FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

Fișele din acest pachet

1. Fișa 1

   Întrebare

   SI base unit of length?

   Răspuns

   The metre, symbol $m$.

2. Fișa 2

   Întrebare

   Slope between two points?

   Răspuns

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

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

3. Fișa 3

   Întrebare

   Net force relationship for constant mass in an inertial frame?

   Răspuns

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

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

4. Fișa 4

   Întrebare

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

   Răspuns

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

5. Fișa 5

   Întrebare

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

   Răspuns

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

6. Fișa 6

   Întrebare

   Probability of the complement of event $A$?

   Răspuns

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

7. Fișa 7

   Întrebare

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

   Răspuns

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

8. Fișa 8

   Întrebare

   SI base unit of mass?

   Răspuns

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

9. Fișa 9

   Întrebare

   Linear equation from slope and intercept?

   Răspuns

   $$y=mx+b$$

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

10. Fișa 10

    Întrebare

    Velocity after time $t$ under constant acceleration?

    Răspuns

    $$v=v_0+at$$

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

11. Fișa 11

    Întrebare

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

    Răspuns

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

12. Fișa 12

    Întrebare

    How is the FE reference handbook available during the exam?

    Răspuns

    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. Fișa 13

    Întrebare

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

    Răspuns

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

14. Fișa 14

    Întrebare

    SI base unit of time?

    Răspuns

    The second, symbol $s$.

15. Fișa 15

    Întrebare

    Linear equation from one point and a slope?

    Răspuns

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

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

16. Fișa 16

    Întrebare

    Position after time $t$ under constant acceleration?

    Răspuns

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

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

17. Fișa 17

    Întrebare

    A project assignment lies outside your competence. Proper response?

    Răspuns

    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. Fișa 18

    Întrebare

    SI base unit of electric current?

    Răspuns

    The ampere, symbol $A$.

19. Fișa 19

    Întrebare

    Future amount under simple interest?

    Răspuns

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

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

20. Fișa 20

    Întrebare

    Distance between two Cartesian points?

    Răspuns

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

    The coordinate components must use the same length unit.

21. Fișa 21

    Întrebare

    Constant-acceleration relation without elapsed time?

    Răspuns

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

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

22. Fișa 22

    Întrebare

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

    Răspuns

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

23. Fișa 23

    Întrebare

    Conditional probability of $A$ given $B$?

    Răspuns

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

    This requires $P(B)>0$.

24. Fișa 24

    Întrebare

    SI base unit of thermodynamic temperature?

    Răspuns

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

25. Fișa 25

    Întrebare

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

    Răspuns

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

26. Fișa 26

    Întrebare

    Midpoint of two Cartesian points?

    Răspuns

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

    Average corresponding coordinates.

27. Fișa 27

    Întrebare

    Linear momentum of a particle?

    Răspuns

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

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

28. Fișa 28

    Întrebare

    Future amount under compound interest?

    Răspuns

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

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

29. Fișa 29

    Întrebare

    Should an FE search workflow depend on Ctrl+F?

    Răspuns

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

30. Fișa 30

    Întrebare

    SI base unit of amount of substance?

    Răspuns

    The mole, symbol $mol$.

31. Fișa 31

    Întrebare

    Joint probability expressed with a conditional probability?

    Răspuns

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

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

32. Fișa 32

    Întrebare

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

    Răspuns

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

    The coordinate units and radius unit must match.

33. Fișa 33

    Întrebare

    Impulse-momentum relationship?

    Răspuns

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

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

34. Fișa 34

    Întrebare

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

    Răspuns

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

35. Fișa 35

    Întrebare

    SI base unit of luminous intensity?

    Răspuns

    The candela, symbol $cd$.

36. Fișa 36

    Întrebare

    Present worth of one future amount?

    Răspuns

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

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

37. Fișa 37

    Întrebare

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

    Răspuns

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

    This form requires $a\ne0$.

38. Fișa 38

    Întrebare

    When is total linear momentum conserved?

    Răspuns

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

39. Fișa 39

    Întrebare

    Why avoid memorizing FE handbook page numbers?

    Răspuns

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

40. Fișa 40

    Întrebare

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

    Răspuns

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

    Independence is not the same as mutual exclusivity.

41. Fișa 41

    Întrebare

    SI unit of frequency in base-unit form?

    Răspuns

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

42. Fișa 42

    Întrebare

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

    Răspuns

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

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

43. Fișa 43

    Întrebare

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

    Răspuns

    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. Fișa 44

    Întrebare

    Work done by a constant force through displacement?

    Răspuns

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

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

45. Fișa 45

    Întrebare

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

    Răspuns

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

46. Fișa 46

    Întrebare

    SI unit of force in base-unit form?

    Răspuns

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

47. Fișa 47

    Întrebare

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

    Răspuns

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

48. Fișa 48

    Întrebare

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

    Răspuns

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

    This requires $P(B)>0$.

49. Fișa 49

    Întrebare

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

    Răspuns

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

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

50. Fișa 50

    Întrebare

    Translational kinetic energy of a particle?

    Răspuns

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

    Mass and speed must use a coherent unit system.

51. Fișa 51

    Întrebare

    SI unit of pressure in force-area form?

    Răspuns

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

52. Fișa 52

    Întrebare

    Equivalent annual amount for present worth $P$?

    Răspuns

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

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

53. Fișa 53

    Întrebare

    May confidential client information be shared for personal benefit?

    Răspuns

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

54. Fișa 54

    Întrebare

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

    Răspuns

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

55. Fișa 55

    Întrebare

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

    Răspuns

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

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

56. Fișa 56

    Întrebare

    Net work-energy relationship for a particle?

    Răspuns

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

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

57. Fișa 57

    Întrebare

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

    Răspuns

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

    Use this when order matters and selection is without replacement.

58. Fișa 58

    Întrebare

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

    Răspuns

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

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

59. Fișa 59

    Întrebare

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

    Răspuns

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

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

60. Fișa 60

    Întrebare

    SI unit of energy in force-distance form?

    Răspuns

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

61. Fișa 61

    Întrebare

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

    Răspuns

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

62. Fișa 62

    Întrebare

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

    Răspuns

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

63. Fișa 63

    Întrebare

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

    Răspuns

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

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

64. Fișa 64

    Întrebare

    Change in gravitational potential energy near Earth's surface?

    Răspuns

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

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

65. Fișa 65

    Întrebare

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

    Răspuns

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

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

66. Fișa 66

    Întrebare

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

    Răspuns

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

    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. Fișa 67

    Întrebare

    A handbook search for an acronym fails. Next move?

    Răspuns

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

68. Fișa 68

    Întrebare

    SI unit of power in energy-time form?

    Răspuns

    The watt, $W=J/s$.

69. Fișa 69

    Întrebare

    Logarithm of a product?

    Răspuns

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

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

70. Fișa 70

    Întrebare

    Conditions for a binomial model?

    Răspuns

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

71. Fișa 71

    Întrebare

    Using another engineer's analysis in your deliverable?

    Răspuns

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

72. Fișa 72

    Întrebare

    SI unit of electric charge in current-time form?

    Răspuns

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

73. Fișa 73

    Întrebare

    Average power from work over elapsed time?

    Răspuns

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

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

74. Fișa 74

    Întrebare

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

    Răspuns

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

    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. Fișa 75

    Întrebare

    Logarithm of a positive quantity raised to a power?

    Răspuns

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

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

76. Fișa 76

    Întrebare

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

    Răspuns

    The volt, $V=J/C$.

77. Fișa 77

    Întrebare

    Instantaneous mechanical power delivered by a force?

    Răspuns

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

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

78. Fișa 78

    Întrebare

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

    Răspuns

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

79. Fișa 79

    Întrebare

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

    Răspuns

    $$E[X]=np$$

80. Fișa 80

    Întrebare

    SI unit of electrical resistance in voltage-current form?

    Răspuns

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

81. Fișa 81

    Întrebare

    Moment of a force about a point?

    Răspuns

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

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

82. Fișa 82

    Întrebare

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

    Răspuns

    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. Fișa 83

    Întrebare

    Inverse relationship between the natural log and exponential?

    Răspuns

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

    The second identity requires $x>0$.

84. Fișa 84

    Întrebare

    SI prefix giga?

    Răspuns

    $G=10^9$.

85. Fișa 85

    Întrebare

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

    Răspuns

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

    Use consistent angular sign convention and radians for angular measures.

86. Fișa 86

    Întrebare

    When should an engineer sign or seal technical work?

    Răspuns

    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. Fișa 87

    Întrebare

    Best memory target for returning to a handbook formula?

    Răspuns

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

88. Fișa 88

    Întrebare

    SI prefix mega?

    Răspuns

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

89. Fișa 89

    Întrebare

    Convert degrees to radians?

    Răspuns

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

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

90. Fișa 90

    Întrebare

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

    Răspuns

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

91. Fișa 91

    Întrebare

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

    Răspuns

    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. Fișa 92

    Întrebare

    Where do licensure and sealing requirements come from?

    Răspuns

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

93. Fișa 93

    Întrebare

    Rotational kinetic energy about a fixed axis?

    Răspuns

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

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

94. Fișa 94

    Întrebare

    SI prefix kilo?

    Răspuns

    $k=10^3$.

95. Fișa 95

    Întrebare

    Right-triangle definition of sine?

    Răspuns

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

96. Fișa 96

    Întrebare

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

    Răspuns

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

97. Fișa 97

    Întrebare

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

    Răspuns

    $$\sum M=I\alpha$$

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

98. Fișa 98

    Întrebare

    SI prefix milli?

    Răspuns

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

99. Fișa 99

    Întrebare

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

    Răspuns

    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. Fișa 100

     Întrebare

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

     Răspuns

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

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

101. Fișa 101

     Întrebare

     Right-triangle definition of cosine?

     Răspuns

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

102. Fișa 102

     Întrebare

     Force-displacement relation for an ideal linear spring?

     Răspuns

     $$F=-kx$$

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

103. Fișa 103

     Întrebare

     May qualifications or project responsibility be exaggerated in a proposal?

     Răspuns

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

104. Fișa 104

     Întrebare

     SI prefix micro?

     Răspuns

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

105. Fișa 105

     Întrebare

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

     Răspuns

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

106. Fișa 106

     Întrebare

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

     Răspuns

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

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

107. Fișa 107

     Întrebare

     Right-triangle definition of tangent?

     Răspuns

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

108. Fișa 108

     Întrebare

     Average normal stress under centered axial load?

     Răspuns

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

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

109. Fișa 109

     Întrebare

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

     Răspuns

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

110. Fișa 110

     Întrebare

     SI prefix nano?

     Răspuns

     $n=10^{-9}$.

111. Fișa 111

     Întrebare

     Fundamental Pythagorean trigonometric identity?

     Răspuns

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

112. Fișa 112

     Întrebare

     Engineering normal strain?

     Răspuns

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

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

113. Fișa 113

     Întrebare

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

     Răspuns

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

114. Fișa 114

     Întrebare

     Technical duty to an employer or client?

     Răspuns

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

115. Fișa 115

     Întrebare

     How does a length conversion factor apply to area?

     Răspuns

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

116. Fișa 116

     Întrebare

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

     Răspuns

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

117. Fișa 117

     Întrebare

     When is a Poisson count model reasonable?

     Răspuns

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

118. Fișa 118

     Întrebare

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

     Răspuns

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

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

119. Fișa 119

     Întrebare

     Linear elastic stress-strain relation in uniaxial loading?

     Răspuns

     $$\sigma=E\varepsilon$$

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

120. Fișa 120

     Întrebare

     How does a length conversion factor apply to volume?

     Răspuns

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

121. Fișa 121

     Întrebare

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

     Răspuns

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

122. Fișa 122

     Întrebare

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

     Răspuns

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

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

123. Fișa 123

     Întrebare

     A supervisor directs an illegal engineering action. Proper response?

     Răspuns

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

124. Fișa 124

     Întrebare

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

     Răspuns

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

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

125. Fișa 125

     Întrebare

     Mass density?

     Răspuns

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

     Use mass, not weight, in the numerator.

126. Fișa 126

     Întrebare

     Inches in one foot?

     Răspuns

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

127. Fișa 127

     Întrebare

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

     Răspuns

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

128. Fișa 128

     Întrebare

     How should subscripts be handled in a retrieved relationship?

     Răspuns

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

129. Fișa 129

     Întrebare

     Dot product from vector magnitudes and included angle?

     Răspuns

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

     The result is a scalar.

130. Fișa 130

     Întrebare

     Average normal pressure on an area?

     Răspuns

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

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

131. Fișa 131

     Întrebare

     Feet in one yard?

     Răspuns

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

132. Fișa 132

     Întrebare

     When are two interest rates equivalent?

     Răspuns

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

133. Fișa 133

     Întrebare

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

     Răspuns

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

134. Fișa 134

     Întrebare

     Expected value of a discrete random variable?

     Răspuns

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

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

135. Fișa 135

     Întrebare

     Dot-product test for perpendicular nonzero vectors?

     Răspuns

     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. Fișa 136

     Întrebare

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

     Răspuns

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

     Depth increases downward and the fluid is at rest.

137. Fișa 137

     Întrebare

     Feet in one statute mile?

     Răspuns

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

138. Fișa 138

     Întrebare

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

     Răspuns

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

     

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139. Fișa 139

     Întrebare

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

     Răspuns

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

140. Fișa 140

     Întrebare

     Magnitude of a vector cross product?

     Răspuns

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

     The direction follows the right-hand rule.

141. Fișa 141

     Întrebare

     Exact inch-to-metre relationship?

     Răspuns

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

142. Fișa 142

     Întrebare

     Volumetric flow rate through a cross-section?

     Răspuns

     $$Q=Av_{avg}$$

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

143. Fișa 143

     Întrebare

     Variance from the mean $\mu$?

     Răspuns

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

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

144. Fișa 144

     Întrebare

     Future-worth acceptance rule for an independent investment?

     Răspuns

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

145. Fișa 145

     Întrebare

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

     Răspuns

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

146. Fișa 146

     Întrebare

     Exact foot-to-metre relationship?

     Răspuns

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

147. Fișa 147

     Întrebare

     How should important uncertainty be communicated?

     Răspuns

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

148. Fișa 148

     Întrebare

     When is the matrix product $AB$ defined?

     Răspuns

     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. Fișa 149

     Întrebare

     Steady one-inlet, one-outlet mass continuity?

     Răspuns

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     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. Fișa 150

     Întrebare

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

     Răspuns

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

151. Fișa 151

     Întrebare

     Square feet in one acre?

     Răspuns

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

152. Fișa 152

     Întrebare

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

     Răspuns

     $$ad-bc$$

153. Fișa 153

     Întrebare

     Bernoulli relationship along a streamline for ideal steady flow?

     Răspuns

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

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

154. Fișa 154

     Întrebare

     May inconvenient measurements be discarded without a technical basis?

     Răspuns

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

155. Fișa 155

     Întrebare

     Annual-worth acceptance rule for an independent investment?

     Răspuns

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

156. Fișa 156

     Întrebare

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

     Răspuns

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

157. Fișa 157

     Întrebare

     Cubic metres in one litre?

     Răspuns

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

158. Fișa 158

     Întrebare

     What does a zero determinant mean for a square matrix?

     Răspuns

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

159. Fișa 159

     Întrebare

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

     Răspuns

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

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

160. Fișa 160

     Întrebare

     Unbiased sample variance for an independent sample from one population?

     Răspuns

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

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

161. Fișa 161

     Întrebare

     How should mutually exclusive alternatives be compared?

     Răspuns

     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. Fișa 162

     Întrebare

     Cubic centimetres in one millilitre?

     Răspuns

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

163. Fișa 163

     Întrebare

     Why keep contemporaneous engineering records?

     Răspuns

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

164. Fișa 164

     Întrebare

     Fast check after substituting into a handbook formula?

     Răspuns

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

165. Fișa 165

     Întrebare

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

     Răspuns

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

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

166. Fișa 166

     Întrebare

     Sensible heat for constant specific heat and no phase change?

     Răspuns

     $$Q=mc\Delta T$$

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

167. Fișa 167

     Întrebare

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

     Răspuns

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

     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. Fișa 168

     Întrebare

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

     Răspuns

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

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

169. Fișa 169

     Întrebare

     Purpose of incremental analysis for mutually exclusive alternatives?

     Răspuns

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

170. Fișa 170

     Întrebare

     Physical meaning of $dy/dx$?

     Răspuns

     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. Fișa 171

     Întrebare

     One-dimensional steady conduction through a plane wall?

     Răspuns

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

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

172. Fișa 172

     Întrebare

     When should you algebraically rearrange a handbook relationship?

     Răspuns

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

173. Fișa 173

     Întrebare

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

     Răspuns

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

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

174. Fișa 174

     Întrebare

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

     Răspuns

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

175. Fișa 175

     Întrebare

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

     Răspuns

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

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

176. Fișa 176

     Întrebare

     Convective heat-transfer rate at a surface?

     Răspuns

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

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

177. Fișa 177

     Întrebare

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

     Răspuns

     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. Fișa 178

     Întrebare

     Internal rate of return?

     Răspuns

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

179. Fișa 179

     Întrebare

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

     Răspuns

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

180. Fișa 180

     Întrebare

     Convert Celsius temperature to kelvin?

     Răspuns

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

     This conversion is for absolute temperature, not temperature difference.

181. Fișa 181

     Întrebare

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

     Răspuns

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

182. Fișa 182

     Întrebare

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

     Răspuns

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

183. Fișa 183

     Întrebare

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

     Răspuns

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

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

184. Fișa 184

     Întrebare

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

     Răspuns

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

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

185. Fișa 185

     Întrebare

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

     Răspuns

     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. Fișa 186

     Întrebare

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

     Răspuns

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

187. Fișa 187

     Întrebare

     Why inspect boundary or initial conditions near a formula?

     Răspuns

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

188. Fișa 188

     Întrebare

     Convert Celsius temperature to Fahrenheit?

     Răspuns

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

189. Fișa 189

     Întrebare

     Ethical basis for expert technical testimony?

     Răspuns

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

190. Fișa 190

     Întrebare

     Meaning of a breakeven value?

     Răspuns

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

191. Fișa 191

     Întrebare

     Derivative of $e^x$?

     Răspuns

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

192. Fișa 192

     Întrebare

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

     Răspuns

     $$\Delta E=Q-W$$

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

193. Fișa 193

     Întrebare

     Frequentist meaning of a 95% confidence procedure?

     Răspuns

     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. Fișa 194

     Întrebare

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

     Răspuns

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

195. Fișa 195

     Întrebare

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

     Răspuns

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

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

196. Fișa 196

     Întrebare

     Relationship between Celsius and kelvin temperature differences?

     Răspuns

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

197. Fișa 197

     Întrebare

     How should credit for team engineering work be assigned?

     Răspuns

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

198. Fișa 198

     Întrebare

     Main limitation of simple payback period?

     Răspuns

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

199. Fișa 199

     Întrebare

     Roles of the null and alternative hypotheses?

     Răspuns

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

200. Fișa 200

     Întrebare

     Ideal-gas equation of state?

     Răspuns

     $$pV=nRT$$

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

201. Fișa 201

     Întrebare

     First check when reading a handbook table?

     Răspuns

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

202. Fișa 202

     Întrebare

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

     Răspuns

     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. Fișa 203

     Întrebare

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

     Răspuns

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

204. Fișa 204

     Întrebare

     Convert Fahrenheit absolute temperature to Rankine?

     Răspuns

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

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. Fișa 205

     Întrebare

     Ohm's law for an ideal resistor?

     Răspuns

     $$V=IR$$

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

206. Fișa 206

     Întrebare

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

     Răspuns

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

207. Fișa 207

     Întrebare

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

     Răspuns

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

208. Fișa 208

     Întrebare

     Is a radian dimensionless?

     Răspuns

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

209. Fișa 209

     Întrebare

     Electrical power absorbed under the passive sign convention?

     Răspuns

     $$P=VI$$

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

210. Fișa 210

     Întrebare

     Meaning of a p-value?

     Răspuns

     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. Fișa 211

     Întrebare

     First check when reading a handbook graph?

     Răspuns

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

212. Fișa 212

     Întrebare

     Difference between mass and weight?

     Răspuns

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

213. Fișa 213

     Întrebare

     Kirchhoff's current law at a node?

     Răspuns

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

214. Fișa 214

     Întrebare

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

     Răspuns

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

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

215. Fișa 215

     Întrebare

     Opportunity cost?

     Răspuns

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

216. Fișa 216

     Întrebare

     Weight from mass in a gravitational field?

     Răspuns

     $$W=mg$$

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

217. Fișa 217

     Întrebare

     Kirchhoff's voltage law around a closed loop?

     Răspuns

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

218. Fișa 218

     Întrebare

     Decision rule using significance level $\alpha$?

     Răspuns

     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. Fișa 219

     Întrebare

     Can proprietary methods from a former employer be reused freely?

     Răspuns

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

220. Fișa 220

     Întrebare

     Pound-force to newtons?

     Răspuns

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

221. Fișa 221

     Întrebare

     When does a definite integral equal ordinary geometric area?

     Răspuns

     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. Fișa 222

     Întrebare

     Charge-voltage relation for an ideal capacitor?

     Răspuns

     $$q=CV$$

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

223. Fișa 223

     Întrebare

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

     Răspuns

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

224. Fișa 224

     Întrebare

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

     Răspuns

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

225. Fișa 225

     Întrebare

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

     Răspuns

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

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

226. Fișa 226

     Întrebare

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

     Răspuns

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

227. Fișa 227

     Întrebare

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

     Răspuns

     $$\tau=RC$$

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

228. Fișa 228

     Întrebare

     What physical quantity does pound-mass measure?

     Răspuns

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

229. Fișa 229

     Întrebare

     Type I error?

     Răspuns

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

230. Fișa 230

     Întrebare

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

     Răspuns

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

231. Fișa 231

     Întrebare

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

     Răspuns

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

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

232. Fișa 232

     Întrebare

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

     Răspuns

     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. Fișa 233

     Întrebare

     Recognizable form of a separable first-order differential equation?

     Răspuns

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

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

234. Fișa 234

     Întrebare

     Using unverified software output in a safety-relevant calculation?

     Răspuns

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

235. Fișa 235

     Întrebare

     Equivalent resistance of ideal resistors in series?

     Răspuns

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

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

236. Fișa 236

     Întrebare

     Pressure conversion from psi to pascals?

     Răspuns

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

237. Fișa 237

     Întrebare

     Type II error?

     Răspuns

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

238. Fișa 238

     Întrebare

     Useful flashcard to make after a failed handbook search?

     Răspuns

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

239. Fișa 239

     Întrebare

     Standard form of a first-order linear differential equation?

     Răspuns

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

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

240. Fișa 240

     Întrebare

     Equivalent resistance of ideal resistors in parallel?

     Răspuns

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

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

241. Fișa 241

     Întrebare

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

     Răspuns

     $$BV_k=B-kD$$

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

242. Fișa 242

     Întrebare

     Standard atmosphere in pascals?

     Răspuns

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

243. Fișa 243

     Întrebare

     Using AI-generated technical content in engineering work?

     Răspuns

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

244. Fișa 244

     Întrebare

     Trial form for a homogeneous linear ODE with constant coefficients?

     Răspuns

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

245. Fișa 245

     Întrebare

     Wave-speed relationship among frequency and wavelength?

     Răspuns

     $$v=f\lambda$$

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

246. Fișa 246

     Întrebare

     Statistical power?

     Răspuns

     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. Fișa 247

     Întrebare

     Bar in pascals?

     Răspuns

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

248. Fișa 248

     Întrebare

     How should handbook navigation be practiced before the FE exam?

     Răspuns

     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. Fișa 249

     Întrebare

     Is depreciation itself a cash outflow?

     Răspuns

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

250. Fișa 250

     Întrebare

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

     Răspuns

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

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

251. Fișa 251

     Întrebare

     Relationship between period and frequency?

     Răspuns

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

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

252. Fișa 252

     Întrebare

     How should foreseeable environmental harm enter an engineering decision?

     Răspuns

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

253. Fișa 253

     Întrebare

     Foot-pound-force in joules?

     Răspuns

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

254. Fișa 254

     Întrebare

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

     Răspuns

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

255. Fișa 255

     Întrebare

     When should you search instead of relying on recall?

     Răspuns

     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. Fișa 256

     Întrebare

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

     Răspuns

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

257. Fișa 257

     Întrebare

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

     Răspuns

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

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

258. Fișa 258

     Întrebare

     General material balance on a control volume?

     Răspuns

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

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

259. Fișa 259

     Întrebare

     Approximate joules in one International Table Btu?

     Răspuns

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

260. Fișa 260

     Întrebare

     What is the defender in a replacement analysis?

     Răspuns

     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. Fișa 261

     Întrebare

     Speaking publicly about a technical matter outside your expertise?

     Răspuns

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

262. Fișa 262

     Întrebare

     Single-interval trapezoidal approximation to an integral?

     Răspuns

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

     It is exact for linear $f$.

263. Fișa 263

     Întrebare

     Energy efficiency of a device?

     Răspuns

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

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

264. Fișa 264

     Întrebare

     Purpose of sensitivity analysis in engineering economics?

     Răspuns

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

265. Fișa 265

     Întrebare

     Can a strong correlation establish causation?

     Răspuns

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

266. Fișa 266

     Întrebare

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

     Răspuns

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

267. Fișa 267

     Întrebare

     Mechanical horsepower in watts?

     Răspuns

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

268. Fișa 268

     Întrebare

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

     Răspuns

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

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

269. Fișa 269

     Întrebare

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

     Răspuns

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

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

270. Fișa 270

     Întrebare

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

     Răspuns

     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. Fișa 271

     Întrebare

     Kilowatt-hour in joules?

     Răspuns

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

272. Fișa 272

     Întrebare

     Percent error relative to an accepted nonzero value?

     Răspuns

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

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

273. Fișa 273

     Întrebare

     Does legal compliance alone settle an engineering ethics question?

     Răspuns

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

274. Fișa 274

     Întrebare

     Does handbook fluency replace discipline-specific problem practice?

     Răspuns

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

275. Fișa 275

     Întrebare

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

     Răspuns

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

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

276. Fișa 276

     Întrebare

     Dimensional requirement for a physically meaningful additive equation?

     Răspuns

     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.