FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

Bu destedeki kartlar

1. Kart 1

   Soru

   SI base unit of length?

   Cevap

   The metre, symbol $m$.

2. Kart 2

   Soru

   Slope between two points?

   Cevap

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

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

3. Kart 3

   Soru

   Net force relationship for constant mass in an inertial frame?

   Cevap

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

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

4. Kart 4

   Soru

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

   Cevap

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

5. Kart 5

   Soru

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

   Cevap

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

6. Kart 6

   Soru

   Probability of the complement of event $A$?

   Cevap

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

7. Kart 7

   Soru

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

   Cevap

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

8. Kart 8

   Soru

   SI base unit of mass?

   Cevap

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

9. Kart 9

   Soru

   Linear equation from slope and intercept?

   Cevap

   $$y=mx+b$$

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

10. Kart 10

    Soru

    Velocity after time $t$ under constant acceleration?

    Cevap

    $$v=v_0+at$$

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

11. Kart 11

    Soru

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

    Cevap

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

12. Kart 12

    Soru

    How is the FE reference handbook available during the exam?

    Cevap

    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. Kart 13

    Soru

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

    Cevap

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

14. Kart 14

    Soru

    SI base unit of time?

    Cevap

    The second, symbol $s$.

15. Kart 15

    Soru

    Linear equation from one point and a slope?

    Cevap

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

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

16. Kart 16

    Soru

    Position after time $t$ under constant acceleration?

    Cevap

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

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

17. Kart 17

    Soru

    A project assignment lies outside your competence. Proper response?

    Cevap

    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. Kart 18

    Soru

    SI base unit of electric current?

    Cevap

    The ampere, symbol $A$.

19. Kart 19

    Soru

    Future amount under simple interest?

    Cevap

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

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

20. Kart 20

    Soru

    Distance between two Cartesian points?

    Cevap

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

    The coordinate components must use the same length unit.

21. Kart 21

    Soru

    Constant-acceleration relation without elapsed time?

    Cevap

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

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

22. Kart 22

    Soru

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

    Cevap

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

23. Kart 23

    Soru

    Conditional probability of $A$ given $B$?

    Cevap

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

    This requires $P(B)>0$.

24. Kart 24

    Soru

    SI base unit of thermodynamic temperature?

    Cevap

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

25. Kart 25

    Soru

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

    Cevap

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

26. Kart 26

    Soru

    Midpoint of two Cartesian points?

    Cevap

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

    Average corresponding coordinates.

27. Kart 27

    Soru

    Linear momentum of a particle?

    Cevap

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

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

28. Kart 28

    Soru

    Future amount under compound interest?

    Cevap

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

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

29. Kart 29

    Soru

    Should an FE search workflow depend on Ctrl+F?

    Cevap

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

30. Kart 30

    Soru

    SI base unit of amount of substance?

    Cevap

    The mole, symbol $mol$.

31. Kart 31

    Soru

    Joint probability expressed with a conditional probability?

    Cevap

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

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

32. Kart 32

    Soru

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

    Cevap

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

    The coordinate units and radius unit must match.

33. Kart 33

    Soru

    Impulse-momentum relationship?

    Cevap

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

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

34. Kart 34

    Soru

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

    Cevap

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

35. Kart 35

    Soru

    SI base unit of luminous intensity?

    Cevap

    The candela, symbol $cd$.

36. Kart 36

    Soru

    Present worth of one future amount?

    Cevap

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

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

37. Kart 37

    Soru

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

    Cevap

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

    This form requires $a\ne0$.

38. Kart 38

    Soru

    When is total linear momentum conserved?

    Cevap

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

39. Kart 39

    Soru

    Why avoid memorizing FE handbook page numbers?

    Cevap

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

40. Kart 40

    Soru

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

    Cevap

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

    Independence is not the same as mutual exclusivity.

41. Kart 41

    Soru

    SI unit of frequency in base-unit form?

    Cevap

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

42. Kart 42

    Soru

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

    Cevap

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

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

43. Kart 43

    Soru

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

    Cevap

    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. Kart 44

    Soru

    Work done by a constant force through displacement?

    Cevap

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

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

45. Kart 45

    Soru

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

    Cevap

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

46. Kart 46

    Soru

    SI unit of force in base-unit form?

    Cevap

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

47. Kart 47

    Soru

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

    Cevap

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

48. Kart 48

    Soru

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

    Cevap

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

    This requires $P(B)>0$.

49. Kart 49

    Soru

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

    Cevap

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

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

50. Kart 50

    Soru

    Translational kinetic energy of a particle?

    Cevap

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

    Mass and speed must use a coherent unit system.

51. Kart 51

    Soru

    SI unit of pressure in force-area form?

    Cevap

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

52. Kart 52

    Soru

    Equivalent annual amount for present worth $P$?

    Cevap

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

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

53. Kart 53

    Soru

    May confidential client information be shared for personal benefit?

    Cevap

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

54. Kart 54

    Soru

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

    Cevap

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

55. Kart 55

    Soru

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

    Cevap

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

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

56. Kart 56

    Soru

    Net work-energy relationship for a particle?

    Cevap

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

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

57. Kart 57

    Soru

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

    Cevap

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

    Use this when order matters and selection is without replacement.

58. Kart 58

    Soru

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

    Cevap

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

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

59. Kart 59

    Soru

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

    Cevap

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

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

60. Kart 60

    Soru

    SI unit of energy in force-distance form?

    Cevap

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

61. Kart 61

    Soru

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

    Cevap

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

62. Kart 62

    Soru

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

    Cevap

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

63. Kart 63

    Soru

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

    Cevap

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

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

64. Kart 64

    Soru

    Change in gravitational potential energy near Earth's surface?

    Cevap

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

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

65. Kart 65

    Soru

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

    Cevap

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

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

66. Kart 66

    Soru

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

    Cevap

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

    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. Kart 67

    Soru

    A handbook search for an acronym fails. Next move?

    Cevap

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

68. Kart 68

    Soru

    SI unit of power in energy-time form?

    Cevap

    The watt, $W=J/s$.

69. Kart 69

    Soru

    Logarithm of a product?

    Cevap

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

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

70. Kart 70

    Soru

    Conditions for a binomial model?

    Cevap

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

71. Kart 71

    Soru

    Using another engineer's analysis in your deliverable?

    Cevap

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

72. Kart 72

    Soru

    SI unit of electric charge in current-time form?

    Cevap

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

73. Kart 73

    Soru

    Average power from work over elapsed time?

    Cevap

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

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

74. Kart 74

    Soru

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

    Cevap

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

    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. Kart 75

    Soru

    Logarithm of a positive quantity raised to a power?

    Cevap

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

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

76. Kart 76

    Soru

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

    Cevap

    The volt, $V=J/C$.

77. Kart 77

    Soru

    Instantaneous mechanical power delivered by a force?

    Cevap

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

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

78. Kart 78

    Soru

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

    Cevap

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

79. Kart 79

    Soru

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

    Cevap

    $$E[X]=np$$

80. Kart 80

    Soru

    SI unit of electrical resistance in voltage-current form?

    Cevap

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

81. Kart 81

    Soru

    Moment of a force about a point?

    Cevap

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

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

82. Kart 82

    Soru

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

    Cevap

    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. Kart 83

    Soru

    Inverse relationship between the natural log and exponential?

    Cevap

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

    The second identity requires $x>0$.

84. Kart 84

    Soru

    SI prefix giga?

    Cevap

    $G=10^9$.

85. Kart 85

    Soru

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

    Cevap

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

    Use consistent angular sign convention and radians for angular measures.

86. Kart 86

    Soru

    When should an engineer sign or seal technical work?

    Cevap

    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. Kart 87

    Soru

    Best memory target for returning to a handbook formula?

    Cevap

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

88. Kart 88

    Soru

    SI prefix mega?

    Cevap

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

89. Kart 89

    Soru

    Convert degrees to radians?

    Cevap

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

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

90. Kart 90

    Soru

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

    Cevap

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

91. Kart 91

    Soru

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

    Cevap

    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. Kart 92

    Soru

    Where do licensure and sealing requirements come from?

    Cevap

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

93. Kart 93

    Soru

    Rotational kinetic energy about a fixed axis?

    Cevap

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

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

94. Kart 94

    Soru

    SI prefix kilo?

    Cevap

    $k=10^3$.

95. Kart 95

    Soru

    Right-triangle definition of sine?

    Cevap

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

96. Kart 96

    Soru

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

    Cevap

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

97. Kart 97

    Soru

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

    Cevap

    $$\sum M=I\alpha$$

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

98. Kart 98

    Soru

    SI prefix milli?

    Cevap

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

99. Kart 99

    Soru

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

    Cevap

    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. Kart 100

     Soru

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

     Cevap

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

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

101. Kart 101

     Soru

     Right-triangle definition of cosine?

     Cevap

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

102. Kart 102

     Soru

     Force-displacement relation for an ideal linear spring?

     Cevap

     $$F=-kx$$

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

103. Kart 103

     Soru

     May qualifications or project responsibility be exaggerated in a proposal?

     Cevap

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

104. Kart 104

     Soru

     SI prefix micro?

     Cevap

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

105. Kart 105

     Soru

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

     Cevap

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

106. Kart 106

     Soru

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

     Cevap

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

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

107. Kart 107

     Soru

     Right-triangle definition of tangent?

     Cevap

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

108. Kart 108

     Soru

     Average normal stress under centered axial load?

     Cevap

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

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

109. Kart 109

     Soru

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

     Cevap

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

110. Kart 110

     Soru

     SI prefix nano?

     Cevap

     $n=10^{-9}$.

111. Kart 111

     Soru

     Fundamental Pythagorean trigonometric identity?

     Cevap

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

112. Kart 112

     Soru

     Engineering normal strain?

     Cevap

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

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

113. Kart 113

     Soru

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

     Cevap

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

114. Kart 114

     Soru

     Technical duty to an employer or client?

     Cevap

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

115. Kart 115

     Soru

     How does a length conversion factor apply to area?

     Cevap

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

116. Kart 116

     Soru

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

     Cevap

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

117. Kart 117

     Soru

     When is a Poisson count model reasonable?

     Cevap

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

118. Kart 118

     Soru

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

     Cevap

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

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

119. Kart 119

     Soru

     Linear elastic stress-strain relation in uniaxial loading?

     Cevap

     $$\sigma=E\varepsilon$$

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

120. Kart 120

     Soru

     How does a length conversion factor apply to volume?

     Cevap

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

121. Kart 121

     Soru

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

     Cevap

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

122. Kart 122

     Soru

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

     Cevap

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

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

123. Kart 123

     Soru

     A supervisor directs an illegal engineering action. Proper response?

     Cevap

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

124. Kart 124

     Soru

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

     Cevap

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

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

125. Kart 125

     Soru

     Mass density?

     Cevap

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

     Use mass, not weight, in the numerator.

126. Kart 126

     Soru

     Inches in one foot?

     Cevap

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

127. Kart 127

     Soru

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

     Cevap

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

128. Kart 128

     Soru

     How should subscripts be handled in a retrieved relationship?

     Cevap

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

129. Kart 129

     Soru

     Dot product from vector magnitudes and included angle?

     Cevap

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

     The result is a scalar.

130. Kart 130

     Soru

     Average normal pressure on an area?

     Cevap

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

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

131. Kart 131

     Soru

     Feet in one yard?

     Cevap

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

132. Kart 132

     Soru

     When are two interest rates equivalent?

     Cevap

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

133. Kart 133

     Soru

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

     Cevap

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

134. Kart 134

     Soru

     Expected value of a discrete random variable?

     Cevap

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

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

135. Kart 135

     Soru

     Dot-product test for perpendicular nonzero vectors?

     Cevap

     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. Kart 136

     Soru

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

     Cevap

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

     Depth increases downward and the fluid is at rest.

137. Kart 137

     Soru

     Feet in one statute mile?

     Cevap

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

138. Kart 138

     Soru

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

     Cevap

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

     

     276 kart

     FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

     Bu desteyle ücretsiz çalış

     Nibomo açılır ve hemen çalışmaya başlayabilirsiniz.

139. Kart 139

     Soru

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

     Cevap

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

140. Kart 140

     Soru

     Magnitude of a vector cross product?

     Cevap

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

     The direction follows the right-hand rule.

141. Kart 141

     Soru

     Exact inch-to-metre relationship?

     Cevap

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

142. Kart 142

     Soru

     Volumetric flow rate through a cross-section?

     Cevap

     $$Q=Av_{avg}$$

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

143. Kart 143

     Soru

     Variance from the mean $\mu$?

     Cevap

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

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

144. Kart 144

     Soru

     Future-worth acceptance rule for an independent investment?

     Cevap

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

145. Kart 145

     Soru

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

     Cevap

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

146. Kart 146

     Soru

     Exact foot-to-metre relationship?

     Cevap

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

147. Kart 147

     Soru

     How should important uncertainty be communicated?

     Cevap

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

148. Kart 148

     Soru

     When is the matrix product $AB$ defined?

     Cevap

     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. Kart 149

     Soru

     Steady one-inlet, one-outlet mass continuity?

     Cevap

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     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. Kart 150

     Soru

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

     Cevap

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

151. Kart 151

     Soru

     Square feet in one acre?

     Cevap

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

152. Kart 152

     Soru

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

     Cevap

     $$ad-bc$$

153. Kart 153

     Soru

     Bernoulli relationship along a streamline for ideal steady flow?

     Cevap

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

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

154. Kart 154

     Soru

     May inconvenient measurements be discarded without a technical basis?

     Cevap

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

155. Kart 155

     Soru

     Annual-worth acceptance rule for an independent investment?

     Cevap

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

156. Kart 156

     Soru

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

     Cevap

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

157. Kart 157

     Soru

     Cubic metres in one litre?

     Cevap

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

158. Kart 158

     Soru

     What does a zero determinant mean for a square matrix?

     Cevap

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

159. Kart 159

     Soru

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

     Cevap

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

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

160. Kart 160

     Soru

     Unbiased sample variance for an independent sample from one population?

     Cevap

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

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

161. Kart 161

     Soru

     How should mutually exclusive alternatives be compared?

     Cevap

     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. Kart 162

     Soru

     Cubic centimetres in one millilitre?

     Cevap

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

163. Kart 163

     Soru

     Why keep contemporaneous engineering records?

     Cevap

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

164. Kart 164

     Soru

     Fast check after substituting into a handbook formula?

     Cevap

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

165. Kart 165

     Soru

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

     Cevap

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

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

166. Kart 166

     Soru

     Sensible heat for constant specific heat and no phase change?

     Cevap

     $$Q=mc\Delta T$$

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

167. Kart 167

     Soru

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

     Cevap

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

     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. Kart 168

     Soru

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

     Cevap

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

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

169. Kart 169

     Soru

     Purpose of incremental analysis for mutually exclusive alternatives?

     Cevap

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

170. Kart 170

     Soru

     Physical meaning of $dy/dx$?

     Cevap

     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. Kart 171

     Soru

     One-dimensional steady conduction through a plane wall?

     Cevap

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

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

172. Kart 172

     Soru

     When should you algebraically rearrange a handbook relationship?

     Cevap

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

173. Kart 173

     Soru

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

     Cevap

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

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

174. Kart 174

     Soru

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

     Cevap

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

175. Kart 175

     Soru

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

     Cevap

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

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

176. Kart 176

     Soru

     Convective heat-transfer rate at a surface?

     Cevap

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

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

177. Kart 177

     Soru

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

     Cevap

     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. Kart 178

     Soru

     Internal rate of return?

     Cevap

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

179. Kart 179

     Soru

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

     Cevap

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

180. Kart 180

     Soru

     Convert Celsius temperature to kelvin?

     Cevap

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

     This conversion is for absolute temperature, not temperature difference.

181. Kart 181

     Soru

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

     Cevap

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

182. Kart 182

     Soru

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

     Cevap

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

183. Kart 183

     Soru

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

     Cevap

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

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

184. Kart 184

     Soru

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

     Cevap

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

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

185. Kart 185

     Soru

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

     Cevap

     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. Kart 186

     Soru

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

     Cevap

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

187. Kart 187

     Soru

     Why inspect boundary or initial conditions near a formula?

     Cevap

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

188. Kart 188

     Soru

     Convert Celsius temperature to Fahrenheit?

     Cevap

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

189. Kart 189

     Soru

     Ethical basis for expert technical testimony?

     Cevap

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

190. Kart 190

     Soru

     Meaning of a breakeven value?

     Cevap

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

191. Kart 191

     Soru

     Derivative of $e^x$?

     Cevap

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

192. Kart 192

     Soru

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

     Cevap

     $$\Delta E=Q-W$$

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

193. Kart 193

     Soru

     Frequentist meaning of a 95% confidence procedure?

     Cevap

     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. Kart 194

     Soru

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

     Cevap

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

195. Kart 195

     Soru

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

     Cevap

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

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

196. Kart 196

     Soru

     Relationship between Celsius and kelvin temperature differences?

     Cevap

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

197. Kart 197

     Soru

     How should credit for team engineering work be assigned?

     Cevap

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

198. Kart 198

     Soru

     Main limitation of simple payback period?

     Cevap

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

199. Kart 199

     Soru

     Roles of the null and alternative hypotheses?

     Cevap

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

200. Kart 200

     Soru

     Ideal-gas equation of state?

     Cevap

     $$pV=nRT$$

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

201. Kart 201

     Soru

     First check when reading a handbook table?

     Cevap

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

202. Kart 202

     Soru

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

     Cevap

     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. Kart 203

     Soru

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

     Cevap

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

204. Kart 204

     Soru

     Convert Fahrenheit absolute temperature to Rankine?

     Cevap

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

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. Kart 205

     Soru

     Ohm's law for an ideal resistor?

     Cevap

     $$V=IR$$

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

206. Kart 206

     Soru

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

     Cevap

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

207. Kart 207

     Soru

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

     Cevap

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

208. Kart 208

     Soru

     Is a radian dimensionless?

     Cevap

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

209. Kart 209

     Soru

     Electrical power absorbed under the passive sign convention?

     Cevap

     $$P=VI$$

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

210. Kart 210

     Soru

     Meaning of a p-value?

     Cevap

     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. Kart 211

     Soru

     First check when reading a handbook graph?

     Cevap

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

212. Kart 212

     Soru

     Difference between mass and weight?

     Cevap

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

213. Kart 213

     Soru

     Kirchhoff's current law at a node?

     Cevap

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

214. Kart 214

     Soru

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

     Cevap

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

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

215. Kart 215

     Soru

     Opportunity cost?

     Cevap

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

216. Kart 216

     Soru

     Weight from mass in a gravitational field?

     Cevap

     $$W=mg$$

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

217. Kart 217

     Soru

     Kirchhoff's voltage law around a closed loop?

     Cevap

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

218. Kart 218

     Soru

     Decision rule using significance level $\alpha$?

     Cevap

     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. Kart 219

     Soru

     Can proprietary methods from a former employer be reused freely?

     Cevap

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

220. Kart 220

     Soru

     Pound-force to newtons?

     Cevap

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

221. Kart 221

     Soru

     When does a definite integral equal ordinary geometric area?

     Cevap

     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. Kart 222

     Soru

     Charge-voltage relation for an ideal capacitor?

     Cevap

     $$q=CV$$

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

223. Kart 223

     Soru

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

     Cevap

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

224. Kart 224

     Soru

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

     Cevap

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

225. Kart 225

     Soru

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

     Cevap

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

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

226. Kart 226

     Soru

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

     Cevap

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

227. Kart 227

     Soru

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

     Cevap

     $$\tau=RC$$

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

228. Kart 228

     Soru

     What physical quantity does pound-mass measure?

     Cevap

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

229. Kart 229

     Soru

     Type I error?

     Cevap

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

230. Kart 230

     Soru

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

     Cevap

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

231. Kart 231

     Soru

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

     Cevap

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

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

232. Kart 232

     Soru

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

     Cevap

     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. Kart 233

     Soru

     Recognizable form of a separable first-order differential equation?

     Cevap

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

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

234. Kart 234

     Soru

     Using unverified software output in a safety-relevant calculation?

     Cevap

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

235. Kart 235

     Soru

     Equivalent resistance of ideal resistors in series?

     Cevap

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

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

236. Kart 236

     Soru

     Pressure conversion from psi to pascals?

     Cevap

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

237. Kart 237

     Soru

     Type II error?

     Cevap

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

238. Kart 238

     Soru

     Useful flashcard to make after a failed handbook search?

     Cevap

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

239. Kart 239

     Soru

     Standard form of a first-order linear differential equation?

     Cevap

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

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

240. Kart 240

     Soru

     Equivalent resistance of ideal resistors in parallel?

     Cevap

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

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

241. Kart 241

     Soru

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

     Cevap

     $$BV_k=B-kD$$

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

242. Kart 242

     Soru

     Standard atmosphere in pascals?

     Cevap

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

243. Kart 243

     Soru

     Using AI-generated technical content in engineering work?

     Cevap

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

244. Kart 244

     Soru

     Trial form for a homogeneous linear ODE with constant coefficients?

     Cevap

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

245. Kart 245

     Soru

     Wave-speed relationship among frequency and wavelength?

     Cevap

     $$v=f\lambda$$

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

246. Kart 246

     Soru

     Statistical power?

     Cevap

     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. Kart 247

     Soru

     Bar in pascals?

     Cevap

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

248. Kart 248

     Soru

     How should handbook navigation be practiced before the FE exam?

     Cevap

     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. Kart 249

     Soru

     Is depreciation itself a cash outflow?

     Cevap

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

250. Kart 250

     Soru

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

     Cevap

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

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

251. Kart 251

     Soru

     Relationship between period and frequency?

     Cevap

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

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

252. Kart 252

     Soru

     How should foreseeable environmental harm enter an engineering decision?

     Cevap

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

253. Kart 253

     Soru

     Foot-pound-force in joules?

     Cevap

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

254. Kart 254

     Soru

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

     Cevap

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

255. Kart 255

     Soru

     When should you search instead of relying on recall?

     Cevap

     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. Kart 256

     Soru

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

     Cevap

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

257. Kart 257

     Soru

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

     Cevap

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

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

258. Kart 258

     Soru

     General material balance on a control volume?

     Cevap

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

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

259. Kart 259

     Soru

     Approximate joules in one International Table Btu?

     Cevap

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

260. Kart 260

     Soru

     What is the defender in a replacement analysis?

     Cevap

     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. Kart 261

     Soru

     Speaking publicly about a technical matter outside your expertise?

     Cevap

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

262. Kart 262

     Soru

     Single-interval trapezoidal approximation to an integral?

     Cevap

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

     It is exact for linear $f$.

263. Kart 263

     Soru

     Energy efficiency of a device?

     Cevap

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

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

264. Kart 264

     Soru

     Purpose of sensitivity analysis in engineering economics?

     Cevap

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

265. Kart 265

     Soru

     Can a strong correlation establish causation?

     Cevap

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

266. Kart 266

     Soru

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

     Cevap

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

267. Kart 267

     Soru

     Mechanical horsepower in watts?

     Cevap

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

268. Kart 268

     Soru

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

     Cevap

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

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

269. Kart 269

     Soru

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

     Cevap

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

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

270. Kart 270

     Soru

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

     Cevap

     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. Kart 271

     Soru

     Kilowatt-hour in joules?

     Cevap

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

272. Kart 272

     Soru

     Percent error relative to an accepted nonzero value?

     Cevap

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

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

273. Kart 273

     Soru

     Does legal compliance alone settle an engineering ethics question?

     Cevap

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

274. Kart 274

     Soru

     Does handbook fluency replace discipline-specific problem practice?

     Cevap

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

275. Kart 275

     Soru

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

     Cevap

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

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

276. Kart 276

     Soru

     Dimensional requirement for a physically meaningful additive equation?

     Cevap

     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.