FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

Карти в това тесте

1. Карта 1

   Въпрос

   SI base unit of length?

   Отговор

   The metre, symbol $m$.

2. Карта 2

   Въпрос

   Slope between two points?

   Отговор

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

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

3. Карта 3

   Въпрос

   Net force relationship for constant mass in an inertial frame?

   Отговор

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

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

4. Карта 4

   Въпрос

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

   Отговор

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

5. Карта 5

   Въпрос

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

   Отговор

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

6. Карта 6

   Въпрос

   Probability of the complement of event $A$?

   Отговор

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

7. Карта 7

   Въпрос

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

   Отговор

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

8. Карта 8

   Въпрос

   SI base unit of mass?

   Отговор

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

9. Карта 9

   Въпрос

   Linear equation from slope and intercept?

   Отговор

   $$y=mx+b$$

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

10. Карта 10

    Въпрос

    Velocity after time $t$ under constant acceleration?

    Отговор

    $$v=v_0+at$$

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

11. Карта 11

    Въпрос

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

    Отговор

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

12. Карта 12

    Въпрос

    How is the FE reference handbook available during the exam?

    Отговор

    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. Карта 13

    Въпрос

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

    Отговор

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

14. Карта 14

    Въпрос

    SI base unit of time?

    Отговор

    The second, symbol $s$.

15. Карта 15

    Въпрос

    Linear equation from one point and a slope?

    Отговор

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

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

16. Карта 16

    Въпрос

    Position after time $t$ under constant acceleration?

    Отговор

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

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

17. Карта 17

    Въпрос

    A project assignment lies outside your competence. Proper response?

    Отговор

    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. Карта 18

    Въпрос

    SI base unit of electric current?

    Отговор

    The ampere, symbol $A$.

19. Карта 19

    Въпрос

    Future amount under simple interest?

    Отговор

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

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

20. Карта 20

    Въпрос

    Distance between two Cartesian points?

    Отговор

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

    The coordinate components must use the same length unit.

21. Карта 21

    Въпрос

    Constant-acceleration relation without elapsed time?

    Отговор

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

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

22. Карта 22

    Въпрос

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

    Отговор

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

23. Карта 23

    Въпрос

    Conditional probability of $A$ given $B$?

    Отговор

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

    This requires $P(B)>0$.

24. Карта 24

    Въпрос

    SI base unit of thermodynamic temperature?

    Отговор

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

25. Карта 25

    Въпрос

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

    Отговор

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

26. Карта 26

    Въпрос

    Midpoint of two Cartesian points?

    Отговор

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

    Average corresponding coordinates.

27. Карта 27

    Въпрос

    Linear momentum of a particle?

    Отговор

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

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

28. Карта 28

    Въпрос

    Future amount under compound interest?

    Отговор

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

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

29. Карта 29

    Въпрос

    Should an FE search workflow depend on Ctrl+F?

    Отговор

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

30. Карта 30

    Въпрос

    SI base unit of amount of substance?

    Отговор

    The mole, symbol $mol$.

31. Карта 31

    Въпрос

    Joint probability expressed with a conditional probability?

    Отговор

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

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

32. Карта 32

    Въпрос

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

    Отговор

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

    The coordinate units and radius unit must match.

33. Карта 33

    Въпрос

    Impulse-momentum relationship?

    Отговор

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

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

34. Карта 34

    Въпрос

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

    Отговор

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

35. Карта 35

    Въпрос

    SI base unit of luminous intensity?

    Отговор

    The candela, symbol $cd$.

36. Карта 36

    Въпрос

    Present worth of one future amount?

    Отговор

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

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

37. Карта 37

    Въпрос

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

    Отговор

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

    This form requires $a\ne0$.

38. Карта 38

    Въпрос

    When is total linear momentum conserved?

    Отговор

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

39. Карта 39

    Въпрос

    Why avoid memorizing FE handbook page numbers?

    Отговор

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

40. Карта 40

    Въпрос

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

    Отговор

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

    Independence is not the same as mutual exclusivity.

41. Карта 41

    Въпрос

    SI unit of frequency in base-unit form?

    Отговор

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

42. Карта 42

    Въпрос

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

    Отговор

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

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

43. Карта 43

    Въпрос

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

    Отговор

    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. Карта 44

    Въпрос

    Work done by a constant force through displacement?

    Отговор

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

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

45. Карта 45

    Въпрос

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

    Отговор

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

46. Карта 46

    Въпрос

    SI unit of force in base-unit form?

    Отговор

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

47. Карта 47

    Въпрос

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

    Отговор

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

48. Карта 48

    Въпрос

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

    Отговор

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

    This requires $P(B)>0$.

49. Карта 49

    Въпрос

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

    Отговор

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

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

50. Карта 50

    Въпрос

    Translational kinetic energy of a particle?

    Отговор

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

    Mass and speed must use a coherent unit system.

51. Карта 51

    Въпрос

    SI unit of pressure in force-area form?

    Отговор

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

52. Карта 52

    Въпрос

    Equivalent annual amount for present worth $P$?

    Отговор

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

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

53. Карта 53

    Въпрос

    May confidential client information be shared for personal benefit?

    Отговор

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

54. Карта 54

    Въпрос

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

    Отговор

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

55. Карта 55

    Въпрос

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

    Отговор

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

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

56. Карта 56

    Въпрос

    Net work-energy relationship for a particle?

    Отговор

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

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

57. Карта 57

    Въпрос

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

    Отговор

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

    Use this when order matters and selection is without replacement.

58. Карта 58

    Въпрос

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

    Отговор

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

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

59. Карта 59

    Въпрос

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

    Отговор

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

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

60. Карта 60

    Въпрос

    SI unit of energy in force-distance form?

    Отговор

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

61. Карта 61

    Въпрос

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

    Отговор

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

62. Карта 62

    Въпрос

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

    Отговор

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

63. Карта 63

    Въпрос

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

    Отговор

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

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

64. Карта 64

    Въпрос

    Change in gravitational potential energy near Earth's surface?

    Отговор

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

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

65. Карта 65

    Въпрос

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

    Отговор

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

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

66. Карта 66

    Въпрос

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

    Отговор

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

    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. Карта 67

    Въпрос

    A handbook search for an acronym fails. Next move?

    Отговор

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

68. Карта 68

    Въпрос

    SI unit of power in energy-time form?

    Отговор

    The watt, $W=J/s$.

69. Карта 69

    Въпрос

    Logarithm of a product?

    Отговор

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

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

70. Карта 70

    Въпрос

    Conditions for a binomial model?

    Отговор

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

71. Карта 71

    Въпрос

    Using another engineer's analysis in your deliverable?

    Отговор

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

72. Карта 72

    Въпрос

    SI unit of electric charge in current-time form?

    Отговор

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

73. Карта 73

    Въпрос

    Average power from work over elapsed time?

    Отговор

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

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

74. Карта 74

    Въпрос

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

    Отговор

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

    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. Карта 75

    Въпрос

    Logarithm of a positive quantity raised to a power?

    Отговор

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

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

76. Карта 76

    Въпрос

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

    Отговор

    The volt, $V=J/C$.

77. Карта 77

    Въпрос

    Instantaneous mechanical power delivered by a force?

    Отговор

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

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

78. Карта 78

    Въпрос

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

    Отговор

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

79. Карта 79

    Въпрос

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

    Отговор

    $$E[X]=np$$

80. Карта 80

    Въпрос

    SI unit of electrical resistance in voltage-current form?

    Отговор

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

81. Карта 81

    Въпрос

    Moment of a force about a point?

    Отговор

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

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

82. Карта 82

    Въпрос

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

    Отговор

    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. Карта 83

    Въпрос

    Inverse relationship between the natural log and exponential?

    Отговор

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

    The second identity requires $x>0$.

84. Карта 84

    Въпрос

    SI prefix giga?

    Отговор

    $G=10^9$.

85. Карта 85

    Въпрос

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

    Отговор

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

    Use consistent angular sign convention and radians for angular measures.

86. Карта 86

    Въпрос

    When should an engineer sign or seal technical work?

    Отговор

    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. Карта 87

    Въпрос

    Best memory target for returning to a handbook formula?

    Отговор

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

88. Карта 88

    Въпрос

    SI prefix mega?

    Отговор

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

89. Карта 89

    Въпрос

    Convert degrees to radians?

    Отговор

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

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

90. Карта 90

    Въпрос

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

    Отговор

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

91. Карта 91

    Въпрос

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

    Отговор

    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. Карта 92

    Въпрос

    Where do licensure and sealing requirements come from?

    Отговор

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

93. Карта 93

    Въпрос

    Rotational kinetic energy about a fixed axis?

    Отговор

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

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

94. Карта 94

    Въпрос

    SI prefix kilo?

    Отговор

    $k=10^3$.

95. Карта 95

    Въпрос

    Right-triangle definition of sine?

    Отговор

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

96. Карта 96

    Въпрос

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

    Отговор

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

97. Карта 97

    Въпрос

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

    Отговор

    $$\sum M=I\alpha$$

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

98. Карта 98

    Въпрос

    SI prefix milli?

    Отговор

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

99. Карта 99

    Въпрос

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

    Отговор

    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. Карта 100

     Въпрос

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

     Отговор

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

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

101. Карта 101

     Въпрос

     Right-triangle definition of cosine?

     Отговор

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

102. Карта 102

     Въпрос

     Force-displacement relation for an ideal linear spring?

     Отговор

     $$F=-kx$$

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

103. Карта 103

     Въпрос

     May qualifications or project responsibility be exaggerated in a proposal?

     Отговор

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

104. Карта 104

     Въпрос

     SI prefix micro?

     Отговор

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

105. Карта 105

     Въпрос

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

     Отговор

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

106. Карта 106

     Въпрос

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

     Отговор

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

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

107. Карта 107

     Въпрос

     Right-triangle definition of tangent?

     Отговор

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

108. Карта 108

     Въпрос

     Average normal stress under centered axial load?

     Отговор

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

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

109. Карта 109

     Въпрос

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

     Отговор

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

110. Карта 110

     Въпрос

     SI prefix nano?

     Отговор

     $n=10^{-9}$.

111. Карта 111

     Въпрос

     Fundamental Pythagorean trigonometric identity?

     Отговор

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

112. Карта 112

     Въпрос

     Engineering normal strain?

     Отговор

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

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

113. Карта 113

     Въпрос

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

     Отговор

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

114. Карта 114

     Въпрос

     Technical duty to an employer or client?

     Отговор

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

115. Карта 115

     Въпрос

     How does a length conversion factor apply to area?

     Отговор

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

116. Карта 116

     Въпрос

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

     Отговор

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

117. Карта 117

     Въпрос

     When is a Poisson count model reasonable?

     Отговор

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

118. Карта 118

     Въпрос

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

     Отговор

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

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

119. Карта 119

     Въпрос

     Linear elastic stress-strain relation in uniaxial loading?

     Отговор

     $$\sigma=E\varepsilon$$

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

120. Карта 120

     Въпрос

     How does a length conversion factor apply to volume?

     Отговор

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

121. Карта 121

     Въпрос

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

     Отговор

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

122. Карта 122

     Въпрос

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

     Отговор

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

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

123. Карта 123

     Въпрос

     A supervisor directs an illegal engineering action. Proper response?

     Отговор

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

124. Карта 124

     Въпрос

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

     Отговор

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

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

125. Карта 125

     Въпрос

     Mass density?

     Отговор

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

     Use mass, not weight, in the numerator.

126. Карта 126

     Въпрос

     Inches in one foot?

     Отговор

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

127. Карта 127

     Въпрос

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

     Отговор

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

128. Карта 128

     Въпрос

     How should subscripts be handled in a retrieved relationship?

     Отговор

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

129. Карта 129

     Въпрос

     Dot product from vector magnitudes and included angle?

     Отговор

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

     The result is a scalar.

130. Карта 130

     Въпрос

     Average normal pressure on an area?

     Отговор

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

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

131. Карта 131

     Въпрос

     Feet in one yard?

     Отговор

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

132. Карта 132

     Въпрос

     When are two interest rates equivalent?

     Отговор

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

133. Карта 133

     Въпрос

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

     Отговор

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

134. Карта 134

     Въпрос

     Expected value of a discrete random variable?

     Отговор

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

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

135. Карта 135

     Въпрос

     Dot-product test for perpendicular nonzero vectors?

     Отговор

     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. Карта 136

     Въпрос

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

     Отговор

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

     Depth increases downward and the fluid is at rest.

137. Карта 137

     Въпрос

     Feet in one statute mile?

     Отговор

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

138. Карта 138

     Въпрос

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

     Отговор

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

     

     276 карти

     FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

     Учете с това тесте безплатно

     Nibomo се отваря, за да започнете да учите.

139. Карта 139

     Въпрос

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

     Отговор

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

140. Карта 140

     Въпрос

     Magnitude of a vector cross product?

     Отговор

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

     The direction follows the right-hand rule.

141. Карта 141

     Въпрос

     Exact inch-to-metre relationship?

     Отговор

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

142. Карта 142

     Въпрос

     Volumetric flow rate through a cross-section?

     Отговор

     $$Q=Av_{avg}$$

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

143. Карта 143

     Въпрос

     Variance from the mean $\mu$?

     Отговор

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

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

144. Карта 144

     Въпрос

     Future-worth acceptance rule for an independent investment?

     Отговор

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

145. Карта 145

     Въпрос

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

     Отговор

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

146. Карта 146

     Въпрос

     Exact foot-to-metre relationship?

     Отговор

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

147. Карта 147

     Въпрос

     How should important uncertainty be communicated?

     Отговор

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

148. Карта 148

     Въпрос

     When is the matrix product $AB$ defined?

     Отговор

     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. Карта 149

     Въпрос

     Steady one-inlet, one-outlet mass continuity?

     Отговор

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     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. Карта 150

     Въпрос

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

     Отговор

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

151. Карта 151

     Въпрос

     Square feet in one acre?

     Отговор

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

152. Карта 152

     Въпрос

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

     Отговор

     $$ad-bc$$

153. Карта 153

     Въпрос

     Bernoulli relationship along a streamline for ideal steady flow?

     Отговор

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

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

154. Карта 154

     Въпрос

     May inconvenient measurements be discarded without a technical basis?

     Отговор

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

155. Карта 155

     Въпрос

     Annual-worth acceptance rule for an independent investment?

     Отговор

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

156. Карта 156

     Въпрос

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

     Отговор

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

157. Карта 157

     Въпрос

     Cubic metres in one litre?

     Отговор

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

158. Карта 158

     Въпрос

     What does a zero determinant mean for a square matrix?

     Отговор

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

159. Карта 159

     Въпрос

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

     Отговор

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

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

160. Карта 160

     Въпрос

     Unbiased sample variance for an independent sample from one population?

     Отговор

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

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

161. Карта 161

     Въпрос

     How should mutually exclusive alternatives be compared?

     Отговор

     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. Карта 162

     Въпрос

     Cubic centimetres in one millilitre?

     Отговор

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

163. Карта 163

     Въпрос

     Why keep contemporaneous engineering records?

     Отговор

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

164. Карта 164

     Въпрос

     Fast check after substituting into a handbook formula?

     Отговор

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

165. Карта 165

     Въпрос

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

     Отговор

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

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

166. Карта 166

     Въпрос

     Sensible heat for constant specific heat and no phase change?

     Отговор

     $$Q=mc\Delta T$$

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

167. Карта 167

     Въпрос

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

     Отговор

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

     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. Карта 168

     Въпрос

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

     Отговор

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

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

169. Карта 169

     Въпрос

     Purpose of incremental analysis for mutually exclusive alternatives?

     Отговор

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

170. Карта 170

     Въпрос

     Physical meaning of $dy/dx$?

     Отговор

     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. Карта 171

     Въпрос

     One-dimensional steady conduction through a plane wall?

     Отговор

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

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

172. Карта 172

     Въпрос

     When should you algebraically rearrange a handbook relationship?

     Отговор

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

173. Карта 173

     Въпрос

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

     Отговор

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

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

174. Карта 174

     Въпрос

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

     Отговор

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

175. Карта 175

     Въпрос

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

     Отговор

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

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

176. Карта 176

     Въпрос

     Convective heat-transfer rate at a surface?

     Отговор

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

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

177. Карта 177

     Въпрос

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

     Отговор

     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. Карта 178

     Въпрос

     Internal rate of return?

     Отговор

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

179. Карта 179

     Въпрос

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

     Отговор

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

180. Карта 180

     Въпрос

     Convert Celsius temperature to kelvin?

     Отговор

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

     This conversion is for absolute temperature, not temperature difference.

181. Карта 181

     Въпрос

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

     Отговор

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

182. Карта 182

     Въпрос

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

     Отговор

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

183. Карта 183

     Въпрос

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

     Отговор

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

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

184. Карта 184

     Въпрос

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

     Отговор

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

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

185. Карта 185

     Въпрос

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

     Отговор

     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. Карта 186

     Въпрос

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

     Отговор

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

187. Карта 187

     Въпрос

     Why inspect boundary or initial conditions near a formula?

     Отговор

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

188. Карта 188

     Въпрос

     Convert Celsius temperature to Fahrenheit?

     Отговор

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

189. Карта 189

     Въпрос

     Ethical basis for expert technical testimony?

     Отговор

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

190. Карта 190

     Въпрос

     Meaning of a breakeven value?

     Отговор

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

191. Карта 191

     Въпрос

     Derivative of $e^x$?

     Отговор

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

192. Карта 192

     Въпрос

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

     Отговор

     $$\Delta E=Q-W$$

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

193. Карта 193

     Въпрос

     Frequentist meaning of a 95% confidence procedure?

     Отговор

     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. Карта 194

     Въпрос

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

     Отговор

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

195. Карта 195

     Въпрос

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

     Отговор

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

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

196. Карта 196

     Въпрос

     Relationship between Celsius and kelvin temperature differences?

     Отговор

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

197. Карта 197

     Въпрос

     How should credit for team engineering work be assigned?

     Отговор

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

198. Карта 198

     Въпрос

     Main limitation of simple payback period?

     Отговор

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

199. Карта 199

     Въпрос

     Roles of the null and alternative hypotheses?

     Отговор

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

200. Карта 200

     Въпрос

     Ideal-gas equation of state?

     Отговор

     $$pV=nRT$$

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

201. Карта 201

     Въпрос

     First check when reading a handbook table?

     Отговор

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

202. Карта 202

     Въпрос

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

     Отговор

     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. Карта 203

     Въпрос

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

     Отговор

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

204. Карта 204

     Въпрос

     Convert Fahrenheit absolute temperature to Rankine?

     Отговор

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

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. Карта 205

     Въпрос

     Ohm's law for an ideal resistor?

     Отговор

     $$V=IR$$

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

206. Карта 206

     Въпрос

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

     Отговор

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

207. Карта 207

     Въпрос

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

     Отговор

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

208. Карта 208

     Въпрос

     Is a radian dimensionless?

     Отговор

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

209. Карта 209

     Въпрос

     Electrical power absorbed under the passive sign convention?

     Отговор

     $$P=VI$$

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

210. Карта 210

     Въпрос

     Meaning of a p-value?

     Отговор

     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. Карта 211

     Въпрос

     First check when reading a handbook graph?

     Отговор

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

212. Карта 212

     Въпрос

     Difference between mass and weight?

     Отговор

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

213. Карта 213

     Въпрос

     Kirchhoff's current law at a node?

     Отговор

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

214. Карта 214

     Въпрос

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

     Отговор

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

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

215. Карта 215

     Въпрос

     Opportunity cost?

     Отговор

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

216. Карта 216

     Въпрос

     Weight from mass in a gravitational field?

     Отговор

     $$W=mg$$

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

217. Карта 217

     Въпрос

     Kirchhoff's voltage law around a closed loop?

     Отговор

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

218. Карта 218

     Въпрос

     Decision rule using significance level $\alpha$?

     Отговор

     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. Карта 219

     Въпрос

     Can proprietary methods from a former employer be reused freely?

     Отговор

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

220. Карта 220

     Въпрос

     Pound-force to newtons?

     Отговор

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

221. Карта 221

     Въпрос

     When does a definite integral equal ordinary geometric area?

     Отговор

     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. Карта 222

     Въпрос

     Charge-voltage relation for an ideal capacitor?

     Отговор

     $$q=CV$$

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

223. Карта 223

     Въпрос

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

     Отговор

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

224. Карта 224

     Въпрос

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

     Отговор

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

225. Карта 225

     Въпрос

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

     Отговор

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

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

226. Карта 226

     Въпрос

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

     Отговор

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

227. Карта 227

     Въпрос

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

     Отговор

     $$\tau=RC$$

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

228. Карта 228

     Въпрос

     What physical quantity does pound-mass measure?

     Отговор

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

229. Карта 229

     Въпрос

     Type I error?

     Отговор

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

230. Карта 230

     Въпрос

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

     Отговор

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

231. Карта 231

     Въпрос

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

     Отговор

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

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

232. Карта 232

     Въпрос

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

     Отговор

     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. Карта 233

     Въпрос

     Recognizable form of a separable first-order differential equation?

     Отговор

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

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

234. Карта 234

     Въпрос

     Using unverified software output in a safety-relevant calculation?

     Отговор

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

235. Карта 235

     Въпрос

     Equivalent resistance of ideal resistors in series?

     Отговор

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

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

236. Карта 236

     Въпрос

     Pressure conversion from psi to pascals?

     Отговор

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

237. Карта 237

     Въпрос

     Type II error?

     Отговор

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

238. Карта 238

     Въпрос

     Useful flashcard to make after a failed handbook search?

     Отговор

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

239. Карта 239

     Въпрос

     Standard form of a first-order linear differential equation?

     Отговор

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

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

240. Карта 240

     Въпрос

     Equivalent resistance of ideal resistors in parallel?

     Отговор

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

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

241. Карта 241

     Въпрос

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

     Отговор

     $$BV_k=B-kD$$

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

242. Карта 242

     Въпрос

     Standard atmosphere in pascals?

     Отговор

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

243. Карта 243

     Въпрос

     Using AI-generated technical content in engineering work?

     Отговор

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

244. Карта 244

     Въпрос

     Trial form for a homogeneous linear ODE with constant coefficients?

     Отговор

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

245. Карта 245

     Въпрос

     Wave-speed relationship among frequency and wavelength?

     Отговор

     $$v=f\lambda$$

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

246. Карта 246

     Въпрос

     Statistical power?

     Отговор

     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. Карта 247

     Въпрос

     Bar in pascals?

     Отговор

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

248. Карта 248

     Въпрос

     How should handbook navigation be practiced before the FE exam?

     Отговор

     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. Карта 249

     Въпрос

     Is depreciation itself a cash outflow?

     Отговор

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

250. Карта 250

     Въпрос

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

     Отговор

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

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

251. Карта 251

     Въпрос

     Relationship between period and frequency?

     Отговор

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

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

252. Карта 252

     Въпрос

     How should foreseeable environmental harm enter an engineering decision?

     Отговор

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

253. Карта 253

     Въпрос

     Foot-pound-force in joules?

     Отговор

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

254. Карта 254

     Въпрос

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

     Отговор

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

255. Карта 255

     Въпрос

     When should you search instead of relying on recall?

     Отговор

     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. Карта 256

     Въпрос

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

     Отговор

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

257. Карта 257

     Въпрос

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

     Отговор

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

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

258. Карта 258

     Въпрос

     General material balance on a control volume?

     Отговор

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

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

259. Карта 259

     Въпрос

     Approximate joules in one International Table Btu?

     Отговор

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

260. Карта 260

     Въпрос

     What is the defender in a replacement analysis?

     Отговор

     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. Карта 261

     Въпрос

     Speaking publicly about a technical matter outside your expertise?

     Отговор

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

262. Карта 262

     Въпрос

     Single-interval trapezoidal approximation to an integral?

     Отговор

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

     It is exact for linear $f$.

263. Карта 263

     Въпрос

     Energy efficiency of a device?

     Отговор

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

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

264. Карта 264

     Въпрос

     Purpose of sensitivity analysis in engineering economics?

     Отговор

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

265. Карта 265

     Въпрос

     Can a strong correlation establish causation?

     Отговор

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

266. Карта 266

     Въпрос

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

     Отговор

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

267. Карта 267

     Въпрос

     Mechanical horsepower in watts?

     Отговор

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

268. Карта 268

     Въпрос

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

     Отговор

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

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

269. Карта 269

     Въпрос

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

     Отговор

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

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

270. Карта 270

     Въпрос

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

     Отговор

     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. Карта 271

     Въпрос

     Kilowatt-hour in joules?

     Отговор

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

272. Карта 272

     Въпрос

     Percent error relative to an accepted nonzero value?

     Отговор

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

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

273. Карта 273

     Въпрос

     Does legal compliance alone settle an engineering ethics question?

     Отговор

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

274. Карта 274

     Въпрос

     Does handbook fluency replace discipline-specific problem practice?

     Отговор

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

275. Карта 275

     Въпрос

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

     Отговор

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

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

276. Карта 276

     Въпрос

     Dimensional requirement for a physically meaningful additive equation?

     Отговор

     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.