FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

Kartičky v tomto balíčku

1. Kartička 1

   Otázka

   SI base unit of length?

   Odpoveď

   The metre, symbol $m$.

2. Kartička 2

   Otázka

   Slope between two points?

   Odpoveď

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

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

3. Kartička 3

   Otázka

   Net force relationship for constant mass in an inertial frame?

   Odpoveď

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

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

4. Kartička 4

   Otázka

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

   Odpoveď

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

5. Kartička 5

   Otázka

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

   Odpoveď

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

6. Kartička 6

   Otázka

   Probability of the complement of event $A$?

   Odpoveď

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

7. Kartička 7

   Otázka

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

   Odpoveď

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

8. Kartička 8

   Otázka

   SI base unit of mass?

   Odpoveď

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

9. Kartička 9

   Otázka

   Linear equation from slope and intercept?

   Odpoveď

   $$y=mx+b$$

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

10. Kartička 10

    Otázka

    Velocity after time $t$ under constant acceleration?

    Odpoveď

    $$v=v_0+at$$

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

11. Kartička 11

    Otázka

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

    Odpoveď

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

12. Kartička 12

    Otázka

    How is the FE reference handbook available during the exam?

    Odpoveď

    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. Kartička 13

    Otázka

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

    Odpoveď

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

14. Kartička 14

    Otázka

    SI base unit of time?

    Odpoveď

    The second, symbol $s$.

15. Kartička 15

    Otázka

    Linear equation from one point and a slope?

    Odpoveď

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

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

16. Kartička 16

    Otázka

    Position after time $t$ under constant acceleration?

    Odpoveď

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

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

17. Kartička 17

    Otázka

    A project assignment lies outside your competence. Proper response?

    Odpoveď

    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. Kartička 18

    Otázka

    SI base unit of electric current?

    Odpoveď

    The ampere, symbol $A$.

19. Kartička 19

    Otázka

    Future amount under simple interest?

    Odpoveď

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

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

20. Kartička 20

    Otázka

    Distance between two Cartesian points?

    Odpoveď

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

    The coordinate components must use the same length unit.

21. Kartička 21

    Otázka

    Constant-acceleration relation without elapsed time?

    Odpoveď

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

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

22. Kartička 22

    Otázka

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

    Odpoveď

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

23. Kartička 23

    Otázka

    Conditional probability of $A$ given $B$?

    Odpoveď

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

    This requires $P(B)>0$.

24. Kartička 24

    Otázka

    SI base unit of thermodynamic temperature?

    Odpoveď

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

25. Kartička 25

    Otázka

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

    Odpoveď

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

26. Kartička 26

    Otázka

    Midpoint of two Cartesian points?

    Odpoveď

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

    Average corresponding coordinates.

27. Kartička 27

    Otázka

    Linear momentum of a particle?

    Odpoveď

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

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

28. Kartička 28

    Otázka

    Future amount under compound interest?

    Odpoveď

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

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

29. Kartička 29

    Otázka

    Should an FE search workflow depend on Ctrl+F?

    Odpoveď

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

30. Kartička 30

    Otázka

    SI base unit of amount of substance?

    Odpoveď

    The mole, symbol $mol$.

31. Kartička 31

    Otázka

    Joint probability expressed with a conditional probability?

    Odpoveď

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

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

32. Kartička 32

    Otázka

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

    Odpoveď

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

    The coordinate units and radius unit must match.

33. Kartička 33

    Otázka

    Impulse-momentum relationship?

    Odpoveď

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

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

34. Kartička 34

    Otázka

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

    Odpoveď

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

35. Kartička 35

    Otázka

    SI base unit of luminous intensity?

    Odpoveď

    The candela, symbol $cd$.

36. Kartička 36

    Otázka

    Present worth of one future amount?

    Odpoveď

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

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

37. Kartička 37

    Otázka

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

    Odpoveď

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

    This form requires $a\ne0$.

38. Kartička 38

    Otázka

    When is total linear momentum conserved?

    Odpoveď

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

39. Kartička 39

    Otázka

    Why avoid memorizing FE handbook page numbers?

    Odpoveď

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

40. Kartička 40

    Otázka

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

    Odpoveď

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

    Independence is not the same as mutual exclusivity.

41. Kartička 41

    Otázka

    SI unit of frequency in base-unit form?

    Odpoveď

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

42. Kartička 42

    Otázka

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

    Odpoveď

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

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

43. Kartička 43

    Otázka

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

    Odpoveď

    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. Kartička 44

    Otázka

    Work done by a constant force through displacement?

    Odpoveď

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

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

45. Kartička 45

    Otázka

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

    Odpoveď

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

46. Kartička 46

    Otázka

    SI unit of force in base-unit form?

    Odpoveď

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

47. Kartička 47

    Otázka

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

    Odpoveď

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

48. Kartička 48

    Otázka

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

    Odpoveď

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

    This requires $P(B)>0$.

49. Kartička 49

    Otázka

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

    Odpoveď

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

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

50. Kartička 50

    Otázka

    Translational kinetic energy of a particle?

    Odpoveď

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

    Mass and speed must use a coherent unit system.

51. Kartička 51

    Otázka

    SI unit of pressure in force-area form?

    Odpoveď

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

52. Kartička 52

    Otázka

    Equivalent annual amount for present worth $P$?

    Odpoveď

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

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

53. Kartička 53

    Otázka

    May confidential client information be shared for personal benefit?

    Odpoveď

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

54. Kartička 54

    Otázka

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

    Odpoveď

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

55. Kartička 55

    Otázka

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

    Odpoveď

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

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

56. Kartička 56

    Otázka

    Net work-energy relationship for a particle?

    Odpoveď

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

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

57. Kartička 57

    Otázka

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

    Odpoveď

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

    Use this when order matters and selection is without replacement.

58. Kartička 58

    Otázka

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

    Odpoveď

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

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

59. Kartička 59

    Otázka

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

    Odpoveď

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

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

60. Kartička 60

    Otázka

    SI unit of energy in force-distance form?

    Odpoveď

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

61. Kartička 61

    Otázka

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

    Odpoveď

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

62. Kartička 62

    Otázka

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

    Odpoveď

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

63. Kartička 63

    Otázka

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

    Odpoveď

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

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

64. Kartička 64

    Otázka

    Change in gravitational potential energy near Earth's surface?

    Odpoveď

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

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

65. Kartička 65

    Otázka

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

    Odpoveď

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

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

66. Kartička 66

    Otázka

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

    Odpoveď

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

    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. Kartička 67

    Otázka

    A handbook search for an acronym fails. Next move?

    Odpoveď

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

68. Kartička 68

    Otázka

    SI unit of power in energy-time form?

    Odpoveď

    The watt, $W=J/s$.

69. Kartička 69

    Otázka

    Logarithm of a product?

    Odpoveď

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

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

70. Kartička 70

    Otázka

    Conditions for a binomial model?

    Odpoveď

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

71. Kartička 71

    Otázka

    Using another engineer's analysis in your deliverable?

    Odpoveď

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

72. Kartička 72

    Otázka

    SI unit of electric charge in current-time form?

    Odpoveď

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

73. Kartička 73

    Otázka

    Average power from work over elapsed time?

    Odpoveď

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

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

74. Kartička 74

    Otázka

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

    Odpoveď

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

    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. Kartička 75

    Otázka

    Logarithm of a positive quantity raised to a power?

    Odpoveď

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

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

76. Kartička 76

    Otázka

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

    Odpoveď

    The volt, $V=J/C$.

77. Kartička 77

    Otázka

    Instantaneous mechanical power delivered by a force?

    Odpoveď

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

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

78. Kartička 78

    Otázka

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

    Odpoveď

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

79. Kartička 79

    Otázka

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

    Odpoveď

    $$E[X]=np$$

80. Kartička 80

    Otázka

    SI unit of electrical resistance in voltage-current form?

    Odpoveď

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

81. Kartička 81

    Otázka

    Moment of a force about a point?

    Odpoveď

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

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

82. Kartička 82

    Otázka

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

    Odpoveď

    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. Kartička 83

    Otázka

    Inverse relationship between the natural log and exponential?

    Odpoveď

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

    The second identity requires $x>0$.

84. Kartička 84

    Otázka

    SI prefix giga?

    Odpoveď

    $G=10^9$.

85. Kartička 85

    Otázka

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

    Odpoveď

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

    Use consistent angular sign convention and radians for angular measures.

86. Kartička 86

    Otázka

    When should an engineer sign or seal technical work?

    Odpoveď

    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. Kartička 87

    Otázka

    Best memory target for returning to a handbook formula?

    Odpoveď

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

88. Kartička 88

    Otázka

    SI prefix mega?

    Odpoveď

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

89. Kartička 89

    Otázka

    Convert degrees to radians?

    Odpoveď

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

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

90. Kartička 90

    Otázka

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

    Odpoveď

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

91. Kartička 91

    Otázka

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

    Odpoveď

    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. Kartička 92

    Otázka

    Where do licensure and sealing requirements come from?

    Odpoveď

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

93. Kartička 93

    Otázka

    Rotational kinetic energy about a fixed axis?

    Odpoveď

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

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

94. Kartička 94

    Otázka

    SI prefix kilo?

    Odpoveď

    $k=10^3$.

95. Kartička 95

    Otázka

    Right-triangle definition of sine?

    Odpoveď

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

96. Kartička 96

    Otázka

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

    Odpoveď

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

97. Kartička 97

    Otázka

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

    Odpoveď

    $$\sum M=I\alpha$$

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

98. Kartička 98

    Otázka

    SI prefix milli?

    Odpoveď

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

99. Kartička 99

    Otázka

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

    Odpoveď

    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. Kartička 100

     Otázka

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

     Odpoveď

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

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

101. Kartička 101

     Otázka

     Right-triangle definition of cosine?

     Odpoveď

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

102. Kartička 102

     Otázka

     Force-displacement relation for an ideal linear spring?

     Odpoveď

     $$F=-kx$$

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

103. Kartička 103

     Otázka

     May qualifications or project responsibility be exaggerated in a proposal?

     Odpoveď

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

104. Kartička 104

     Otázka

     SI prefix micro?

     Odpoveď

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

105. Kartička 105

     Otázka

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

     Odpoveď

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

106. Kartička 106

     Otázka

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

     Odpoveď

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

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

107. Kartička 107

     Otázka

     Right-triangle definition of tangent?

     Odpoveď

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

108. Kartička 108

     Otázka

     Average normal stress under centered axial load?

     Odpoveď

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

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

109. Kartička 109

     Otázka

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

     Odpoveď

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

110. Kartička 110

     Otázka

     SI prefix nano?

     Odpoveď

     $n=10^{-9}$.

111. Kartička 111

     Otázka

     Fundamental Pythagorean trigonometric identity?

     Odpoveď

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

112. Kartička 112

     Otázka

     Engineering normal strain?

     Odpoveď

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

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

113. Kartička 113

     Otázka

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

     Odpoveď

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

114. Kartička 114

     Otázka

     Technical duty to an employer or client?

     Odpoveď

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

115. Kartička 115

     Otázka

     How does a length conversion factor apply to area?

     Odpoveď

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

116. Kartička 116

     Otázka

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

     Odpoveď

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

117. Kartička 117

     Otázka

     When is a Poisson count model reasonable?

     Odpoveď

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

118. Kartička 118

     Otázka

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

     Odpoveď

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

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

119. Kartička 119

     Otázka

     Linear elastic stress-strain relation in uniaxial loading?

     Odpoveď

     $$\sigma=E\varepsilon$$

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

120. Kartička 120

     Otázka

     How does a length conversion factor apply to volume?

     Odpoveď

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

121. Kartička 121

     Otázka

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

     Odpoveď

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

122. Kartička 122

     Otázka

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

     Odpoveď

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

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

123. Kartička 123

     Otázka

     A supervisor directs an illegal engineering action. Proper response?

     Odpoveď

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

124. Kartička 124

     Otázka

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

     Odpoveď

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

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

125. Kartička 125

     Otázka

     Mass density?

     Odpoveď

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

     Use mass, not weight, in the numerator.

126. Kartička 126

     Otázka

     Inches in one foot?

     Odpoveď

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

127. Kartička 127

     Otázka

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

     Odpoveď

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

128. Kartička 128

     Otázka

     How should subscripts be handled in a retrieved relationship?

     Odpoveď

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

129. Kartička 129

     Otázka

     Dot product from vector magnitudes and included angle?

     Odpoveď

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

     The result is a scalar.

130. Kartička 130

     Otázka

     Average normal pressure on an area?

     Odpoveď

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

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

131. Kartička 131

     Otázka

     Feet in one yard?

     Odpoveď

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

132. Kartička 132

     Otázka

     When are two interest rates equivalent?

     Odpoveď

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

133. Kartička 133

     Otázka

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

     Odpoveď

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

134. Kartička 134

     Otázka

     Expected value of a discrete random variable?

     Odpoveď

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

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

135. Kartička 135

     Otázka

     Dot-product test for perpendicular nonzero vectors?

     Odpoveď

     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. Kartička 136

     Otázka

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

     Odpoveď

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

     Depth increases downward and the fluid is at rest.

137. Kartička 137

     Otázka

     Feet in one statute mile?

     Odpoveď

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

138. Kartička 138

     Otázka

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

     Odpoveď

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

     

     276 kartičiek

     FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

     Učiť sa tento balíček zadarmo

     Otvorí sa Nibomo, aby ste sa mohli začať učiť.

139. Kartička 139

     Otázka

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

     Odpoveď

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

140. Kartička 140

     Otázka

     Magnitude of a vector cross product?

     Odpoveď

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

     The direction follows the right-hand rule.

141. Kartička 141

     Otázka

     Exact inch-to-metre relationship?

     Odpoveď

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

142. Kartička 142

     Otázka

     Volumetric flow rate through a cross-section?

     Odpoveď

     $$Q=Av_{avg}$$

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

143. Kartička 143

     Otázka

     Variance from the mean $\mu$?

     Odpoveď

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

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

144. Kartička 144

     Otázka

     Future-worth acceptance rule for an independent investment?

     Odpoveď

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

145. Kartička 145

     Otázka

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

     Odpoveď

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

146. Kartička 146

     Otázka

     Exact foot-to-metre relationship?

     Odpoveď

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

147. Kartička 147

     Otázka

     How should important uncertainty be communicated?

     Odpoveď

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

148. Kartička 148

     Otázka

     When is the matrix product $AB$ defined?

     Odpoveď

     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. Kartička 149

     Otázka

     Steady one-inlet, one-outlet mass continuity?

     Odpoveď

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     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. Kartička 150

     Otázka

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

     Odpoveď

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

151. Kartička 151

     Otázka

     Square feet in one acre?

     Odpoveď

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

152. Kartička 152

     Otázka

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

     Odpoveď

     $$ad-bc$$

153. Kartička 153

     Otázka

     Bernoulli relationship along a streamline for ideal steady flow?

     Odpoveď

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

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

154. Kartička 154

     Otázka

     May inconvenient measurements be discarded without a technical basis?

     Odpoveď

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

155. Kartička 155

     Otázka

     Annual-worth acceptance rule for an independent investment?

     Odpoveď

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

156. Kartička 156

     Otázka

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

     Odpoveď

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

157. Kartička 157

     Otázka

     Cubic metres in one litre?

     Odpoveď

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

158. Kartička 158

     Otázka

     What does a zero determinant mean for a square matrix?

     Odpoveď

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

159. Kartička 159

     Otázka

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

     Odpoveď

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

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

160. Kartička 160

     Otázka

     Unbiased sample variance for an independent sample from one population?

     Odpoveď

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

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

161. Kartička 161

     Otázka

     How should mutually exclusive alternatives be compared?

     Odpoveď

     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. Kartička 162

     Otázka

     Cubic centimetres in one millilitre?

     Odpoveď

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

163. Kartička 163

     Otázka

     Why keep contemporaneous engineering records?

     Odpoveď

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

164. Kartička 164

     Otázka

     Fast check after substituting into a handbook formula?

     Odpoveď

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

165. Kartička 165

     Otázka

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

     Odpoveď

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

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

166. Kartička 166

     Otázka

     Sensible heat for constant specific heat and no phase change?

     Odpoveď

     $$Q=mc\Delta T$$

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

167. Kartička 167

     Otázka

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

     Odpoveď

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

     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. Kartička 168

     Otázka

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

     Odpoveď

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

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

169. Kartička 169

     Otázka

     Purpose of incremental analysis for mutually exclusive alternatives?

     Odpoveď

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

170. Kartička 170

     Otázka

     Physical meaning of $dy/dx$?

     Odpoveď

     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. Kartička 171

     Otázka

     One-dimensional steady conduction through a plane wall?

     Odpoveď

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

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

172. Kartička 172

     Otázka

     When should you algebraically rearrange a handbook relationship?

     Odpoveď

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

173. Kartička 173

     Otázka

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

     Odpoveď

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

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

174. Kartička 174

     Otázka

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

     Odpoveď

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

175. Kartička 175

     Otázka

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

     Odpoveď

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

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

176. Kartička 176

     Otázka

     Convective heat-transfer rate at a surface?

     Odpoveď

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

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

177. Kartička 177

     Otázka

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

     Odpoveď

     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. Kartička 178

     Otázka

     Internal rate of return?

     Odpoveď

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

179. Kartička 179

     Otázka

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

     Odpoveď

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

180. Kartička 180

     Otázka

     Convert Celsius temperature to kelvin?

     Odpoveď

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

     This conversion is for absolute temperature, not temperature difference.

181. Kartička 181

     Otázka

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

     Odpoveď

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

182. Kartička 182

     Otázka

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

     Odpoveď

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

183. Kartička 183

     Otázka

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

     Odpoveď

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

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

184. Kartička 184

     Otázka

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

     Odpoveď

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

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

185. Kartička 185

     Otázka

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

     Odpoveď

     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. Kartička 186

     Otázka

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

     Odpoveď

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

187. Kartička 187

     Otázka

     Why inspect boundary or initial conditions near a formula?

     Odpoveď

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

188. Kartička 188

     Otázka

     Convert Celsius temperature to Fahrenheit?

     Odpoveď

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

189. Kartička 189

     Otázka

     Ethical basis for expert technical testimony?

     Odpoveď

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

190. Kartička 190

     Otázka

     Meaning of a breakeven value?

     Odpoveď

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

191. Kartička 191

     Otázka

     Derivative of $e^x$?

     Odpoveď

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

192. Kartička 192

     Otázka

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

     Odpoveď

     $$\Delta E=Q-W$$

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

193. Kartička 193

     Otázka

     Frequentist meaning of a 95% confidence procedure?

     Odpoveď

     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. Kartička 194

     Otázka

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

     Odpoveď

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

195. Kartička 195

     Otázka

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

     Odpoveď

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

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

196. Kartička 196

     Otázka

     Relationship between Celsius and kelvin temperature differences?

     Odpoveď

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

197. Kartička 197

     Otázka

     How should credit for team engineering work be assigned?

     Odpoveď

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

198. Kartička 198

     Otázka

     Main limitation of simple payback period?

     Odpoveď

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

199. Kartička 199

     Otázka

     Roles of the null and alternative hypotheses?

     Odpoveď

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

200. Kartička 200

     Otázka

     Ideal-gas equation of state?

     Odpoveď

     $$pV=nRT$$

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

201. Kartička 201

     Otázka

     First check when reading a handbook table?

     Odpoveď

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

202. Kartička 202

     Otázka

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

     Odpoveď

     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. Kartička 203

     Otázka

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

     Odpoveď

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

204. Kartička 204

     Otázka

     Convert Fahrenheit absolute temperature to Rankine?

     Odpoveď

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

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. Kartička 205

     Otázka

     Ohm's law for an ideal resistor?

     Odpoveď

     $$V=IR$$

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

206. Kartička 206

     Otázka

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

     Odpoveď

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

207. Kartička 207

     Otázka

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

     Odpoveď

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

208. Kartička 208

     Otázka

     Is a radian dimensionless?

     Odpoveď

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

209. Kartička 209

     Otázka

     Electrical power absorbed under the passive sign convention?

     Odpoveď

     $$P=VI$$

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

210. Kartička 210

     Otázka

     Meaning of a p-value?

     Odpoveď

     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. Kartička 211

     Otázka

     First check when reading a handbook graph?

     Odpoveď

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

212. Kartička 212

     Otázka

     Difference between mass and weight?

     Odpoveď

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

213. Kartička 213

     Otázka

     Kirchhoff's current law at a node?

     Odpoveď

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

214. Kartička 214

     Otázka

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

     Odpoveď

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

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

215. Kartička 215

     Otázka

     Opportunity cost?

     Odpoveď

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

216. Kartička 216

     Otázka

     Weight from mass in a gravitational field?

     Odpoveď

     $$W=mg$$

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

217. Kartička 217

     Otázka

     Kirchhoff's voltage law around a closed loop?

     Odpoveď

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

218. Kartička 218

     Otázka

     Decision rule using significance level $\alpha$?

     Odpoveď

     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. Kartička 219

     Otázka

     Can proprietary methods from a former employer be reused freely?

     Odpoveď

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

220. Kartička 220

     Otázka

     Pound-force to newtons?

     Odpoveď

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

221. Kartička 221

     Otázka

     When does a definite integral equal ordinary geometric area?

     Odpoveď

     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. Kartička 222

     Otázka

     Charge-voltage relation for an ideal capacitor?

     Odpoveď

     $$q=CV$$

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

223. Kartička 223

     Otázka

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

     Odpoveď

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

224. Kartička 224

     Otázka

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

     Odpoveď

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

225. Kartička 225

     Otázka

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

     Odpoveď

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

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

226. Kartička 226

     Otázka

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

     Odpoveď

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

227. Kartička 227

     Otázka

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

     Odpoveď

     $$\tau=RC$$

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

228. Kartička 228

     Otázka

     What physical quantity does pound-mass measure?

     Odpoveď

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

229. Kartička 229

     Otázka

     Type I error?

     Odpoveď

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

230. Kartička 230

     Otázka

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

     Odpoveď

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

231. Kartička 231

     Otázka

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

     Odpoveď

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

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

232. Kartička 232

     Otázka

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

     Odpoveď

     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. Kartička 233

     Otázka

     Recognizable form of a separable first-order differential equation?

     Odpoveď

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

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

234. Kartička 234

     Otázka

     Using unverified software output in a safety-relevant calculation?

     Odpoveď

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

235. Kartička 235

     Otázka

     Equivalent resistance of ideal resistors in series?

     Odpoveď

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

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

236. Kartička 236

     Otázka

     Pressure conversion from psi to pascals?

     Odpoveď

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

237. Kartička 237

     Otázka

     Type II error?

     Odpoveď

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

238. Kartička 238

     Otázka

     Useful flashcard to make after a failed handbook search?

     Odpoveď

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

239. Kartička 239

     Otázka

     Standard form of a first-order linear differential equation?

     Odpoveď

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

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

240. Kartička 240

     Otázka

     Equivalent resistance of ideal resistors in parallel?

     Odpoveď

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

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

241. Kartička 241

     Otázka

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

     Odpoveď

     $$BV_k=B-kD$$

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

242. Kartička 242

     Otázka

     Standard atmosphere in pascals?

     Odpoveď

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

243. Kartička 243

     Otázka

     Using AI-generated technical content in engineering work?

     Odpoveď

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

244. Kartička 244

     Otázka

     Trial form for a homogeneous linear ODE with constant coefficients?

     Odpoveď

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

245. Kartička 245

     Otázka

     Wave-speed relationship among frequency and wavelength?

     Odpoveď

     $$v=f\lambda$$

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

246. Kartička 246

     Otázka

     Statistical power?

     Odpoveď

     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. Kartička 247

     Otázka

     Bar in pascals?

     Odpoveď

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

248. Kartička 248

     Otázka

     How should handbook navigation be practiced before the FE exam?

     Odpoveď

     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. Kartička 249

     Otázka

     Is depreciation itself a cash outflow?

     Odpoveď

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

250. Kartička 250

     Otázka

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

     Odpoveď

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

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

251. Kartička 251

     Otázka

     Relationship between period and frequency?

     Odpoveď

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

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

252. Kartička 252

     Otázka

     How should foreseeable environmental harm enter an engineering decision?

     Odpoveď

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

253. Kartička 253

     Otázka

     Foot-pound-force in joules?

     Odpoveď

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

254. Kartička 254

     Otázka

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

     Odpoveď

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

255. Kartička 255

     Otázka

     When should you search instead of relying on recall?

     Odpoveď

     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. Kartička 256

     Otázka

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

     Odpoveď

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

257. Kartička 257

     Otázka

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

     Odpoveď

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

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

258. Kartička 258

     Otázka

     General material balance on a control volume?

     Odpoveď

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

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

259. Kartička 259

     Otázka

     Approximate joules in one International Table Btu?

     Odpoveď

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

260. Kartička 260

     Otázka

     What is the defender in a replacement analysis?

     Odpoveď

     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. Kartička 261

     Otázka

     Speaking publicly about a technical matter outside your expertise?

     Odpoveď

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

262. Kartička 262

     Otázka

     Single-interval trapezoidal approximation to an integral?

     Odpoveď

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

     It is exact for linear $f$.

263. Kartička 263

     Otázka

     Energy efficiency of a device?

     Odpoveď

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

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

264. Kartička 264

     Otázka

     Purpose of sensitivity analysis in engineering economics?

     Odpoveď

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

265. Kartička 265

     Otázka

     Can a strong correlation establish causation?

     Odpoveď

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

266. Kartička 266

     Otázka

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

     Odpoveď

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

267. Kartička 267

     Otázka

     Mechanical horsepower in watts?

     Odpoveď

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

268. Kartička 268

     Otázka

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

     Odpoveď

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

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

269. Kartička 269

     Otázka

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

     Odpoveď

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

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

270. Kartička 270

     Otázka

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

     Odpoveď

     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. Kartička 271

     Otázka

     Kilowatt-hour in joules?

     Odpoveď

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

272. Kartička 272

     Otázka

     Percent error relative to an accepted nonzero value?

     Odpoveď

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

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

273. Kartička 273

     Otázka

     Does legal compliance alone settle an engineering ethics question?

     Odpoveď

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

274. Kartička 274

     Otázka

     Does handbook fluency replace discipline-specific problem practice?

     Odpoveď

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

275. Kartička 275

     Otázka

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

     Odpoveď

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

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

276. Kartička 276

     Otázka

     Dimensional requirement for a physically meaningful additive equation?

     Odpoveď

     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.