B is
24
109. ToA=torque in Newton-meters (Nm) about point-o due to force-A is
0
110. ToB dirction is
counter-clockwise
111. ToB vector-dirction is perpendicular to the figure and is directed
out
112. Torque (Nm) about point-o due to force-A and force-B simultaneously is
24
113. Torque direction about point-o due to force-A and force-B simultaneously is
counter-clockwise
114. Torque vector direction about point-o due to force-A and force-B simultaneously is
out
115. Force-A + Force-B is equal to Force-C
true
116. Force-C can be replaced by force-A and force-B
true
117. Force-C can be resolved into force-A and force-B.
true
118. The two components of force-C are force-A and force-B.
true
119. ToC=torque in Newton-meters (Nm) about point-o due to force-C is
24
120. ToC direction is
counter-clockwise
121. ToC vector-dirction is perpendicular to the figure and is directed
out
122. The angle measured in radians is
the arc length divided by the radius
123. An angle of one radian occurs when the ____ and the arc length are ___
124. Torque about the nut axis in Fig. 1
is force multiplied by distance that is perpendicular to the force
125. The nut axis in Fig. 1
perpendicular to the page
126. The torque direction in Fig. 1 is
counterclockwise
127. The vector-torque direction in Fig. 1 according to the right-hand rule is
perpendicular to the page (nut axis) pointing out
128. The torque applied to the lug nut in Fig. 2 is
downward force multiplied by the distance from his hand to the nut axis
129. The purpose for the wrench extention in Fig. 3 is
both of these
130. The purpose for the wrench extra extention in Fig. 4 is
both of these
131. The removal of the truck-lug nut as demonstrated is possible if the nut is
left handed
132. At 2:10, the number of equations in the green box is
2
133. At 2:10, the equations in the green box are linear because
• the graph of y(x) is linear
• x and y are raised to the first power
134. At 2:10, the slope of 4x+5y=23 is
-4/5
135. At 2:10, the slope of 6x-7y=-9 is
6/7
136. At 2:10, the y-axis intercept of 4x+5y=23 is
23/5
137. At 2:10, the y-axis intercept of 6x-7y=-9 is
9/7
138. At 2:10, the number of equations in the blue box is
1
139. At 2:10, the first matrix in the blue box is
two-by-two or 2x2
140. At 2:10, the second matrix in the blue box is
two-by-one or 2x1
141. At 2:10, the third matrix in the blue box is
two-by-one or 2x1
142. At 2:10, a is
a matrix with four elements
143. At 2:10, b is
a matrix or vector with two elements
144. At 2:10, c is
a matrix or vector with two elements
145. At 2:10, a(1,2) is
5
146. At 2:10, a(2,1) is
6
147. At 2:10, a(2,2) is
-7
148. At 2:10, c(2,1) is
-9
149. At 3:00, the top equation in the blue box
enters the four elements of the 2x2 a matrix
150. At 3:00, the middle equation in the blue box
enters the two elements of the 2x1 c matrix
151. At 3:00, the third equation in the blue box
solves for the variables x and y
152. At 3:00, the commas in the blue box separates
elements in that row
153. At 3:00, the semi-colons in the blue box separates
rows
154. The matrix method in solving simulaneously linear equations is most efficient because
the unknown variables, x and y, are not entered into the calculator
155. B(1,1)=
7
156. B(1,2)=
10
157. B(2,1)=
15
158. B(2,2)
22
159. C=
-2
160. D(1,1)
1
161. D(1,2)
0
162. D(2,1)
0
163. D(2,2)
1
164. A(1,1)
1
165. E(1,1)
-2
166. E(1,2)
1
167. E(2,1)
1.5
168. E(2,2)
-0.5
 Author: lacythecoolest ID: 309221 Card Set: ENT 300 set 1 Updated: 2015-10-08 16:45:43 Tags: engineering math Folders: Description: quiz questions for exam 1 Show Answers: