FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

Targetes d'aquesta baralla

1. Targeta 1

   Pregunta

   SI base unit of length?

   Resposta

   The metre, symbol $m$.

2. Targeta 2

   Pregunta

   Slope between two points?

   Resposta

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

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

3. Targeta 3

   Pregunta

   Net force relationship for constant mass in an inertial frame?

   Resposta

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

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

4. Targeta 4

   Pregunta

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

   Resposta

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

5. Targeta 5

   Pregunta

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

   Resposta

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

6. Targeta 6

   Pregunta

   Probability of the complement of event $A$?

   Resposta

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

7. Targeta 7

   Pregunta

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

   Resposta

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

8. Targeta 8

   Pregunta

   SI base unit of mass?

   Resposta

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

9. Targeta 9

   Pregunta

   Linear equation from slope and intercept?

   Resposta

   $$y=mx+b$$

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

10. Targeta 10

    Pregunta

    Velocity after time $t$ under constant acceleration?

    Resposta

    $$v=v_0+at$$

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

11. Targeta 11

    Pregunta

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

    Resposta

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

12. Targeta 12

    Pregunta

    How is the FE reference handbook available during the exam?

    Resposta

    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. Targeta 13

    Pregunta

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

    Resposta

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

14. Targeta 14

    Pregunta

    SI base unit of time?

    Resposta

    The second, symbol $s$.

15. Targeta 15

    Pregunta

    Linear equation from one point and a slope?

    Resposta

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

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

16. Targeta 16

    Pregunta

    Position after time $t$ under constant acceleration?

    Resposta

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

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

17. Targeta 17

    Pregunta

    A project assignment lies outside your competence. Proper response?

    Resposta

    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. Targeta 18

    Pregunta

    SI base unit of electric current?

    Resposta

    The ampere, symbol $A$.

19. Targeta 19

    Pregunta

    Future amount under simple interest?

    Resposta

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

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

20. Targeta 20

    Pregunta

    Distance between two Cartesian points?

    Resposta

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

    The coordinate components must use the same length unit.

21. Targeta 21

    Pregunta

    Constant-acceleration relation without elapsed time?

    Resposta

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

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

22. Targeta 22

    Pregunta

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

    Resposta

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

23. Targeta 23

    Pregunta

    Conditional probability of $A$ given $B$?

    Resposta

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

    This requires $P(B)>0$.

24. Targeta 24

    Pregunta

    SI base unit of thermodynamic temperature?

    Resposta

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

25. Targeta 25

    Pregunta

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

    Resposta

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

26. Targeta 26

    Pregunta

    Midpoint of two Cartesian points?

    Resposta

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

    Average corresponding coordinates.

27. Targeta 27

    Pregunta

    Linear momentum of a particle?

    Resposta

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

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

28. Targeta 28

    Pregunta

    Future amount under compound interest?

    Resposta

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

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

29. Targeta 29

    Pregunta

    Should an FE search workflow depend on Ctrl+F?

    Resposta

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

30. Targeta 30

    Pregunta

    SI base unit of amount of substance?

    Resposta

    The mole, symbol $mol$.

31. Targeta 31

    Pregunta

    Joint probability expressed with a conditional probability?

    Resposta

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

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

32. Targeta 32

    Pregunta

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

    Resposta

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

    The coordinate units and radius unit must match.

33. Targeta 33

    Pregunta

    Impulse-momentum relationship?

    Resposta

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

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

34. Targeta 34

    Pregunta

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

    Resposta

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

35. Targeta 35

    Pregunta

    SI base unit of luminous intensity?

    Resposta

    The candela, symbol $cd$.

36. Targeta 36

    Pregunta

    Present worth of one future amount?

    Resposta

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

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

37. Targeta 37

    Pregunta

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

    Resposta

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

    This form requires $a\ne0$.

38. Targeta 38

    Pregunta

    When is total linear momentum conserved?

    Resposta

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

39. Targeta 39

    Pregunta

    Why avoid memorizing FE handbook page numbers?

    Resposta

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

40. Targeta 40

    Pregunta

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

    Resposta

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

    Independence is not the same as mutual exclusivity.

41. Targeta 41

    Pregunta

    SI unit of frequency in base-unit form?

    Resposta

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

42. Targeta 42

    Pregunta

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

    Resposta

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

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

43. Targeta 43

    Pregunta

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

    Resposta

    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. Targeta 44

    Pregunta

    Work done by a constant force through displacement?

    Resposta

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

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

45. Targeta 45

    Pregunta

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

    Resposta

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

46. Targeta 46

    Pregunta

    SI unit of force in base-unit form?

    Resposta

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

47. Targeta 47

    Pregunta

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

    Resposta

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

48. Targeta 48

    Pregunta

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

    Resposta

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

    This requires $P(B)>0$.

49. Targeta 49

    Pregunta

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

    Resposta

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

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

50. Targeta 50

    Pregunta

    Translational kinetic energy of a particle?

    Resposta

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

    Mass and speed must use a coherent unit system.

51. Targeta 51

    Pregunta

    SI unit of pressure in force-area form?

    Resposta

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

52. Targeta 52

    Pregunta

    Equivalent annual amount for present worth $P$?

    Resposta

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

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

53. Targeta 53

    Pregunta

    May confidential client information be shared for personal benefit?

    Resposta

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

54. Targeta 54

    Pregunta

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

    Resposta

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

55. Targeta 55

    Pregunta

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

    Resposta

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

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

56. Targeta 56

    Pregunta

    Net work-energy relationship for a particle?

    Resposta

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

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

57. Targeta 57

    Pregunta

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

    Resposta

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

    Use this when order matters and selection is without replacement.

58. Targeta 58

    Pregunta

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

    Resposta

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

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

59. Targeta 59

    Pregunta

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

    Resposta

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

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

60. Targeta 60

    Pregunta

    SI unit of energy in force-distance form?

    Resposta

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

61. Targeta 61

    Pregunta

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

    Resposta

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

62. Targeta 62

    Pregunta

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

    Resposta

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

63. Targeta 63

    Pregunta

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

    Resposta

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

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

64. Targeta 64

    Pregunta

    Change in gravitational potential energy near Earth's surface?

    Resposta

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

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

65. Targeta 65

    Pregunta

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

    Resposta

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

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

66. Targeta 66

    Pregunta

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

    Resposta

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

    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. Targeta 67

    Pregunta

    A handbook search for an acronym fails. Next move?

    Resposta

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

68. Targeta 68

    Pregunta

    SI unit of power in energy-time form?

    Resposta

    The watt, $W=J/s$.

69. Targeta 69

    Pregunta

    Logarithm of a product?

    Resposta

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

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

70. Targeta 70

    Pregunta

    Conditions for a binomial model?

    Resposta

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

71. Targeta 71

    Pregunta

    Using another engineer's analysis in your deliverable?

    Resposta

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

72. Targeta 72

    Pregunta

    SI unit of electric charge in current-time form?

    Resposta

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

73. Targeta 73

    Pregunta

    Average power from work over elapsed time?

    Resposta

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

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

74. Targeta 74

    Pregunta

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

    Resposta

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

    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. Targeta 75

    Pregunta

    Logarithm of a positive quantity raised to a power?

    Resposta

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

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

76. Targeta 76

    Pregunta

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

    Resposta

    The volt, $V=J/C$.

77. Targeta 77

    Pregunta

    Instantaneous mechanical power delivered by a force?

    Resposta

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

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

78. Targeta 78

    Pregunta

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

    Resposta

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

79. Targeta 79

    Pregunta

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

    Resposta

    $$E[X]=np$$

80. Targeta 80

    Pregunta

    SI unit of electrical resistance in voltage-current form?

    Resposta

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

81. Targeta 81

    Pregunta

    Moment of a force about a point?

    Resposta

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

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

82. Targeta 82

    Pregunta

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

    Resposta

    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. Targeta 83

    Pregunta

    Inverse relationship between the natural log and exponential?

    Resposta

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

    The second identity requires $x>0$.

84. Targeta 84

    Pregunta

    SI prefix giga?

    Resposta

    $G=10^9$.

85. Targeta 85

    Pregunta

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

    Resposta

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

    Use consistent angular sign convention and radians for angular measures.

86. Targeta 86

    Pregunta

    When should an engineer sign or seal technical work?

    Resposta

    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. Targeta 87

    Pregunta

    Best memory target for returning to a handbook formula?

    Resposta

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

88. Targeta 88

    Pregunta

    SI prefix mega?

    Resposta

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

89. Targeta 89

    Pregunta

    Convert degrees to radians?

    Resposta

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

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

90. Targeta 90

    Pregunta

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

    Resposta

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

91. Targeta 91

    Pregunta

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

    Resposta

    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. Targeta 92

    Pregunta

    Where do licensure and sealing requirements come from?

    Resposta

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

93. Targeta 93

    Pregunta

    Rotational kinetic energy about a fixed axis?

    Resposta

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

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

94. Targeta 94

    Pregunta

    SI prefix kilo?

    Resposta

    $k=10^3$.

95. Targeta 95

    Pregunta

    Right-triangle definition of sine?

    Resposta

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

96. Targeta 96

    Pregunta

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

    Resposta

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

97. Targeta 97

    Pregunta

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

    Resposta

    $$\sum M=I\alpha$$

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

98. Targeta 98

    Pregunta

    SI prefix milli?

    Resposta

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

99. Targeta 99

    Pregunta

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

    Resposta

    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. Targeta 100

     Pregunta

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

     Resposta

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

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

101. Targeta 101

     Pregunta

     Right-triangle definition of cosine?

     Resposta

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

102. Targeta 102

     Pregunta

     Force-displacement relation for an ideal linear spring?

     Resposta

     $$F=-kx$$

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

103. Targeta 103

     Pregunta

     May qualifications or project responsibility be exaggerated in a proposal?

     Resposta

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

104. Targeta 104

     Pregunta

     SI prefix micro?

     Resposta

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

105. Targeta 105

     Pregunta

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

     Resposta

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

106. Targeta 106

     Pregunta

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

     Resposta

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

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

107. Targeta 107

     Pregunta

     Right-triangle definition of tangent?

     Resposta

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

108. Targeta 108

     Pregunta

     Average normal stress under centered axial load?

     Resposta

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

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

109. Targeta 109

     Pregunta

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

     Resposta

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

110. Targeta 110

     Pregunta

     SI prefix nano?

     Resposta

     $n=10^{-9}$.

111. Targeta 111

     Pregunta

     Fundamental Pythagorean trigonometric identity?

     Resposta

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

112. Targeta 112

     Pregunta

     Engineering normal strain?

     Resposta

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

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

113. Targeta 113

     Pregunta

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

     Resposta

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

114. Targeta 114

     Pregunta

     Technical duty to an employer or client?

     Resposta

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

115. Targeta 115

     Pregunta

     How does a length conversion factor apply to area?

     Resposta

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

116. Targeta 116

     Pregunta

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

     Resposta

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

117. Targeta 117

     Pregunta

     When is a Poisson count model reasonable?

     Resposta

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

118. Targeta 118

     Pregunta

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

     Resposta

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

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

119. Targeta 119

     Pregunta

     Linear elastic stress-strain relation in uniaxial loading?

     Resposta

     $$\sigma=E\varepsilon$$

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

120. Targeta 120

     Pregunta

     How does a length conversion factor apply to volume?

     Resposta

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

121. Targeta 121

     Pregunta

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

     Resposta

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

122. Targeta 122

     Pregunta

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

     Resposta

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

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

123. Targeta 123

     Pregunta

     A supervisor directs an illegal engineering action. Proper response?

     Resposta

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

124. Targeta 124

     Pregunta

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

     Resposta

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

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

125. Targeta 125

     Pregunta

     Mass density?

     Resposta

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

     Use mass, not weight, in the numerator.

126. Targeta 126

     Pregunta

     Inches in one foot?

     Resposta

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

127. Targeta 127

     Pregunta

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

     Resposta

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

128. Targeta 128

     Pregunta

     How should subscripts be handled in a retrieved relationship?

     Resposta

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

129. Targeta 129

     Pregunta

     Dot product from vector magnitudes and included angle?

     Resposta

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

     The result is a scalar.

130. Targeta 130

     Pregunta

     Average normal pressure on an area?

     Resposta

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

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

131. Targeta 131

     Pregunta

     Feet in one yard?

     Resposta

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

132. Targeta 132

     Pregunta

     When are two interest rates equivalent?

     Resposta

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

133. Targeta 133

     Pregunta

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

     Resposta

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

134. Targeta 134

     Pregunta

     Expected value of a discrete random variable?

     Resposta

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

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

135. Targeta 135

     Pregunta

     Dot-product test for perpendicular nonzero vectors?

     Resposta

     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. Targeta 136

     Pregunta

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

     Resposta

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

     Depth increases downward and the fluid is at rest.

137. Targeta 137

     Pregunta

     Feet in one statute mile?

     Resposta

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

138. Targeta 138

     Pregunta

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

     Resposta

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

     

     276 targetes

     FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

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139. Targeta 139

     Pregunta

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

     Resposta

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

140. Targeta 140

     Pregunta

     Magnitude of a vector cross product?

     Resposta

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

     The direction follows the right-hand rule.

141. Targeta 141

     Pregunta

     Exact inch-to-metre relationship?

     Resposta

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

142. Targeta 142

     Pregunta

     Volumetric flow rate through a cross-section?

     Resposta

     $$Q=Av_{avg}$$

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

143. Targeta 143

     Pregunta

     Variance from the mean $\mu$?

     Resposta

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

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

144. Targeta 144

     Pregunta

     Future-worth acceptance rule for an independent investment?

     Resposta

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

145. Targeta 145

     Pregunta

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

     Resposta

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

146. Targeta 146

     Pregunta

     Exact foot-to-metre relationship?

     Resposta

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

147. Targeta 147

     Pregunta

     How should important uncertainty be communicated?

     Resposta

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

148. Targeta 148

     Pregunta

     When is the matrix product $AB$ defined?

     Resposta

     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. Targeta 149

     Pregunta

     Steady one-inlet, one-outlet mass continuity?

     Resposta

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     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. Targeta 150

     Pregunta

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

     Resposta

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

151. Targeta 151

     Pregunta

     Square feet in one acre?

     Resposta

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

152. Targeta 152

     Pregunta

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

     Resposta

     $$ad-bc$$

153. Targeta 153

     Pregunta

     Bernoulli relationship along a streamline for ideal steady flow?

     Resposta

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

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

154. Targeta 154

     Pregunta

     May inconvenient measurements be discarded without a technical basis?

     Resposta

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

155. Targeta 155

     Pregunta

     Annual-worth acceptance rule for an independent investment?

     Resposta

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

156. Targeta 156

     Pregunta

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

     Resposta

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

157. Targeta 157

     Pregunta

     Cubic metres in one litre?

     Resposta

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

158. Targeta 158

     Pregunta

     What does a zero determinant mean for a square matrix?

     Resposta

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

159. Targeta 159

     Pregunta

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

     Resposta

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

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

160. Targeta 160

     Pregunta

     Unbiased sample variance for an independent sample from one population?

     Resposta

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

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

161. Targeta 161

     Pregunta

     How should mutually exclusive alternatives be compared?

     Resposta

     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. Targeta 162

     Pregunta

     Cubic centimetres in one millilitre?

     Resposta

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

163. Targeta 163

     Pregunta

     Why keep contemporaneous engineering records?

     Resposta

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

164. Targeta 164

     Pregunta

     Fast check after substituting into a handbook formula?

     Resposta

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

165. Targeta 165

     Pregunta

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

     Resposta

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

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

166. Targeta 166

     Pregunta

     Sensible heat for constant specific heat and no phase change?

     Resposta

     $$Q=mc\Delta T$$

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

167. Targeta 167

     Pregunta

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

     Resposta

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

     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. Targeta 168

     Pregunta

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

     Resposta

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

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

169. Targeta 169

     Pregunta

     Purpose of incremental analysis for mutually exclusive alternatives?

     Resposta

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

170. Targeta 170

     Pregunta

     Physical meaning of $dy/dx$?

     Resposta

     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. Targeta 171

     Pregunta

     One-dimensional steady conduction through a plane wall?

     Resposta

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

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

172. Targeta 172

     Pregunta

     When should you algebraically rearrange a handbook relationship?

     Resposta

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

173. Targeta 173

     Pregunta

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

     Resposta

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

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

174. Targeta 174

     Pregunta

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

     Resposta

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

175. Targeta 175

     Pregunta

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

     Resposta

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

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

176. Targeta 176

     Pregunta

     Convective heat-transfer rate at a surface?

     Resposta

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

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

177. Targeta 177

     Pregunta

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

     Resposta

     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. Targeta 178

     Pregunta

     Internal rate of return?

     Resposta

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

179. Targeta 179

     Pregunta

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

     Resposta

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

180. Targeta 180

     Pregunta

     Convert Celsius temperature to kelvin?

     Resposta

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

     This conversion is for absolute temperature, not temperature difference.

181. Targeta 181

     Pregunta

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

     Resposta

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

182. Targeta 182

     Pregunta

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

     Resposta

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

183. Targeta 183

     Pregunta

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

     Resposta

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

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

184. Targeta 184

     Pregunta

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

     Resposta

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

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

185. Targeta 185

     Pregunta

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

     Resposta

     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. Targeta 186

     Pregunta

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

     Resposta

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

187. Targeta 187

     Pregunta

     Why inspect boundary or initial conditions near a formula?

     Resposta

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

188. Targeta 188

     Pregunta

     Convert Celsius temperature to Fahrenheit?

     Resposta

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

189. Targeta 189

     Pregunta

     Ethical basis for expert technical testimony?

     Resposta

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

190. Targeta 190

     Pregunta

     Meaning of a breakeven value?

     Resposta

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

191. Targeta 191

     Pregunta

     Derivative of $e^x$?

     Resposta

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

192. Targeta 192

     Pregunta

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

     Resposta

     $$\Delta E=Q-W$$

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

193. Targeta 193

     Pregunta

     Frequentist meaning of a 95% confidence procedure?

     Resposta

     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. Targeta 194

     Pregunta

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

     Resposta

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

195. Targeta 195

     Pregunta

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

     Resposta

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

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

196. Targeta 196

     Pregunta

     Relationship between Celsius and kelvin temperature differences?

     Resposta

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

197. Targeta 197

     Pregunta

     How should credit for team engineering work be assigned?

     Resposta

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

198. Targeta 198

     Pregunta

     Main limitation of simple payback period?

     Resposta

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

199. Targeta 199

     Pregunta

     Roles of the null and alternative hypotheses?

     Resposta

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

200. Targeta 200

     Pregunta

     Ideal-gas equation of state?

     Resposta

     $$pV=nRT$$

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

201. Targeta 201

     Pregunta

     First check when reading a handbook table?

     Resposta

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

202. Targeta 202

     Pregunta

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

     Resposta

     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. Targeta 203

     Pregunta

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

     Resposta

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

204. Targeta 204

     Pregunta

     Convert Fahrenheit absolute temperature to Rankine?

     Resposta

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

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. Targeta 205

     Pregunta

     Ohm's law for an ideal resistor?

     Resposta

     $$V=IR$$

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

206. Targeta 206

     Pregunta

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

     Resposta

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

207. Targeta 207

     Pregunta

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

     Resposta

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

208. Targeta 208

     Pregunta

     Is a radian dimensionless?

     Resposta

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

209. Targeta 209

     Pregunta

     Electrical power absorbed under the passive sign convention?

     Resposta

     $$P=VI$$

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

210. Targeta 210

     Pregunta

     Meaning of a p-value?

     Resposta

     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. Targeta 211

     Pregunta

     First check when reading a handbook graph?

     Resposta

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

212. Targeta 212

     Pregunta

     Difference between mass and weight?

     Resposta

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

213. Targeta 213

     Pregunta

     Kirchhoff's current law at a node?

     Resposta

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

214. Targeta 214

     Pregunta

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

     Resposta

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

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

215. Targeta 215

     Pregunta

     Opportunity cost?

     Resposta

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

216. Targeta 216

     Pregunta

     Weight from mass in a gravitational field?

     Resposta

     $$W=mg$$

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

217. Targeta 217

     Pregunta

     Kirchhoff's voltage law around a closed loop?

     Resposta

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

218. Targeta 218

     Pregunta

     Decision rule using significance level $\alpha$?

     Resposta

     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. Targeta 219

     Pregunta

     Can proprietary methods from a former employer be reused freely?

     Resposta

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

220. Targeta 220

     Pregunta

     Pound-force to newtons?

     Resposta

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

221. Targeta 221

     Pregunta

     When does a definite integral equal ordinary geometric area?

     Resposta

     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. Targeta 222

     Pregunta

     Charge-voltage relation for an ideal capacitor?

     Resposta

     $$q=CV$$

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

223. Targeta 223

     Pregunta

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

     Resposta

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

224. Targeta 224

     Pregunta

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

     Resposta

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

225. Targeta 225

     Pregunta

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

     Resposta

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

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

226. Targeta 226

     Pregunta

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

     Resposta

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

227. Targeta 227

     Pregunta

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

     Resposta

     $$\tau=RC$$

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

228. Targeta 228

     Pregunta

     What physical quantity does pound-mass measure?

     Resposta

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

229. Targeta 229

     Pregunta

     Type I error?

     Resposta

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

230. Targeta 230

     Pregunta

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

     Resposta

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

231. Targeta 231

     Pregunta

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

     Resposta

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

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

232. Targeta 232

     Pregunta

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

     Resposta

     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. Targeta 233

     Pregunta

     Recognizable form of a separable first-order differential equation?

     Resposta

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

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

234. Targeta 234

     Pregunta

     Using unverified software output in a safety-relevant calculation?

     Resposta

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

235. Targeta 235

     Pregunta

     Equivalent resistance of ideal resistors in series?

     Resposta

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

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

236. Targeta 236

     Pregunta

     Pressure conversion from psi to pascals?

     Resposta

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

237. Targeta 237

     Pregunta

     Type II error?

     Resposta

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

238. Targeta 238

     Pregunta

     Useful flashcard to make after a failed handbook search?

     Resposta

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

239. Targeta 239

     Pregunta

     Standard form of a first-order linear differential equation?

     Resposta

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

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

240. Targeta 240

     Pregunta

     Equivalent resistance of ideal resistors in parallel?

     Resposta

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

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

241. Targeta 241

     Pregunta

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

     Resposta

     $$BV_k=B-kD$$

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

242. Targeta 242

     Pregunta

     Standard atmosphere in pascals?

     Resposta

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

243. Targeta 243

     Pregunta

     Using AI-generated technical content in engineering work?

     Resposta

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

244. Targeta 244

     Pregunta

     Trial form for a homogeneous linear ODE with constant coefficients?

     Resposta

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

245. Targeta 245

     Pregunta

     Wave-speed relationship among frequency and wavelength?

     Resposta

     $$v=f\lambda$$

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

246. Targeta 246

     Pregunta

     Statistical power?

     Resposta

     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. Targeta 247

     Pregunta

     Bar in pascals?

     Resposta

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

248. Targeta 248

     Pregunta

     How should handbook navigation be practiced before the FE exam?

     Resposta

     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. Targeta 249

     Pregunta

     Is depreciation itself a cash outflow?

     Resposta

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

250. Targeta 250

     Pregunta

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

     Resposta

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

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

251. Targeta 251

     Pregunta

     Relationship between period and frequency?

     Resposta

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

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

252. Targeta 252

     Pregunta

     How should foreseeable environmental harm enter an engineering decision?

     Resposta

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

253. Targeta 253

     Pregunta

     Foot-pound-force in joules?

     Resposta

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

254. Targeta 254

     Pregunta

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

     Resposta

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

255. Targeta 255

     Pregunta

     When should you search instead of relying on recall?

     Resposta

     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. Targeta 256

     Pregunta

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

     Resposta

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

257. Targeta 257

     Pregunta

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

     Resposta

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

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

258. Targeta 258

     Pregunta

     General material balance on a control volume?

     Resposta

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

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

259. Targeta 259

     Pregunta

     Approximate joules in one International Table Btu?

     Resposta

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

260. Targeta 260

     Pregunta

     What is the defender in a replacement analysis?

     Resposta

     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. Targeta 261

     Pregunta

     Speaking publicly about a technical matter outside your expertise?

     Resposta

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

262. Targeta 262

     Pregunta

     Single-interval trapezoidal approximation to an integral?

     Resposta

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

     It is exact for linear $f$.

263. Targeta 263

     Pregunta

     Energy efficiency of a device?

     Resposta

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

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

264. Targeta 264

     Pregunta

     Purpose of sensitivity analysis in engineering economics?

     Resposta

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

265. Targeta 265

     Pregunta

     Can a strong correlation establish causation?

     Resposta

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

266. Targeta 266

     Pregunta

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

     Resposta

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

267. Targeta 267

     Pregunta

     Mechanical horsepower in watts?

     Resposta

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

268. Targeta 268

     Pregunta

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

     Resposta

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

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

269. Targeta 269

     Pregunta

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

     Resposta

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

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

270. Targeta 270

     Pregunta

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

     Resposta

     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. Targeta 271

     Pregunta

     Kilowatt-hour in joules?

     Resposta

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

272. Targeta 272

     Pregunta

     Percent error relative to an accepted nonzero value?

     Resposta

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

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

273. Targeta 273

     Pregunta

     Does legal compliance alone settle an engineering ethics question?

     Resposta

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

274. Targeta 274

     Pregunta

     Does handbook fluency replace discipline-specific problem practice?

     Resposta

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

275. Targeta 275

     Pregunta

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

     Resposta

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

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

276. Targeta 276

     Pregunta

     Dimensional requirement for a physically meaningful additive equation?

     Resposta

     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.