FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

Karten in diesem Lernkartenset

1. Karte 1

   Frage

   SI base unit of length?

   Antwort

   The metre, symbol $m$.

2. Karte 2

   Frage

   Slope between two points?

   Antwort

   $$m=\frac{y_2-y_1}{x_2-x_1}$$

   This requires $x_2\ne x_1$; slope is the change in the dependent variable per unit change in the independent variable.

3. Karte 3

   Frage

   Net force relationship for constant mass in an inertial frame?

   Antwort

   $$\sum\mathbf{F}=m\mathbf{a}$$

   Use a coherent unit system and include only external forces on the chosen body.

4. Karte 4

   Frage

   Cash-flow sign convention from the decision maker's viewpoint?

   Antwort

   Receipts are positive and disbursements are negative. Choose one viewpoint and keep it consistent across the cash-flow diagram and equations.

5. Karte 5

   Frage

   Where should an FE candidate get the current reference handbook for practice?

   Antwort

   From the candidate's MyNCEES account. Use the current supplied file rather than an old indexed copy or a third-party mirror.

6. Karte 6

   Frage

   Probability of the complement of event $A$?

   Antwort

   $$P(A^c)=1-P(A)$$

7. Karte 7

   Frage

   An engineering judgment conflicts with pressure to protect schedule or cost. First duty?

   Antwort

   Protect public health, safety, and welfare. Document the technical concern and escalate through appropriate channels.

8. Karte 8

   Frage

   SI base unit of mass?

   Antwort

   The kilogram, symbol $kg$. It is a mass unit, not a force unit.

9. Karte 9

   Frage

   Linear equation from slope and intercept?

   Antwort

   $$y=mx+b$$

   Here $m$ is slope and $b$ is the value of $y$ where $x=0$.

10. Karte 10

    Frage

    Velocity after time $t$ under constant acceleration?

    Antwort

    $$v=v_0+at$$

    This one-dimensional form requires constant $a$ and a consistent positive direction.

11. Karte 11

    Frage

    Where is an end-of-period cash flow placed?

    Antwort

    At the boundary marking the end of that period. Interest factors assume consistent period lengths and cash-flow timing.

12. Karte 12

    Frage

    How is the FE reference handbook available during the exam?

    Antwort

    It is supplied onscreen as a searchable PDF. Practice locating information in the same current reference rather than relying on memory of a printed layout.

13. Karte 13

    Frage

    Probability of $A$ or $B$ for possibly overlapping events?

    Antwort

    $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$

14. Karte 14

    Frage

    SI base unit of time?

    Antwort

    The second, symbol $s$.

15. Karte 15

    Frage

    Linear equation from one point and a slope?

    Antwort

    $$y-y_1=m(x-x_1)$$

    Use it when the line passes through $(x_1,y_1)$ and has slope $m$.

16. Karte 16

    Frage

    Position after time $t$ under constant acceleration?

    Antwort

    $$x=x_0+v_0t+\frac{1}{2}at^2$$

    The acceleration is constant and all signed components use one coordinate direction.

17. Karte 17

    Frage

    A project assignment lies outside your competence. Proper response?

    Antwort

    Accept only the parts you are qualified to perform, or obtain qualified supervision or support. Do not present unfamiliar work as your own competent judgment.

18. Karte 18

    Frage

    SI base unit of electric current?

    Antwort

    The ampere, symbol $A$.

19. Karte 19

    Frage

    Future amount under simple interest?

    Antwort

    $$F=P(1+in)$$

    Here $P$ is principal, $i$ is interest per period, and $n$ is the number of periods; interest is earned only on principal.

20. Karte 20

    Frage

    Distance between two Cartesian points?

    Antwort

    $$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$

    The coordinate components must use the same length unit.

21. Karte 21

    Frage

    Constant-acceleration relation without elapsed time?

    Antwort

    $$v^2=v_0^2+2a(x-x_0)$$

    Use signed one-dimensional components and constant $a$.

22. Karte 22

    Frage

    Where do you search the supplied reference material in the exam interface?

    Antwort

    Use the exam software's search box beside the supplied reference material.

23. Karte 23

    Frage

    Conditional probability of $A$ given $B$?

    Antwort

    $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$

    This requires $P(B)>0$.

24. Karte 24

    Frage

    SI base unit of thermodynamic temperature?

    Antwort

    The kelvin, symbol $K$. Kelvin is written without a degree sign.

25. Karte 25

    Frage

    A client asks you to remove an unfavorable test result from a report. Proper response?

    Antwort

    Keep the material result and explain it accurately. Engineering statements should be objective, complete enough to avoid deception, and supported by evidence.

26. Karte 26

    Frage

    Midpoint of two Cartesian points?

    Antwort

    $$\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$

    Average corresponding coordinates.

27. Karte 27

    Frage

    Linear momentum of a particle?

    Antwort

    $$\mathbf{p}=m\mathbf{v}$$

    For constant mass, SI units are $kg\cdot m/s$.

28. Karte 28

    Frage

    Future amount under compound interest?

    Antwort

    $$F=P(1+i)^n$$

    The rate period must match the period used for $n$.

29. Karte 29

    Frage

    Should an FE search workflow depend on Ctrl+F?

    Antwort

    No. The May 2026 NCEES Examinee Guide says Ctrl+F isn't available; practice with the exam interface's own search box.

30. Karte 30

    Frage

    SI base unit of amount of substance?

    Antwort

    The mole, symbol $mol$.

31. Karte 31

    Frage

    Joint probability expressed with a conditional probability?

    Antwort

    $$P(A\cap B)=P(A\mid B)P(B)$$

    This elementary formula requires $P(B)>0$.

32. Karte 32

    Frage

    Standard equation of a circle centered at $(h,k)$?

    Antwort

    $$(x-h)^2+(y-k)^2=r^2$$

    The coordinate units and radius unit must match.

33. Karte 33

    Frage

    Impulse-momentum relationship?

    Antwort

    $$\int_{t_1}^{t_2}\sum\mathbf{F}\,dt=\mathbf{p}_2-\mathbf{p}_1$$

    The force is the net external force on the chosen system.

34. Karte 34

    Frage

    You discover a financial interest that could affect your recommendation. Proper response?

    Antwort

    Disclose the conflict promptly to affected parties and obtain appropriate consent or withdraw. Hidden personal interests undermine independent judgment.

35. Karte 35

    Frage

    SI base unit of luminous intensity?

    Antwort

    The candela, symbol $cd$.

36. Karte 36

    Frage

    Present worth of one future amount?

    Antwort

    $$P=\frac{F}{(1+i)^n}$$

    Use an effective rate $i$ per period consistent with $n$.

37. Karte 37

    Frage

    Roots of $ax^2+bx+c=0$?

    Antwort

    $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

    This form requires $a\ne0$.

38. Karte 38

    Frage

    When is total linear momentum conserved?

    Antwort

    When net external impulse on the system is zero. Internal forces can redistribute momentum but do not change the system total.

39. Karte 39

    Frage

    Why avoid memorizing FE handbook page numbers?

    Antwort

    Pagination and layout can change. Remember section names, concepts, and strong search terms instead.

40. Karte 40

    Frage

    Probability condition that defines independence of $A$ and $B$?

    Antwort

    $$P(A\cap B)=P(A)P(B)$$

    Independence is not the same as mutual exclusivity.

41. Karte 41

    Frage

    SI unit of frequency in base-unit form?

    Antwort

    The hertz, $Hz=s^{-1}$, applies to periodic phenomena. One hertz is one cycle per second.

42. Karte 42

    Frage

    Present worth of an end-of-period uniform series $A$?

    Antwort

    $$P=A\frac{(1+i)^n-1}{i(1+i)^n}$$

    This requires $i\ne0$; at $i=0$, $P=An$.

43. Karte 43

    Frage

    What does $b^2-4ac$ reveal for a real-coefficient quadratic?

    Antwort

    It determines the root type: positive gives two distinct real roots, zero gives one repeated real root, and negative gives a complex-conjugate pair.

44. Karte 44

    Frage

    Work done by a constant force through displacement?

    Antwort

    $$W=\mathbf{F}\cdot\mathbf{s}=Fs\cos\theta$$

    Use the angle between force and displacement; SI units are joules.

45. Karte 45

    Frage

    A vendor offers a valuable gift while you evaluate bids. Proper response?

    Antwort

    Decline it and follow the organization's disclosure policy. Even an intended courtesy can create an actual or apparent conflict.

46. Karte 46

    Frage

    SI unit of force in base-unit form?

    Antwort

    The newton, $N=kg\cdot m/s^2$.

47. Karte 47

    Frage

    First search cue for a named quantity such as coefficient of thermal expansion?

    Antwort

    Search the exact technical noun phrase. Distinctive nouns usually narrow results better than a whole question sentence.

48. Karte 48

    Frage

    Bayes' rule for $P(A\mid B)$?

    Antwort

    $$P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}$$

    This requires $P(B)>0$.

49. Karte 49

    Frage

    Product of powers with the same positive base and real exponents?

    Antwort

    $$a^m a^n=a^{m+n}$$

    This form assumes $a>0$ and real exponents $m$ and $n$.

50. Karte 50

    Frage

    Translational kinetic energy of a particle?

    Antwort

    $$K=\frac{1}{2}mv^2$$

    Mass and speed must use a coherent unit system.

51. Karte 51

    Frage

    SI unit of pressure in force-area form?

    Antwort

    The pascal, $Pa=N/m^2$. It is the SI derived unit for pressure and stress.

52. Karte 52

    Frage

    Equivalent annual amount for present worth $P$?

    Antwort

    $$A=P\frac{i(1+i)^n}{(1+i)^n-1}$$

    For the displayed formula, $i\ne0$; at $i=0$, $A=P/n$. Payments occur at period ends and $i$ matches that period.

53. Karte 53

    Frage

    May confidential client information be shared for personal benefit?

    Antwort

    No. Protect it unless the client authorizes disclosure or law, safety, or professional duty requires it.

54. Karte 54

    Frage

    A handbook search term returns too many results. Best refinement?

    Antwort

    Add one meaningful qualifier, such as the phenomenon, geometry, distribution, or material property you need.

55. Karte 55

    Frage

    Quotient of powers with the same positive base and real exponents?

    Antwort

    $$\frac{a^m}{a^n}=a^{m-n}$$

    This form assumes $a>0$ and real exponents $m$ and $n$.

56. Karte 56

    Frage

    Net work-energy relationship for a particle?

    Antwort

    $$W_{net}=K_2-K_1$$

    The net work includes the work of all forces represented in the particle model.

57. Karte 57

    Frage

    Ordered selections of $r$ objects from $n$ distinct objects?

    Antwort

    $$P(n,r)=\frac{n!}{(n-r)!}$$

    Use this when order matters and selection is without replacement.

58. Karte 58

    Frage

    Future worth of an end-of-period uniform series $A$?

    Antwort

    $$F=A\frac{(1+i)^n-1}{i}$$

    This requires $i\ne0$; at $i=0$, $F=An$.

59. Karte 59

    Frage

    Power of a power for a positive base and real exponents?

    Antwort

    $$(a^m)^n=a^{mn}$$

    This form assumes $a>0$ and real exponents $m$ and $n$.

60. Karte 60

    Frage

    SI unit of energy in force-distance form?

    Antwort

    The joule, $J=N\cdot m$.

61. Karte 61

    Frage

    A problem gives only an unfamiliar symbol. Best search preparation?

    Antwort

    Translate the symbol into its likely quantity name and discipline context before searching; symbol-only searches are often ambiguous.

62. Karte 62

    Frage

    Confidential information reveals an imminent public-safety risk. What comes first?

    Antwort

    Take steps required to protect people, using appropriate legal and organizational channels. Share only what is necessary and document the basis for escalation.

63. Karte 63

    Frage

    Unordered selections of $r$ objects from $n$ distinct objects?

    Antwort

    $$C(n,r)=\frac{n!}{r!(n-r)!}$$

    Use this when order does not matter and selection is without replacement.

64. Karte 64

    Frage

    Change in gravitational potential energy near Earth's surface?

    Antwort

    $$\Delta U_g=mg\Delta h$$

    Use approximately constant $g$ and a clearly chosen height datum.

65. Karte 65

    Frage

    Negative-exponent rule for a positive base and real exponent?

    Antwort

    $$a^{-n}=\frac{1}{a^n}$$

    This form assumes $a>0$ and real exponent $n$.

66. Karte 66

    Frage

    Uniform end-of-period deposit needed for future amount $F$?

    Antwort

    $$A=F\frac{i}{(1+i)^n-1}$$

    For the displayed formula, $i\ne0$; at $i=0$, $A=F/n$. The first deposit is one period from now and the last occurs at period $n$.

67. Karte 67

    Frage

    A handbook search for an acronym fails. Next move?

    Antwort

    Try the expanded term and a common alternate name. Acronyms vary by section and discipline.

68. Karte 68

    Frage

    SI unit of power in energy-time form?

    Antwort

    The watt, $W=J/s$.

69. Karte 69

    Frage

    Logarithm of a product?

    Antwort

    $$\log_b(xy)=\log_b x+\log_b y$$

    For real logarithms, $b>0$, $b\ne1$, and both arguments are positive.

70. Karte 70

    Frage

    Conditions for a binomial model?

    Antwort

    A fixed number of independent trials, two outcomes per trial, and the same success probability on every trial.

71. Karte 71

    Frage

    Using another engineer's analysis in your deliverable?

    Antwort

    Credit the source and verify the analysis before relying on it. Do not present someone else's work as your own.

72. Karte 72

    Frage

    SI unit of electric charge in current-time form?

    Antwort

    The coulomb, $C=A\cdot s$.

73. Karte 73

    Frage

    Average power from work over elapsed time?

    Antwort

    $$P_{avg}=\frac{W}{\Delta t}$$

    Use consistent energy and time units; watts are joules per second.

74. Karte 74

    Frage

    Annual equivalent of cost $P$ with salvage $S$ after $n$ periods?

    Antwort

    $$A=P\frac{i(1+i)^n}{(1+i)^n-1}-S\frac{i}{(1+i)^n-1}$$

    The first factor converts present cost to an annual amount; the second converts future salvage. Use the same effective rate and period basis. At $i=0$, $A=(P-S)/n$.

75. Karte 75

    Frage

    Logarithm of a positive quantity raised to a power?

    Antwort

    $$\log_b(x^p)=p\log_b x$$

    For real logarithms, $x>0$, $b>0$, and $b\ne1$.

76. Karte 76

    Frage

    SI unit of electric potential difference in energy-charge form?

    Antwort

    The volt, $V=J/C$.

77. Karte 77

    Frage

    Instantaneous mechanical power delivered by a force?

    Antwort

    $$P=\mathbf{F}\cdot\mathbf{v}$$

    Use the velocity of the force's point of application.

78. Karte 78

    Frage

    A precise handbook term gives no useful match. Next move?

    Antwort

    Try a standard synonym or the broader parent concept, then narrow within the relevant section.

79. Karte 79

    Frage

    Mean of $X\sim\operatorname{Binomial}(n,p)$?

    Antwort

    $$E[X]=np$$

80. Karte 80

    Frage

    SI unit of electrical resistance in voltage-current form?

    Antwort

    The ohm, $\Omega=V/A$.

81. Karte 81

    Frage

    Moment of a force about a point?

    Antwort

    $$\mathbf{M}=\mathbf{r}\times\mathbf{F}$$

    Vector $\mathbf{r}$ runs from the moment point to a point on the force's line of action.

82. Karte 82

    Frage

    Cash-flow pattern described by an arithmetic gradient $G$?

    Antwort

    A series that changes by the same amount $G$ each period. In the usual convention, the first gradient increment appears after the first base payment.

83. Karte 83

    Frage

    Inverse relationship between the natural log and exponential?

    Antwort

    $$\ln(e^x)=x,\qquad e^{\ln x}=x$$

    The second identity requires $x>0$.

84. Karte 84

    Frage

    SI prefix giga?

    Antwort

    $G=10^9$.

85. Karte 85

    Frage

    Angular velocity after time $t$ under constant angular acceleration?

    Antwort

    $$\omega=\omega_0+\alpha t$$

    Use consistent angular sign convention and radians for angular measures.

86. Karte 86

    Frage

    When should an engineer sign or seal technical work?

    Antwort

    Only when authorized and when the work was prepared by the engineer or under the level of responsible charge required by the applicable jurisdiction.

87. Karte 87

    Frage

    Best memory target for returning to a handbook formula?

    Antwort

    The section or concept name plus a distinctive search phrase. That survives layout changes better than a page number.

88. Karte 88

    Frage

    SI prefix mega?

    Antwort

    $M=10^6$. Uppercase matters: lowercase $m$ means milli.

89. Karte 89

    Frage

    Convert degrees to radians?

    Antwort

    $$\theta_{rad}=\theta_{deg}\frac{\pi}{180}$$

    Use radians in calculus formulas unless a formula explicitly says otherwise.

90. Karte 90

    Frage

    Variance of $X\sim\operatorname{Binomial}(n,p)$?

    Antwort

    $$\operatorname{Var}(X)=np(1-p)$$

91. Karte 91

    Frage

    Cash-flow pattern described by a geometric gradient rate $g$?

    Antwort

    A series in which each payment is the previous payment multiplied by $1+g$. Keep $g$ on the same period basis as the interest rate.

92. Karte 92

    Frage

    Where do licensure and sealing requirements come from?

    Antwort

    The applicable jurisdiction's current laws and board rules. Confirm local requirements rather than assuming one state's rules apply everywhere.

93. Karte 93

    Frage

    Rotational kinetic energy about a fixed axis?

    Antwort

    $$K_{rot}=\frac{1}{2}I\omega^2$$

    $I$ is the mass moment of inertia about that axis.

94. Karte 94

    Frage

    SI prefix kilo?

    Antwort

    $k=10^3$.

95. Karte 95

    Frage

    Right-triangle definition of sine?

    Antwort

    Sine is opposite over hypotenuse. This definition applies to an acute angle in a right triangle.

96. Karte 96

    Frage

    After search lands near a result, what should you scan first?

    Antwort

    The section heading and nearby subheading. They establish whether the result belongs to the right model and subject.

97. Karte 97

    Frage

    Rotational analogue of Newton's second law about a fixed principal axis?

    Antwort

    $$\sum M=I\alpha$$

    This scalar form assumes the stated fixed-axis model and a consistent sign convention.

98. Karte 98

    Frage

    SI prefix milli?

    Antwort

    $m=10^{-3}$. Context distinguishes the prefix from the metre symbol.

99. Karte 99

    Frage

    Meaning of a nominal annual rate compounded $m$ times per year?

    Antwort

    It is a quoted annual rate equal to $m$ times the periodic rate. It is not itself the effective annual rate unless compounding is annual.

100. Karte 100

     Frage

     Standardize an observation $x$ from a distribution with mean $\mu$ and standard deviation $\sigma$?

     Antwort

     $$z=\frac{x-\mu}{\sigma}$$

     This requires $\sigma>0$; using a normal probability table also assumes an appropriate normal model.

101. Karte 101

     Frage

     Right-triangle definition of cosine?

     Antwort

     Cosine is adjacent over hypotenuse. This definition applies to an acute angle in a right triangle.

102. Karte 102

     Frage

     Force-displacement relation for an ideal linear spring?

     Antwort

     $$F=-kx$$

     The minus sign shows restoring direction; the model applies within the spring's linear range.

103. Karte 103

     Frage

     May qualifications or project responsibility be exaggerated in a proposal?

     Antwort

     No. State education, licensure, experience, and responsibility accurately, including the actual roles of collaborators.

104. Karte 104

     Frage

     SI prefix micro?

     Antwort

     $\mu=10^{-6}$.

105. Karte 105

     Frage

     A handbook symbol conflicts with your usual notation. What controls?

     Antwort

     The definition beside the selected relationship. Symbols can represent different quantities in different sections.

106. Karte 106

     Frage

     Periodic rate from nominal annual rate $r$ compounded $m$ times per year?

     Antwort

     $$i=\frac{r}{m}$$

     Use consistent decimal units, and pair this rate with the number of compounding periods.

107. Karte 107

     Frage

     Right-triangle definition of tangent?

     Antwort

     Tangent is opposite over adjacent, or $\sin\theta/\cos\theta$ where $\cos\theta\ne0$.

108. Karte 108

     Frage

     Average normal stress under centered axial load?

     Antwort

     $$\sigma=\frac{F}{A}$$

     $F$ is normal to area $A$; the average ignores local stress concentrations.

109. Karte 109

     Frage

     Mean, median, and mode of a symmetric normal distribution?

     Antwort

     They are equal and located at $\mu$. The distribution is symmetric about that center.

110. Karte 110

     Frage

     SI prefix nano?

     Antwort

     $n=10^{-9}$.

111. Karte 111

     Frage

     Fundamental Pythagorean trigonometric identity?

     Antwort

     $$\sin^2\theta+\cos^2\theta=1$$

112. Karte 112

     Frage

     Engineering normal strain?

     Antwort

     $$\varepsilon=\frac{\Delta L}{L_0}$$

     It is dimensionless and uses original gauge length $L_0$.

113. Karte 113

     Frage

     A candidate retrieves a formula from the handbook. What must be checked with it?

     Antwort

     Its applicability assumptions and variable definitions. A familiar equation used under the wrong model is still wrong.

114. Karte 114

     Frage

     Technical duty to an employer or client?

     Antwort

     Act as a faithful professional within lawful, ethical limits, communicate material risks, and preserve independent technical judgment.

115. Karte 115

     Frage

     How does a length conversion factor apply to area?

     Antwort

     Square it. If $1\,u=a\,v$, then $1\,u^2=a^2\,v^2$.

116. Karte 116

     Frage

     Effective annual rate from nominal rate $r$ compounded $m$ times per year?

     Antwort

     $$i_{eff}=\left(1+\frac{r}{m}\right)^m-1$$

117. Karte 117

     Frage

     When is a Poisson count model reasonable?

     Antwort

     For counts in a fixed interval when events occur independently at an approximately constant average rate and simultaneous events are negligible.

118. Karte 118

     Frage

     Relationship for the third side of a non-right triangle?

     Antwort

     $$c^2=a^2+b^2-2ab\cos C$$

     Angle $C$ lies between sides $a$ and $b$, opposite side $c$.

119. Karte 119

     Frage

     Linear elastic stress-strain relation in uniaxial loading?

     Antwort

     $$\sigma=E\varepsilon$$

     Use it in the material's linear elastic range; $E$ has stress units.

120. Karte 120

     Frage

     How does a length conversion factor apply to volume?

     Antwort

     Cube it. If $1\,u=a\,v$, then $1\,u^3=a^3\,v^3$.

121. Karte 121

     Frage

     What should you record for every variable in a retrieved equation?

     Antwort

     Its meaning and expected unit or dimension. This catches swapped symbols and incompatible substitutions.

122. Karte 122

     Frage

     Effective annual rate for continuous compounding at nominal rate $r$?

     Antwort

     $$i_{eff}=e^r-1$$

     Here $r$ is expressed as a decimal per year.

123. Karte 123

     Frage

     A supervisor directs an illegal engineering action. Proper response?

     Antwort

     Refuse the illegal action, document the direction, and escalate through appropriate legal or organizational channels.

124. Karte 124

     Frage

     Magnitude of a three-component vector $\mathbf{v}$?

     Antwort

     $$\lVert\mathbf{v}\rVert=\sqrt{v_x^2+v_y^2+v_z^2}$$

     All components must represent the same physical quantity in compatible units.

125. Karte 125

     Frage

     Mass density?

     Antwort

     $$\rho=\frac{m}{V}$$

     Use mass, not weight, in the numerator.

126. Karte 126

     Frage

     Inches in one foot?

     Antwort

     $12\,in=1\,ft$.

127. Karte 127

     Frage

     Mean and variance of $X\sim\operatorname{Poisson}(\lambda)$?

     Antwort

     Both equal $\lambda$. The standard deviation is $\sqrt{\lambda}$.

128. Karte 128

     Frage

     How should subscripts be handled in a retrieved relationship?

     Antwort

     Read what each subscript identifies—state, direction, phase, location, or reference—before substituting values.

129. Karte 129

     Frage

     Dot product from vector magnitudes and included angle?

     Antwort

     $$\mathbf{a}\cdot\mathbf{b}=\lVert\mathbf{a}\rVert\lVert\mathbf{b}\rVert\cos\theta$$

     The result is a scalar.

130. Karte 130

     Frage

     Average normal pressure on an area?

     Antwort

     $$p=\frac{F_n}{A}$$

     $F_n$ is the normal force; pressure is scalar in a fluid at rest.

131. Karte 131

     Frage

     Feet in one yard?

     Antwort

     $3\,ft=1\,yd$.

132. Karte 132

     Frage

     When are two interest rates equivalent?

     Antwort

     When they produce the same accumulation over the same time interval. Convert both rates to a common effective period before comparing them.

133. Karte 133

     Frage

     You discover a material error in issued work. Proper response?

     Antwort

     Notify responsible parties promptly, assess the safety impact, correct the record, and document the response. Do not hide the error.

134. Karte 134

     Frage

     Expected value of a discrete random variable?

     Antwort

     $$E[X]=\sum_x xP(X=x)$$

     Sum over all possible values with a valid probability mass function.

135. Karte 135

     Frage

     Dot-product test for perpendicular nonzero vectors?

     Antwort

     Their dot product is zero. The zero vector also has zero dot product with every vector, so require both vectors to be nonzero before concluding perpendicularity.

136. Karte 136

     Frage

     Hydrostatic pressure change with vertical depth in a constant-density fluid?

     Antwort

     $$\Delta p=\rho g\Delta h$$

     Depth increases downward and the fluid is at rest.

137. Karte 137

     Frage

     Feet in one statute mile?

     Antwort

     $5280\,ft=1\,mi$.

138. Karte 138

     Frage

     Present-worth acceptance rule for an independent investment at the minimum attractive rate of return?

     Antwort

     Accept it when net present worth is nonnegative. All cash flows must be discounted to the same time using the chosen comparison rate.

     

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139. Karte 139

     Frage

     A retrieved formula contains signed quantities. What should you confirm?

     Antwort

     The stated sign convention and positive direction. Do not mix magnitudes with signed components silently.

140. Karte 140

     Frage

     Magnitude of a vector cross product?

     Antwort

     $$\lVert\mathbf{a}\times\mathbf{b}\rVert=\lVert\mathbf{a}\rVert\lVert\mathbf{b}\rVert\sin\theta$$

     The direction follows the right-hand rule.

141. Karte 141

     Frage

     Exact inch-to-metre relationship?

     Antwort

     $1\,in=0.0254\,m$ exactly.

142. Karte 142

     Frage

     Volumetric flow rate through a cross-section?

     Antwort

     $$Q=Av_{avg}$$

     Velocity is the area-average component normal to the section.

143. Karte 143

     Frage

     Variance from the mean $\mu$?

     Antwort

     $$\operatorname{Var}(X)=E[(X-\mu)^2]$$

     Variance has squared units; standard deviation has the original units.

144. Karte 144

     Frage

     Future-worth acceptance rule for an independent investment?

     Antwort

     Accept it when net future worth at the study horizon is nonnegative, using the minimum attractive rate of return consistently.

145. Karte 145

     Frage

     What coordinate detail should be checked before using a vector or mechanics formula?

     Antwort

     Axis directions and the reference point or origin. Components and moments depend on those choices.

146. Karte 146

     Frage

     Exact foot-to-metre relationship?

     Antwort

     $1\,ft=0.3048\,m$ exactly.

147. Karte 147

     Frage

     How should important uncertainty be communicated?

     Antwort

     State the assumptions, limits, and plausible consequences clearly enough for the decision maker to understand the risk.

148. Karte 148

     Frage

     When is the matrix product $AB$ defined?

     Antwort

     It is defined when the number of columns of $A$ equals the number of rows of $B$. If $A$ is $m\times n$ and $B$ is $n\times p$, then $AB$ is $m\times p$.

149. Karte 149

     Frage

     Steady one-inlet, one-outlet mass continuity?

     Antwort

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     Here $v_1$ and $v_2$ are cross-sectional average velocity components normal to their sections, with density treated as uniform over each section. For incompressible flow with constant density, this reduces to $A_1v_1=A_2v_2$.

150. Karte 150

     Frage

     Sample mean of observations $x_1,\ldots,x_n$?

     Antwort

     $$\bar{x}=\frac{1}{n}\sum_{i=1}^n x_i$$

151. Karte 151

     Frage

     Square feet in one acre?

     Antwort

     $1\,acre=43{,}560\,ft^2$.

152. Karte 152

     Frage

     Determinant of $\begin{bmatrix}a&b\\c&d\end{bmatrix}$?

     Antwort

     $$ad-bc$$

153. Karte 153

     Frage

     Bernoulli relationship along a streamline for ideal steady flow?

     Antwort

     $$\frac{p}{\rho g}+\frac{v^2}{2g}+z=\text{constant}$$

     This basic form assumes steady, incompressible, negligible-viscosity flow with no shaft work or heat effects between points.

154. Karte 154

     Frage

     May inconvenient measurements be discarded without a technical basis?

     Antwort

     No. Use a documented, technically justified rule for excluding data and preserve the original record.

155. Karte 155

     Frage

     Annual-worth acceptance rule for an independent investment?

     Antwort

     Accept it when equivalent annual worth is nonnegative. Compare alternatives over compatible service assumptions.

156. Karte 156

     Frage

     Before using a handbook equation, what unit-system check matters?

     Antwort

     Confirm that every input and any embedded constant use one compatible unit system. Convert first when necessary.

157. Karte 157

     Frage

     Cubic metres in one litre?

     Antwort

     $1\,L=10^{-3}\,m^3$.

158. Karte 158

     Frage

     What does a zero determinant mean for a square matrix?

     Antwort

     The matrix is singular and has no inverse. A corresponding linear system cannot have one unique solution.

159. Karte 159

     Frage

     Reynolds number for internal flow using characteristic length $L$?

     Antwort

     $$Re=\frac{\rho vL}{\mu}=\frac{vL}{\nu}$$

     It is dimensionless; use consistent properties and the geometry-appropriate characteristic length.

160. Karte 160

     Frage

     Unbiased sample variance for an independent sample from one population?

     Antwort

     $$s^2=\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})^2$$

     This requires at least two observations, so $n\ge2$. The $n-1$ denominator estimates population variance after fitting the sample mean.

161. Karte 161

     Frage

     How should mutually exclusive alternatives be compared?

     Antwort

     Use one consistent economic measure over a common study period and select the economically preferred feasible alternative; do not accept every alternative with a positive individual worth.

162. Karte 162

     Frage

     Cubic centimetres in one millilitre?

     Antwort

     $1\,mL=1\,cm^3$.

163. Karte 163

     Frage

     Why keep contemporaneous engineering records?

     Antwort

     They preserve assumptions, decisions, calculations, approvals, and changes so the work can be checked and responsibilities understood.

164. Karte 164

     Frage

     Fast check after substituting into a handbook formula?

     Antwort

     Verify that the resulting dimensions match the requested quantity and that additive terms share dimensions.

165. Karte 165

     Frage

     Matrix solution of $A\mathbf{x}=\mathbf{b}$ when $A$ is invertible?

     Antwort

     $$\mathbf{x}=A^{-1}\mathbf{b}$$

     In numerical work, direct factorization is usually preferable to explicitly forming the inverse.

166. Karte 166

     Frage

     Sensible heat for constant specific heat and no phase change?

     Antwort

     $$Q=mc\Delta T$$

     $c$ must match the material, temperature range, mass unit, and temperature-difference unit.

167. Karte 167

     Frage

     Standard error of the mean for an i.i.d. sample with population standard deviation $\sigma$?

     Antwort

     $$SE(\bar{x})=\frac{\sigma}{\sqrt{n}}$$

     The observations are independent and identically distributed with common variance $\sigma^2$. Use $s$ for unknown $\sigma$ only when the selected inference method allows it.

168. Karte 168

     Frage

     Safe setup for converting $25\,ft^2$ to square metres?

     Antwort

     $$25\,ft^2\left(\frac{0.3048\,m}{1\,ft}\right)^2$$

     The squared length factor cancels $ft^2$ and leaves $m^2$.

169. Karte 169

     Frage

     Purpose of incremental analysis for mutually exclusive alternatives?

     Antwort

     It tests whether the additional investment in the higher-cost option earns the required return compared with the lower-cost option.

170. Karte 170

     Frage

     Physical meaning of $dy/dx$?

     Antwort

     It is the instantaneous rate of change of $y$ with respect to $x$, with units of the $y$ unit divided by the $x$ unit.

171. Karte 171

     Frage

     One-dimensional steady conduction through a plane wall?

     Antwort

     $$\dot Q=-kA\frac{dT}{dx}$$

     The minus sign indicates heat flows toward lower temperature; $k$ is thermal conductivity.

172. Karte 172

     Frage

     When should you algebraically rearrange a handbook relationship?

     Antwort

     After confirming the correct equation, definitions, assumptions, and sign convention. Then isolate the requested variable without changing its domain restrictions.

173. Karte 173

     Frage

     Safe setup for converting $2\,in^3$ to cubic metres?

     Antwort

     $$2\,in^3\left(\frac{0.0254\,m}{1\,in}\right)^3$$

     Cube the exact length conversion because the original quantity is volume.

174. Karte 174

     Frage

     A client changes a safety-critical design requirement verbally. Proper response?

     Antwort

     Confirm the change in writing, analyze its consequences, and obtain the required approvals before relying on it.

175. Karte 175

     Frage

     Derivative of $x^n$ for constant $n$?

     Antwort

     $$\frac{d}{dx}x^n=nx^{n-1}$$

     Apply domain restrictions when $n$ is non-integer or negative.

176. Karte 176

     Frage

     Convective heat-transfer rate at a surface?

     Antwort

     $$\dot Q=hA(T_s-T_\infty)$$

     $h$ depends on the flow and geometry; the sign follows the chosen temperature difference.

177. Karte 177

     Frage

     What does the central limit theorem say about a sample mean?

     Antwort

     For sufficiently large independent, identically distributed samples with finite variance, the sampling distribution of the properly standardized mean approaches normality. It does not make the raw data normal.

178. Karte 178

     Frage

     Internal rate of return?

     Antwort

     The discount rate that makes net present worth zero. Multiple sign changes in cash flow can produce multiple or no meaningful real rates.

179. Karte 179

     Frage

     Several similar handbook equations appear together. How do you choose?

     Antwort

     Match each equation's stated geometry, boundary conditions, material model, and variable definitions to the problem.

180. Karte 180

     Frage

     Convert Celsius temperature to kelvin?

     Antwort

     $$T_K=T_{^\circ C}+273.15$$

     This conversion is for absolute temperature, not temperature difference.

181. Karte 181

     Frage

     Derivative of a product $u(x)v(x)$?

     Antwort

     $$(uv)'=u'v+uv'$$

182. Karte 182

     Frage

     Internal escalation does not resolve a serious public-safety threat. Next step?

     Antwort

     Use the next appropriate authority or reporting channel, consistent with law and the urgency of the hazard. Keep a factual record.

183. Karte 183

     Frage

     Two-sided confidence interval for a population mean with known $\sigma$?

     Antwort

     $$\bar{x}\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$$

     Use the normal-model conditions and the critical value for confidence level $1-\alpha$.

184. Karte 184

     Frage

     Net thermal radiation from a small gray surface to large surroundings?

     Antwort

     $$\dot Q=\varepsilon\sigma A(T_s^4-T_{sur}^4)$$

     Use absolute temperatures; the model assumes the stated gray-surface surroundings.

185. Karte 185

     Frage

     Basic benefit-cost acceptance rule for an independent public project?

     Antwort

     Accept when the consistently defined benefit-cost ratio is at least one. For mutually exclusive choices, use an incremental comparison rather than ranking by individual ratios alone.

186. Karte 186

     Frage

     Derivative of a composite function $f(g(x))$?

     Antwort

     $$\frac{d}{dx}f(g(x))=f'(g(x))g'(x)$$

187. Karte 187

     Frage

     Why inspect boundary or initial conditions near a formula?

     Antwort

     They determine which solution form applies and can eliminate constants or terms. A formula without its conditions may be unusable.

188. Karte 188

     Frage

     Convert Celsius temperature to Fahrenheit?

     Antwort

     $$T_{^\circ F}=\frac{9}{5}T_{^\circ C}+32$$

189. Karte 189

     Frage

     Ethical basis for expert technical testimony?

     Antwort

     Offer opinions only within your competence, disclose important assumptions and limitations, and distinguish facts from professional judgment.

190. Karte 190

     Frage

     Meaning of a breakeven value?

     Antwort

     The value of a selected variable that makes two alternatives economically equivalent or makes net worth zero. Other assumptions are held fixed.

191. Karte 191

     Frage

     Derivative of $e^x$?

     Antwort

     $$\frac{d}{dx}e^x=e^x$$

192. Karte 192

     Frage

     First-law energy balance for a closed system with work positive out?

     Antwort

     $$\Delta E=Q-W$$

     $Q$ is heat into the system and $W$ is work done by the system; state a different sign convention before using it.

193. Karte 193

     Frage

     Frequentist meaning of a 95% confidence procedure?

     Antwort

     Across repeated samples, about 95% of intervals built by the procedure would contain the fixed population parameter. It is not a 95% probability assigned to this already-computed interval.

194. Karte 194

     Frage

     A needed value falls between handbook table entries. What is the cue?

     Antwort

     Check whether interpolation is appropriate, keep both axes and units straight, and avoid extrapolating unless the source supports it.

195. Karte 195

     Frage

     Derivative of $\ln x$ over the real domain?

     Antwort

     $$\frac{d}{dx}\ln x=\frac{1}{x}$$

     This real-valued form requires $x>0$.

196. Karte 196

     Frage

     Relationship between Celsius and kelvin temperature differences?

     Antwort

     $1\,K$ of temperature difference equals $1\,^{\circ}C$ of temperature difference. Do not add $273.15$ to a difference.

197. Karte 197

     Frage

     How should credit for team engineering work be assigned?

     Antwort

     Accurately recognize each contributor's work and responsibility. Do not claim sole credit for a collaborative result.

198. Karte 198

     Frage

     Main limitation of simple payback period?

     Antwort

     It ignores the time value of money and usually ignores cash flows after payback. Discounted payback fixes the first issue, not the second.

199. Karte 199

     Frage

     Roles of the null and alternative hypotheses?

     Antwort

     The null states the baseline parameter claim tested; the alternative states the competing direction or difference supported when evidence is strong enough.

200. Karte 200

     Frage

     Ideal-gas equation of state?

     Antwort

     $$pV=nRT$$

     Use absolute temperature and a gas constant consistent with pressure, volume, amount, and energy units.

201. Karte 201

     Frage

     First check when reading a handbook table?

     Antwort

     Read the title, column headings, units, notes, and basis conditions before selecting a value.

202. Karte 202

     Frage

     Candidates for absolute extrema of a continuous function on a closed interval?

     Antwort

     The endpoints and every interior point where the first derivative is zero or does not exist. Evaluate the function at each candidate; the largest and smallest values are the absolute extrema.

203. Karte 203

     Frage

     How should a sunk cost affect a current engineering-economy decision?

     Antwort

     It should not affect the choice because it cannot be changed by the decision. Use future incremental cash flows instead.

204. Karte 204

     Frage

     Convert Fahrenheit absolute temperature to Rankine?

     Antwort

     $$T_{^\circ R}=T_{^\circ F}+459.67$$

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. Karte 205

     Frage

     Ohm's law for an ideal resistor?

     Antwort

     $$V=IR$$

     Use a consistent passive sign convention; $R$ is constant only over the assumed operating range.

206. Karte 206

     Frage

     You have confidential details about a competitor's bid. Proper response?

     Antwort

     Do not use or disclose improperly obtained information. Notify the appropriate procurement or ethics contact.

207. Karte 207

     Frage

     Physical meaning of a definite integral $\int_a^b f(x)\,dx$?

     Antwort

     It is signed accumulation of $f$ from $a$ to $b$. Its units are the units of $f$ multiplied by the units of $x$.

208. Karte 208

     Frage

     Is a radian dimensionless?

     Antwort

     Yes. It is the ratio of arc length to radius, so the length units cancel; keep $rad$ when it clarifies angular meaning.

209. Karte 209

     Frage

     Electrical power absorbed under the passive sign convention?

     Antwort

     $$P=VI$$

     For a resistor, this also gives $P=I^2R=V^2/R$ when Ohm's law applies.

210. Karte 210

     Frage

     Meaning of a p-value?

     Antwort

     Assuming the null hypothesis and model are correct, it is the probability of a result at least as extreme as the observed result. It is not the probability that the null is true.

211. Karte 211

     Frage

     First check when reading a handbook graph?

     Antwort

     Identify both axes, scales, units, curve labels, and any log scale before estimating a value.

212. Karte 212

     Frage

     Difference between mass and weight?

     Antwort

     Mass measures inertia; weight is gravitational force on that mass. Their dimensions and units are different.

213. Karte 213

     Frage

     Kirchhoff's current law at a node?

     Antwort

     The algebraic sum of currents at a node is zero. Choose one sign convention, such as currents entering positive, and apply it consistently.

214. Karte 214

     Frage

     Evaluate $\int_a^b f(x)\,dx$ from an antiderivative $F$?

     Antwort

     $$\int_a^b f(x)\,dx=F(b)-F(a)$$

     This applies when $F'=f$ on the interval under the usual continuity conditions.

215. Karte 215

     Frage

     Opportunity cost?

     Antwort

     The value of the best forgone alternative. Include it when choosing one use of a scarce resource prevents another valuable use.

216. Karte 216

     Frage

     Weight from mass in a gravitational field?

     Antwort

     $$W=mg$$

     Use compatible units; $g$ is local gravitational acceleration, not a universal constant for every location.

217. Karte 217

     Frage

     Kirchhoff's voltage law around a closed loop?

     Antwort

     The algebraic sum of voltage rises and drops around the loop is zero. Traverse the loop once with a consistent polarity convention.

218. Karte 218

     Frage

     Decision rule using significance level $\alpha$?

     Antwort

     Reject the null when the p-value is at most $\alpha$; otherwise fail to reject it. Failing to reject does not prove the null.

219. Karte 219

     Frage

     Can proprietary methods from a former employer be reused freely?

     Antwort

     Only if you have the legal right or permission to use them. General skill and experience may transfer; confidential proprietary material does not.

220. Karte 220

     Frage

     Pound-force to newtons?

     Antwort

     $1\,lbf\approx4.44822\,N$. Use more digits only when the required precision justifies them.

221. Karte 221

     Frage

     When does a definite integral equal ordinary geometric area?

     Antwort

     When the integrand is nonnegative over the interval. If it changes sign, the integral is signed area; integrate the absolute value or split the interval for total area.

222. Karte 222

     Frage

     Charge-voltage relation for an ideal capacitor?

     Antwort

     $$q=CV$$

     $C$ is capacitance in farads; $V$ is the voltage across the capacitor under the chosen polarity.

223. Karte 223

     Frage

     Searching for a material or fluid property: what qualifiers often matter?

     Antwort

     Material identity, phase, temperature, pressure, and composition. Use only the qualifiers relevant to that property source.

224. Karte 224

     Frage

     Force produced when one slug accelerates at $1\,ft/s^2$?

     Antwort

     $1\,lbf$. Equivalently, $1\,lbf=1\,slug\cdot ft/s^2$.

225. Karte 225

     Frage

     Relationship among nominal rate $i$, real rate $r$, and inflation $f$?

     Antwort

     $$1+i=(1+r)(1+f)$$

     Keep cash-flow dollars and discount rates on the same real-or-nominal basis.

226. Karte 226

     Frage

     Antiderivative of $x^n$ for $n\ne-1$?

     Antwort

     $$\int x^n\,dx=\frac{x^{n+1}}{n+1}+C$$

227. Karte 227

     Frage

     Time constant of a first-order resistor-capacitor circuit?

     Antwort

     $$\tau=RC$$

     Use the resistance seen by the capacitor in the applicable first-order linear circuit.

228. Karte 228

     Frage

     What physical quantity does pound-mass measure?

     Antwort

     Mass. Do not substitute $lbm$ directly where a force unit such as $lbf$ is required.

229. Karte 229

     Frage

     Type I error?

     Antwort

     Rejecting a true null hypothesis. Its probability is controlled by the chosen significance level under the test assumptions.

230. Karte 230

     Frage

     A search hit contains the right words. Is that enough?

     Antwort

     No. Read the surrounding definition, equation label, units, and notes to confirm the hit answers the actual question.

231. Karte 231

     Frage

     Annual straight-line depreciation from basis $B$ to salvage $S$ over $n$ years?

     Antwort

     $$D=\frac{B-S}{n}$$

     This is an accounting allocation, not a market-value forecast.

232. Karte 232

     Frage

     Purpose of $g_c$ in some US customary force-mass equations?

     Antwort

     It reconciles chosen $lbm$, $lbf$, foot, and second units. Include it only when the equation and unit convention require it; coherent SI equations do not use it.

233. Karte 233

     Frage

     Recognizable form of a separable first-order differential equation?

     Antwort

     $$\frac{dy}{dx}=g(x)h(y)$$

     Rearrange to place the $y$ terms with $dy$ and the $x$ terms with $dx$, while checking for solutions lost by division.

234. Karte 234

     Frage

     Using unverified software output in a safety-relevant calculation?

     Antwort

     Check inputs, assumptions, units, and results with an independent method appropriate to the risk. The engineer remains responsible for professional judgment.

235. Karte 235

     Frage

     Equivalent resistance of ideal resistors in series?

     Antwort

     $$R_{eq}=\sum_i R_i$$

     Series elements carry the same current with no branching node between them.

236. Karte 236

     Frage

     Pressure conversion from psi to pascals?

     Antwort

     $1\,psi\approx6894.76\,Pa$. Keep enough significant figures for the problem's data.

237. Karte 237

     Frage

     Type II error?

     Antwort

     Failing to reject a false null hypothesis. Its probability is $\beta$ for a specified alternative.

238. Karte 238

     Frage

     Useful flashcard to make after a failed handbook search?

     Antwort

     A short scenario-to-search-cue card recording the section name and terms that eventually worked—not a copied problem or page number.

239. Karte 239

     Frage

     Standard form of a first-order linear differential equation?

     Antwort

     $$\frac{dy}{dx}+P(x)y=Q(x)$$

     An integrating factor is $e^{\int P(x)\,dx}$.

240. Karte 240

     Frage

     Equivalent resistance of ideal resistors in parallel?

     Antwort

     $$\frac{1}{R_{eq}}=\sum_i\frac{1}{R_i}$$

     Parallel elements share the same two nodes and therefore the same voltage.

241. Karte 241

     Frage

     Book value after $k$ years of straight-line depreciation?

     Antwort

     $$BV_k=B-kD$$

     Apply it within the depreciable life and do not depreciate below the assumed salvage value.

242. Karte 242

     Frage

     Standard atmosphere in pascals?

     Antwort

     $1\,atm=101{,}325\,Pa$ exactly.

243. Karte 243

     Frage

     Using AI-generated technical content in engineering work?

     Antwort

     Treat it as unverified input: protect confidential data, check sources and calculations, disclose use when required, and keep accountable human review.

244. Karte 244

     Frage

     Trial form for a homogeneous linear ODE with constant coefficients?

     Antwort

     Use $y=e^{rx}$ to obtain the characteristic polynomial in $r$. Repeated or complex roots require the corresponding standard solution forms.

245. Karte 245

     Frage

     Wave-speed relationship among frequency and wavelength?

     Antwort

     $$v=f\lambda$$

     Use frequency in cycles per second and wavelength in compatible length units.

246. Karte 246

     Frage

     Statistical power?

     Antwort

     The probability of rejecting the null when a specified alternative is true: $1-\beta$. Larger effects, larger samples, or lower variability commonly increase power.

247. Karte 247

     Frage

     Bar in pascals?

     Antwort

     $1\,bar=100{,}000\,Pa$ exactly.

248. Karte 248

     Frage

     How should handbook navigation be practiced before the FE exam?

     Antwort

     Use the current handbook from MyNCEES while solving original or properly licensed practice problems, and rehearse the exact search terms that find definitions and assumptions.

249. Karte 249

     Frage

     Is depreciation itself a cash outflow?

     Antwort

     No. It is a noncash accounting expense, though it can affect taxes and therefore after-tax cash flow.

250. Karte 250

     Frage

     First-order linear approximation of $f(x)$ near $x=a$?

     Antwort

     $$f(x)\approx f(a)+f'(a)(x-a)$$

     It is most accurate for $x$ close to $a$ when higher derivatives stay bounded.

251. Karte 251

     Frage

     Relationship between period and frequency?

     Antwort

     $$T=\frac{1}{f}$$

     This requires $f>0$; $T$ has time units.

252. Karte 252

     Frage

     How should foreseeable environmental harm enter an engineering decision?

     Antwort

     Identify and communicate it, follow applicable requirements, and consider practicable ways to reduce harm without compromising public safety.

253. Karte 253

     Frage

     Foot-pound-force in joules?

     Antwort

     $1\,ft\cdot lbf\approx1.35582\,J$. This is a work or energy conversion; keep torque labeled as force times distance even though its dimensions match energy.

254. Karte 254

     Frage

     Allowed range and sign meaning of Pearson correlation $r$?

     Antwort

     $-1\le r\le1$. The sign gives the direction of linear association, and magnitude measures its linear strength.

255. Karte 255

     Frage

     When should you search instead of relying on recall?

     Antwort

     Search when a constant, coefficient, convention, specialized relationship, or applicability detail could change the result. Recall can start the route; the reference should confirm details.

256. Karte 256

     Frage

     After-tax effect of a deductible expense $E$ at marginal tax rate $t$?

     Antwort

     The net cost is $E(1-t)$ under the simplified assumption that the deduction can be used fully in that period.

257. Karte 257

     Frage

     Centered finite-difference approximation to $f'(x)$?

     Antwort

     $$f'(x)\approx\frac{f(x+h)-f(x-h)}{2h}$$

     For smooth $f$, truncation error is proportional to $h^2$ before roundoff dominates.

258. Karte 258

     Frage

     General material balance on a control volume?

     Antwort

     $$\text{accumulation}=\text{in}-\text{out}+\text{generation}-\text{consumption}$$

     At steady state, accumulation is zero; generation and consumption depend on reactions or sources.

259. Karte 259

     Frage

     Approximate joules in one International Table Btu?

     Antwort

     $1\,Btu_{IT}\approx1055.06\,J$. Identify the Btu convention when precision matters.

260. Karte 260

     Frage

     What is the defender in a replacement analysis?

     Antwort

     The currently owned asset being compared with a proposed replacement. Its current market value is an opportunity cost; its original purchase price is sunk.

261. Karte 261

     Frage

     Speaking publicly about a technical matter outside your expertise?

     Antwort

     Limit claims to what you can support, identify the boundary of your expertise, and avoid implying qualifications you do not have.

262. Karte 262

     Frage

     Single-interval trapezoidal approximation to an integral?

     Antwort

     $$\int_a^b f(x)\,dx\approx\frac{b-a}{2}[f(a)+f(b)]$$

     It is exact for linear $f$.

263. Karte 263

     Frage

     Energy efficiency of a device?

     Antwort

     $$\eta=\frac{\text{useful output energy}}{\text{input energy}}$$

     Use the same energy basis in numerator and denominator; a real passive device has $0\le\eta\le1$.

264. Karte 264

     Frage

     Purpose of sensitivity analysis in engineering economics?

     Antwort

     It shows how the decision changes when an uncertain input changes. Vary inputs over plausible ranges while preserving units and model relationships.

265. Karte 265

     Frage

     Can a strong correlation establish causation?

     Antwort

     No. Correlation alone cannot rule out confounding, reverse direction, selection effects, or coincidence.

266. Karte 266

     Frage

     Where should you confirm the tested topics for your FE discipline?

     Antwort

     Use the discipline specification linked from the official NCEES FE exam hub. This common deck does not replace that discipline-specific boundary.

267. Karte 267

     Frage

     Mechanical horsepower in watts?

     Antwort

     $1\,hp\approx745.7\,W$, based on $550\,ft\cdot lbf/s$. Distinguish it from metric horsepower.

268. Karte 268

     Frage

     Combine independent standard uncertainties $u_1,\ldots,u_n$ in a sum or difference?

     Antwort

     $$u_c=\sqrt{u_1^2+u_2^2+\cdots+u_n^2}$$

     This root-sum-square form assumes uncorrelated inputs and coefficients of magnitude one; otherwise include sensitivities and covariance.

269. Karte 269

     Frage

     Newton iteration for a root of $f(x)=0$?

     Antwort

     $$x_{k+1}=x_k-\frac{f(x_k)}{f'(x_k)}$$

     It requires $f'(x_k)\ne0$ and a suitable starting value; convergence is not guaranteed.

270. Karte 270

     Frage

     Meaning of slope in simple linear regression of $y$ on $x$?

     Antwort

     It is the estimated change in mean response $y$ for a one-unit increase in $x$, under the fitted linear model. Its units are $y$ units per $x$ unit.

271. Karte 271

     Frage

     Kilowatt-hour in joules?

     Antwort

     $1\,kW\cdot h=3.6\times10^6\,J$. It is energy, not power.

272. Karte 272

     Frage

     Percent error relative to an accepted nonzero value?

     Antwort

     $$\%\,error=\left|\frac{x_{measured}-x_{accepted}}{x_{accepted}}\right|100\%$$

     The accepted value must be nonzero and both values must use compatible units.

273. Karte 273

     Frage

     Does legal compliance alone settle an engineering ethics question?

     Antwort

     No. Law sets mandatory boundaries, while professional duties can require stronger action, especially when safety, honesty, or conflicts are involved.

274. Karte 274

     Frage

     Does handbook fluency replace discipline-specific problem practice?

     Antwort

     No. Pair navigation and common recall with the current discipline specification and timed, rights-safe problems that match your selected FE discipline.

275. Karte 275

     Frage

     Linear interpolation between $(x_1,y_1)$ and $(x_2,y_2)$?

     Antwort

     $$y\approx y_1+(y_2-y_1)\frac{x-x_1}{x_2-x_1}$$

     Use it between distinct $x$ values when local linear behavior is reasonable.

276. Karte 276

     Frage

     Dimensional requirement for a physically meaningful additive equation?

     Antwort

     Every term being added or equated must have the same dimensions. A dimensionally consistent equation can still be physically wrong, but an inconsistent one is wrong.