ENT 300 set 1

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Author:
lacythecoolest
ID:
309221
Filename:
ENT 300 set 1
Updated:
2015-10-08 12:45:43
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engineering math
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quiz questions for exam 1
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  1. 1. y=sin(x), x can be _____, but without units is always _____.
    radians or degrees, radians
  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
    radian
  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
    radians
  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
    4 answers
    • 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
    • 0.927 radians
  58. Complex numbers can be
    • all of these
    • multiplied and divided
    • added and subtracted
    • 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
    0.927 radians
  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 ___
    radius, the same
  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

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