FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

Kartice u ovom špilu

1. Kartica 1

   Pitanje

   SI base unit of length?

   Odgovor

   The metre, symbol $m$.

2. Kartica 2

   Pitanje

   Slope between two points?

   Odgovor

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

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

3. Kartica 3

   Pitanje

   Net force relationship for constant mass in an inertial frame?

   Odgovor

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

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

4. Kartica 4

   Pitanje

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

   Odgovor

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

5. Kartica 5

   Pitanje

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

   Odgovor

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

6. Kartica 6

   Pitanje

   Probability of the complement of event $A$?

   Odgovor

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

7. Kartica 7

   Pitanje

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

   Odgovor

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

8. Kartica 8

   Pitanje

   SI base unit of mass?

   Odgovor

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

9. Kartica 9

   Pitanje

   Linear equation from slope and intercept?

   Odgovor

   $$y=mx+b$$

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

10. Kartica 10

    Pitanje

    Velocity after time $t$ under constant acceleration?

    Odgovor

    $$v=v_0+at$$

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

11. Kartica 11

    Pitanje

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

    Odgovor

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

12. Kartica 12

    Pitanje

    How is the FE reference handbook available during the exam?

    Odgovor

    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. Kartica 13

    Pitanje

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

    Odgovor

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

14. Kartica 14

    Pitanje

    SI base unit of time?

    Odgovor

    The second, symbol $s$.

15. Kartica 15

    Pitanje

    Linear equation from one point and a slope?

    Odgovor

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

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

16. Kartica 16

    Pitanje

    Position after time $t$ under constant acceleration?

    Odgovor

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

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

17. Kartica 17

    Pitanje

    A project assignment lies outside your competence. Proper response?

    Odgovor

    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. Kartica 18

    Pitanje

    SI base unit of electric current?

    Odgovor

    The ampere, symbol $A$.

19. Kartica 19

    Pitanje

    Future amount under simple interest?

    Odgovor

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

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

20. Kartica 20

    Pitanje

    Distance between two Cartesian points?

    Odgovor

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

    The coordinate components must use the same length unit.

21. Kartica 21

    Pitanje

    Constant-acceleration relation without elapsed time?

    Odgovor

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

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

22. Kartica 22

    Pitanje

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

    Odgovor

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

23. Kartica 23

    Pitanje

    Conditional probability of $A$ given $B$?

    Odgovor

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

    This requires $P(B)>0$.

24. Kartica 24

    Pitanje

    SI base unit of thermodynamic temperature?

    Odgovor

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

25. Kartica 25

    Pitanje

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

    Odgovor

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

26. Kartica 26

    Pitanje

    Midpoint of two Cartesian points?

    Odgovor

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

    Average corresponding coordinates.

27. Kartica 27

    Pitanje

    Linear momentum of a particle?

    Odgovor

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

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

28. Kartica 28

    Pitanje

    Future amount under compound interest?

    Odgovor

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

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

29. Kartica 29

    Pitanje

    Should an FE search workflow depend on Ctrl+F?

    Odgovor

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

30. Kartica 30

    Pitanje

    SI base unit of amount of substance?

    Odgovor

    The mole, symbol $mol$.

31. Kartica 31

    Pitanje

    Joint probability expressed with a conditional probability?

    Odgovor

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

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

32. Kartica 32

    Pitanje

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

    Odgovor

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

    The coordinate units and radius unit must match.

33. Kartica 33

    Pitanje

    Impulse-momentum relationship?

    Odgovor

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

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

34. Kartica 34

    Pitanje

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

    Odgovor

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

35. Kartica 35

    Pitanje

    SI base unit of luminous intensity?

    Odgovor

    The candela, symbol $cd$.

36. Kartica 36

    Pitanje

    Present worth of one future amount?

    Odgovor

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

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

37. Kartica 37

    Pitanje

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

    Odgovor

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

    This form requires $a\ne0$.

38. Kartica 38

    Pitanje

    When is total linear momentum conserved?

    Odgovor

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

39. Kartica 39

    Pitanje

    Why avoid memorizing FE handbook page numbers?

    Odgovor

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

40. Kartica 40

    Pitanje

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

    Odgovor

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

    Independence is not the same as mutual exclusivity.

41. Kartica 41

    Pitanje

    SI unit of frequency in base-unit form?

    Odgovor

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

42. Kartica 42

    Pitanje

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

    Odgovor

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

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

43. Kartica 43

    Pitanje

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

    Odgovor

    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. Kartica 44

    Pitanje

    Work done by a constant force through displacement?

    Odgovor

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

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

45. Kartica 45

    Pitanje

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

    Odgovor

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

46. Kartica 46

    Pitanje

    SI unit of force in base-unit form?

    Odgovor

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

47. Kartica 47

    Pitanje

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

    Odgovor

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

48. Kartica 48

    Pitanje

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

    Odgovor

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

    This requires $P(B)>0$.

49. Kartica 49

    Pitanje

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

    Odgovor

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

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

50. Kartica 50

    Pitanje

    Translational kinetic energy of a particle?

    Odgovor

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

    Mass and speed must use a coherent unit system.

51. Kartica 51

    Pitanje

    SI unit of pressure in force-area form?

    Odgovor

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

52. Kartica 52

    Pitanje

    Equivalent annual amount for present worth $P$?

    Odgovor

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

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

53. Kartica 53

    Pitanje

    May confidential client information be shared for personal benefit?

    Odgovor

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

54. Kartica 54

    Pitanje

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

    Odgovor

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

55. Kartica 55

    Pitanje

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

    Odgovor

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

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

56. Kartica 56

    Pitanje

    Net work-energy relationship for a particle?

    Odgovor

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

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

57. Kartica 57

    Pitanje

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

    Odgovor

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

    Use this when order matters and selection is without replacement.

58. Kartica 58

    Pitanje

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

    Odgovor

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

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

59. Kartica 59

    Pitanje

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

    Odgovor

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

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

60. Kartica 60

    Pitanje

    SI unit of energy in force-distance form?

    Odgovor

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

61. Kartica 61

    Pitanje

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

    Odgovor

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

62. Kartica 62

    Pitanje

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

    Odgovor

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

63. Kartica 63

    Pitanje

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

    Odgovor

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

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

64. Kartica 64

    Pitanje

    Change in gravitational potential energy near Earth's surface?

    Odgovor

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

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

65. Kartica 65

    Pitanje

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

    Odgovor

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

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

66. Kartica 66

    Pitanje

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

    Odgovor

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

    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. Kartica 67

    Pitanje

    A handbook search for an acronym fails. Next move?

    Odgovor

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

68. Kartica 68

    Pitanje

    SI unit of power in energy-time form?

    Odgovor

    The watt, $W=J/s$.

69. Kartica 69

    Pitanje

    Logarithm of a product?

    Odgovor

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

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

70. Kartica 70

    Pitanje

    Conditions for a binomial model?

    Odgovor

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

71. Kartica 71

    Pitanje

    Using another engineer's analysis in your deliverable?

    Odgovor

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

72. Kartica 72

    Pitanje

    SI unit of electric charge in current-time form?

    Odgovor

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

73. Kartica 73

    Pitanje

    Average power from work over elapsed time?

    Odgovor

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

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

74. Kartica 74

    Pitanje

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

    Odgovor

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

    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. Kartica 75

    Pitanje

    Logarithm of a positive quantity raised to a power?

    Odgovor

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

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

76. Kartica 76

    Pitanje

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

    Odgovor

    The volt, $V=J/C$.

77. Kartica 77

    Pitanje

    Instantaneous mechanical power delivered by a force?

    Odgovor

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

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

78. Kartica 78

    Pitanje

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

    Odgovor

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

79. Kartica 79

    Pitanje

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

    Odgovor

    $$E[X]=np$$

80. Kartica 80

    Pitanje

    SI unit of electrical resistance in voltage-current form?

    Odgovor

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

81. Kartica 81

    Pitanje

    Moment of a force about a point?

    Odgovor

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

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

82. Kartica 82

    Pitanje

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

    Odgovor

    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. Kartica 83

    Pitanje

    Inverse relationship between the natural log and exponential?

    Odgovor

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

    The second identity requires $x>0$.

84. Kartica 84

    Pitanje

    SI prefix giga?

    Odgovor

    $G=10^9$.

85. Kartica 85

    Pitanje

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

    Odgovor

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

    Use consistent angular sign convention and radians for angular measures.

86. Kartica 86

    Pitanje

    When should an engineer sign or seal technical work?

    Odgovor

    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. Kartica 87

    Pitanje

    Best memory target for returning to a handbook formula?

    Odgovor

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

88. Kartica 88

    Pitanje

    SI prefix mega?

    Odgovor

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

89. Kartica 89

    Pitanje

    Convert degrees to radians?

    Odgovor

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

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

90. Kartica 90

    Pitanje

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

    Odgovor

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

91. Kartica 91

    Pitanje

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

    Odgovor

    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. Kartica 92

    Pitanje

    Where do licensure and sealing requirements come from?

    Odgovor

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

93. Kartica 93

    Pitanje

    Rotational kinetic energy about a fixed axis?

    Odgovor

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

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

94. Kartica 94

    Pitanje

    SI prefix kilo?

    Odgovor

    $k=10^3$.

95. Kartica 95

    Pitanje

    Right-triangle definition of sine?

    Odgovor

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

96. Kartica 96

    Pitanje

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

    Odgovor

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

97. Kartica 97

    Pitanje

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

    Odgovor

    $$\sum M=I\alpha$$

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

98. Kartica 98

    Pitanje

    SI prefix milli?

    Odgovor

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

99. Kartica 99

    Pitanje

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

    Odgovor

    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. Kartica 100

     Pitanje

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

     Odgovor

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

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

101. Kartica 101

     Pitanje

     Right-triangle definition of cosine?

     Odgovor

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

102. Kartica 102

     Pitanje

     Force-displacement relation for an ideal linear spring?

     Odgovor

     $$F=-kx$$

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

103. Kartica 103

     Pitanje

     May qualifications or project responsibility be exaggerated in a proposal?

     Odgovor

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

104. Kartica 104

     Pitanje

     SI prefix micro?

     Odgovor

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

105. Kartica 105

     Pitanje

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

     Odgovor

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

106. Kartica 106

     Pitanje

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

     Odgovor

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

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

107. Kartica 107

     Pitanje

     Right-triangle definition of tangent?

     Odgovor

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

108. Kartica 108

     Pitanje

     Average normal stress under centered axial load?

     Odgovor

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

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

109. Kartica 109

     Pitanje

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

     Odgovor

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

110. Kartica 110

     Pitanje

     SI prefix nano?

     Odgovor

     $n=10^{-9}$.

111. Kartica 111

     Pitanje

     Fundamental Pythagorean trigonometric identity?

     Odgovor

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

112. Kartica 112

     Pitanje

     Engineering normal strain?

     Odgovor

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

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

113. Kartica 113

     Pitanje

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

     Odgovor

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

114. Kartica 114

     Pitanje

     Technical duty to an employer or client?

     Odgovor

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

115. Kartica 115

     Pitanje

     How does a length conversion factor apply to area?

     Odgovor

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

116. Kartica 116

     Pitanje

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

     Odgovor

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

117. Kartica 117

     Pitanje

     When is a Poisson count model reasonable?

     Odgovor

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

118. Kartica 118

     Pitanje

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

     Odgovor

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

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

119. Kartica 119

     Pitanje

     Linear elastic stress-strain relation in uniaxial loading?

     Odgovor

     $$\sigma=E\varepsilon$$

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

120. Kartica 120

     Pitanje

     How does a length conversion factor apply to volume?

     Odgovor

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

121. Kartica 121

     Pitanje

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

     Odgovor

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

122. Kartica 122

     Pitanje

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

     Odgovor

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

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

123. Kartica 123

     Pitanje

     A supervisor directs an illegal engineering action. Proper response?

     Odgovor

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

124. Kartica 124

     Pitanje

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

     Odgovor

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

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

125. Kartica 125

     Pitanje

     Mass density?

     Odgovor

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

     Use mass, not weight, in the numerator.

126. Kartica 126

     Pitanje

     Inches in one foot?

     Odgovor

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

127. Kartica 127

     Pitanje

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

     Odgovor

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

128. Kartica 128

     Pitanje

     How should subscripts be handled in a retrieved relationship?

     Odgovor

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

129. Kartica 129

     Pitanje

     Dot product from vector magnitudes and included angle?

     Odgovor

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

     The result is a scalar.

130. Kartica 130

     Pitanje

     Average normal pressure on an area?

     Odgovor

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

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

131. Kartica 131

     Pitanje

     Feet in one yard?

     Odgovor

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

132. Kartica 132

     Pitanje

     When are two interest rates equivalent?

     Odgovor

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

133. Kartica 133

     Pitanje

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

     Odgovor

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

134. Kartica 134

     Pitanje

     Expected value of a discrete random variable?

     Odgovor

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

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

135. Kartica 135

     Pitanje

     Dot-product test for perpendicular nonzero vectors?

     Odgovor

     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. Kartica 136

     Pitanje

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

     Odgovor

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

     Depth increases downward and the fluid is at rest.

137. Kartica 137

     Pitanje

     Feet in one statute mile?

     Odgovor

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

138. Kartica 138

     Pitanje

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

     Odgovor

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

     

     276 kartica

     FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

     Učite iz ovog špila besplatno

     Nibomo se otvara kako biste mogli početi učiti.

139. Kartica 139

     Pitanje

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

     Odgovor

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

140. Kartica 140

     Pitanje

     Magnitude of a vector cross product?

     Odgovor

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

     The direction follows the right-hand rule.

141. Kartica 141

     Pitanje

     Exact inch-to-metre relationship?

     Odgovor

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

142. Kartica 142

     Pitanje

     Volumetric flow rate through a cross-section?

     Odgovor

     $$Q=Av_{avg}$$

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

143. Kartica 143

     Pitanje

     Variance from the mean $\mu$?

     Odgovor

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

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

144. Kartica 144

     Pitanje

     Future-worth acceptance rule for an independent investment?

     Odgovor

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

145. Kartica 145

     Pitanje

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

     Odgovor

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

146. Kartica 146

     Pitanje

     Exact foot-to-metre relationship?

     Odgovor

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

147. Kartica 147

     Pitanje

     How should important uncertainty be communicated?

     Odgovor

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

148. Kartica 148

     Pitanje

     When is the matrix product $AB$ defined?

     Odgovor

     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. Kartica 149

     Pitanje

     Steady one-inlet, one-outlet mass continuity?

     Odgovor

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     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. Kartica 150

     Pitanje

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

     Odgovor

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

151. Kartica 151

     Pitanje

     Square feet in one acre?

     Odgovor

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

152. Kartica 152

     Pitanje

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

     Odgovor

     $$ad-bc$$

153. Kartica 153

     Pitanje

     Bernoulli relationship along a streamline for ideal steady flow?

     Odgovor

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

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

154. Kartica 154

     Pitanje

     May inconvenient measurements be discarded without a technical basis?

     Odgovor

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

155. Kartica 155

     Pitanje

     Annual-worth acceptance rule for an independent investment?

     Odgovor

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

156. Kartica 156

     Pitanje

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

     Odgovor

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

157. Kartica 157

     Pitanje

     Cubic metres in one litre?

     Odgovor

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

158. Kartica 158

     Pitanje

     What does a zero determinant mean for a square matrix?

     Odgovor

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

159. Kartica 159

     Pitanje

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

     Odgovor

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

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

160. Kartica 160

     Pitanje

     Unbiased sample variance for an independent sample from one population?

     Odgovor

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

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

161. Kartica 161

     Pitanje

     How should mutually exclusive alternatives be compared?

     Odgovor

     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. Kartica 162

     Pitanje

     Cubic centimetres in one millilitre?

     Odgovor

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

163. Kartica 163

     Pitanje

     Why keep contemporaneous engineering records?

     Odgovor

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

164. Kartica 164

     Pitanje

     Fast check after substituting into a handbook formula?

     Odgovor

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

165. Kartica 165

     Pitanje

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

     Odgovor

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

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

166. Kartica 166

     Pitanje

     Sensible heat for constant specific heat and no phase change?

     Odgovor

     $$Q=mc\Delta T$$

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

167. Kartica 167

     Pitanje

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

     Odgovor

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

     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. Kartica 168

     Pitanje

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

     Odgovor

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

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

169. Kartica 169

     Pitanje

     Purpose of incremental analysis for mutually exclusive alternatives?

     Odgovor

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

170. Kartica 170

     Pitanje

     Physical meaning of $dy/dx$?

     Odgovor

     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. Kartica 171

     Pitanje

     One-dimensional steady conduction through a plane wall?

     Odgovor

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

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

172. Kartica 172

     Pitanje

     When should you algebraically rearrange a handbook relationship?

     Odgovor

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

173. Kartica 173

     Pitanje

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

     Odgovor

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

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

174. Kartica 174

     Pitanje

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

     Odgovor

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

175. Kartica 175

     Pitanje

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

     Odgovor

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

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

176. Kartica 176

     Pitanje

     Convective heat-transfer rate at a surface?

     Odgovor

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

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

177. Kartica 177

     Pitanje

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

     Odgovor

     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. Kartica 178

     Pitanje

     Internal rate of return?

     Odgovor

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

179. Kartica 179

     Pitanje

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

     Odgovor

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

180. Kartica 180

     Pitanje

     Convert Celsius temperature to kelvin?

     Odgovor

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

     This conversion is for absolute temperature, not temperature difference.

181. Kartica 181

     Pitanje

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

     Odgovor

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

182. Kartica 182

     Pitanje

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

     Odgovor

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

183. Kartica 183

     Pitanje

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

     Odgovor

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

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

184. Kartica 184

     Pitanje

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

     Odgovor

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

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

185. Kartica 185

     Pitanje

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

     Odgovor

     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. Kartica 186

     Pitanje

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

     Odgovor

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

187. Kartica 187

     Pitanje

     Why inspect boundary or initial conditions near a formula?

     Odgovor

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

188. Kartica 188

     Pitanje

     Convert Celsius temperature to Fahrenheit?

     Odgovor

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

189. Kartica 189

     Pitanje

     Ethical basis for expert technical testimony?

     Odgovor

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

190. Kartica 190

     Pitanje

     Meaning of a breakeven value?

     Odgovor

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

191. Kartica 191

     Pitanje

     Derivative of $e^x$?

     Odgovor

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

192. Kartica 192

     Pitanje

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

     Odgovor

     $$\Delta E=Q-W$$

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

193. Kartica 193

     Pitanje

     Frequentist meaning of a 95% confidence procedure?

     Odgovor

     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. Kartica 194

     Pitanje

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

     Odgovor

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

195. Kartica 195

     Pitanje

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

     Odgovor

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

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

196. Kartica 196

     Pitanje

     Relationship between Celsius and kelvin temperature differences?

     Odgovor

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

197. Kartica 197

     Pitanje

     How should credit for team engineering work be assigned?

     Odgovor

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

198. Kartica 198

     Pitanje

     Main limitation of simple payback period?

     Odgovor

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

199. Kartica 199

     Pitanje

     Roles of the null and alternative hypotheses?

     Odgovor

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

200. Kartica 200

     Pitanje

     Ideal-gas equation of state?

     Odgovor

     $$pV=nRT$$

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

201. Kartica 201

     Pitanje

     First check when reading a handbook table?

     Odgovor

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

202. Kartica 202

     Pitanje

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

     Odgovor

     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. Kartica 203

     Pitanje

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

     Odgovor

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

204. Kartica 204

     Pitanje

     Convert Fahrenheit absolute temperature to Rankine?

     Odgovor

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

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. Kartica 205

     Pitanje

     Ohm's law for an ideal resistor?

     Odgovor

     $$V=IR$$

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

206. Kartica 206

     Pitanje

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

     Odgovor

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

207. Kartica 207

     Pitanje

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

     Odgovor

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

208. Kartica 208

     Pitanje

     Is a radian dimensionless?

     Odgovor

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

209. Kartica 209

     Pitanje

     Electrical power absorbed under the passive sign convention?

     Odgovor

     $$P=VI$$

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

210. Kartica 210

     Pitanje

     Meaning of a p-value?

     Odgovor

     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. Kartica 211

     Pitanje

     First check when reading a handbook graph?

     Odgovor

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

212. Kartica 212

     Pitanje

     Difference between mass and weight?

     Odgovor

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

213. Kartica 213

     Pitanje

     Kirchhoff's current law at a node?

     Odgovor

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

214. Kartica 214

     Pitanje

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

     Odgovor

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

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

215. Kartica 215

     Pitanje

     Opportunity cost?

     Odgovor

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

216. Kartica 216

     Pitanje

     Weight from mass in a gravitational field?

     Odgovor

     $$W=mg$$

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

217. Kartica 217

     Pitanje

     Kirchhoff's voltage law around a closed loop?

     Odgovor

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

218. Kartica 218

     Pitanje

     Decision rule using significance level $\alpha$?

     Odgovor

     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. Kartica 219

     Pitanje

     Can proprietary methods from a former employer be reused freely?

     Odgovor

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

220. Kartica 220

     Pitanje

     Pound-force to newtons?

     Odgovor

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

221. Kartica 221

     Pitanje

     When does a definite integral equal ordinary geometric area?

     Odgovor

     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. Kartica 222

     Pitanje

     Charge-voltage relation for an ideal capacitor?

     Odgovor

     $$q=CV$$

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

223. Kartica 223

     Pitanje

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

     Odgovor

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

224. Kartica 224

     Pitanje

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

     Odgovor

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

225. Kartica 225

     Pitanje

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

     Odgovor

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

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

226. Kartica 226

     Pitanje

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

     Odgovor

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

227. Kartica 227

     Pitanje

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

     Odgovor

     $$\tau=RC$$

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

228. Kartica 228

     Pitanje

     What physical quantity does pound-mass measure?

     Odgovor

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

229. Kartica 229

     Pitanje

     Type I error?

     Odgovor

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

230. Kartica 230

     Pitanje

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

     Odgovor

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

231. Kartica 231

     Pitanje

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

     Odgovor

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

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

232. Kartica 232

     Pitanje

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

     Odgovor

     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. Kartica 233

     Pitanje

     Recognizable form of a separable first-order differential equation?

     Odgovor

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

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

234. Kartica 234

     Pitanje

     Using unverified software output in a safety-relevant calculation?

     Odgovor

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

235. Kartica 235

     Pitanje

     Equivalent resistance of ideal resistors in series?

     Odgovor

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

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

236. Kartica 236

     Pitanje

     Pressure conversion from psi to pascals?

     Odgovor

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

237. Kartica 237

     Pitanje

     Type II error?

     Odgovor

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

238. Kartica 238

     Pitanje

     Useful flashcard to make after a failed handbook search?

     Odgovor

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

239. Kartica 239

     Pitanje

     Standard form of a first-order linear differential equation?

     Odgovor

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

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

240. Kartica 240

     Pitanje

     Equivalent resistance of ideal resistors in parallel?

     Odgovor

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

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

241. Kartica 241

     Pitanje

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

     Odgovor

     $$BV_k=B-kD$$

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

242. Kartica 242

     Pitanje

     Standard atmosphere in pascals?

     Odgovor

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

243. Kartica 243

     Pitanje

     Using AI-generated technical content in engineering work?

     Odgovor

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

244. Kartica 244

     Pitanje

     Trial form for a homogeneous linear ODE with constant coefficients?

     Odgovor

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

245. Kartica 245

     Pitanje

     Wave-speed relationship among frequency and wavelength?

     Odgovor

     $$v=f\lambda$$

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

246. Kartica 246

     Pitanje

     Statistical power?

     Odgovor

     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. Kartica 247

     Pitanje

     Bar in pascals?

     Odgovor

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

248. Kartica 248

     Pitanje

     How should handbook navigation be practiced before the FE exam?

     Odgovor

     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. Kartica 249

     Pitanje

     Is depreciation itself a cash outflow?

     Odgovor

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

250. Kartica 250

     Pitanje

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

     Odgovor

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

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

251. Kartica 251

     Pitanje

     Relationship between period and frequency?

     Odgovor

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

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

252. Kartica 252

     Pitanje

     How should foreseeable environmental harm enter an engineering decision?

     Odgovor

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

253. Kartica 253

     Pitanje

     Foot-pound-force in joules?

     Odgovor

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

254. Kartica 254

     Pitanje

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

     Odgovor

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

255. Kartica 255

     Pitanje

     When should you search instead of relying on recall?

     Odgovor

     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. Kartica 256

     Pitanje

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

     Odgovor

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

257. Kartica 257

     Pitanje

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

     Odgovor

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

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

258. Kartica 258

     Pitanje

     General material balance on a control volume?

     Odgovor

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

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

259. Kartica 259

     Pitanje

     Approximate joules in one International Table Btu?

     Odgovor

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

260. Kartica 260

     Pitanje

     What is the defender in a replacement analysis?

     Odgovor

     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. Kartica 261

     Pitanje

     Speaking publicly about a technical matter outside your expertise?

     Odgovor

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

262. Kartica 262

     Pitanje

     Single-interval trapezoidal approximation to an integral?

     Odgovor

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

     It is exact for linear $f$.

263. Kartica 263

     Pitanje

     Energy efficiency of a device?

     Odgovor

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

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

264. Kartica 264

     Pitanje

     Purpose of sensitivity analysis in engineering economics?

     Odgovor

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

265. Kartica 265

     Pitanje

     Can a strong correlation establish causation?

     Odgovor

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

266. Kartica 266

     Pitanje

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

     Odgovor

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

267. Kartica 267

     Pitanje

     Mechanical horsepower in watts?

     Odgovor

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

268. Kartica 268

     Pitanje

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

     Odgovor

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

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

269. Kartica 269

     Pitanje

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

     Odgovor

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

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

270. Kartica 270

     Pitanje

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

     Odgovor

     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. Kartica 271

     Pitanje

     Kilowatt-hour in joules?

     Odgovor

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

272. Kartica 272

     Pitanje

     Percent error relative to an accepted nonzero value?

     Odgovor

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

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

273. Kartica 273

     Pitanje

     Does legal compliance alone settle an engineering ethics question?

     Odgovor

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

274. Kartica 274

     Pitanje

     Does handbook fluency replace discipline-specific problem practice?

     Odgovor

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

275. Kartica 275

     Pitanje

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

     Odgovor

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

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

276. Kartica 276

     Pitanje

     Dimensional requirement for a physically meaningful additive equation?

     Odgovor

     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.