FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

Kártyák ebben a pakliban

1. 1. kártya

   Kérdés

   SI base unit of length?

   Válasz

   The metre, symbol $m$.

2. 2. kártya

   Kérdés

   Slope between two points?

   Válasz

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

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

3. 3. kártya

   Kérdés

   Net force relationship for constant mass in an inertial frame?

   Válasz

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

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

4. 4. kártya

   Kérdés

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

   Válasz

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

5. 5. kártya

   Kérdés

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

   Válasz

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

6. 6. kártya

   Kérdés

   Probability of the complement of event $A$?

   Válasz

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

7. 7. kártya

   Kérdés

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

   Válasz

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

8. 8. kártya

   Kérdés

   SI base unit of mass?

   Válasz

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

9. 9. kártya

   Kérdés

   Linear equation from slope and intercept?

   Válasz

   $$y=mx+b$$

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

10. 10. kártya

    Kérdés

    Velocity after time $t$ under constant acceleration?

    Válasz

    $$v=v_0+at$$

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

11. 11. kártya

    Kérdés

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

    Válasz

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

12. 12. kártya

    Kérdés

    How is the FE reference handbook available during the exam?

    Válasz

    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. 13. kártya

    Kérdés

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

    Válasz

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

14. 14. kártya

    Kérdés

    SI base unit of time?

    Válasz

    The second, symbol $s$.

15. 15. kártya

    Kérdés

    Linear equation from one point and a slope?

    Válasz

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

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

16. 16. kártya

    Kérdés

    Position after time $t$ under constant acceleration?

    Válasz

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

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

17. 17. kártya

    Kérdés

    A project assignment lies outside your competence. Proper response?

    Válasz

    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. 18. kártya

    Kérdés

    SI base unit of electric current?

    Válasz

    The ampere, symbol $A$.

19. 19. kártya

    Kérdés

    Future amount under simple interest?

    Válasz

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

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

20. 20. kártya

    Kérdés

    Distance between two Cartesian points?

    Válasz

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

    The coordinate components must use the same length unit.

21. 21. kártya

    Kérdés

    Constant-acceleration relation without elapsed time?

    Válasz

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

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

22. 22. kártya

    Kérdés

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

    Válasz

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

23. 23. kártya

    Kérdés

    Conditional probability of $A$ given $B$?

    Válasz

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

    This requires $P(B)>0$.

24. 24. kártya

    Kérdés

    SI base unit of thermodynamic temperature?

    Válasz

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

25. 25. kártya

    Kérdés

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

    Válasz

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

26. 26. kártya

    Kérdés

    Midpoint of two Cartesian points?

    Válasz

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

    Average corresponding coordinates.

27. 27. kártya

    Kérdés

    Linear momentum of a particle?

    Válasz

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

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

28. 28. kártya

    Kérdés

    Future amount under compound interest?

    Válasz

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

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

29. 29. kártya

    Kérdés

    Should an FE search workflow depend on Ctrl+F?

    Válasz

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

30. 30. kártya

    Kérdés

    SI base unit of amount of substance?

    Válasz

    The mole, symbol $mol$.

31. 31. kártya

    Kérdés

    Joint probability expressed with a conditional probability?

    Válasz

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

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

32. 32. kártya

    Kérdés

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

    Válasz

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

    The coordinate units and radius unit must match.

33. 33. kártya

    Kérdés

    Impulse-momentum relationship?

    Válasz

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

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

34. 34. kártya

    Kérdés

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

    Válasz

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

35. 35. kártya

    Kérdés

    SI base unit of luminous intensity?

    Válasz

    The candela, symbol $cd$.

36. 36. kártya

    Kérdés

    Present worth of one future amount?

    Válasz

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

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

37. 37. kártya

    Kérdés

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

    Válasz

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

    This form requires $a\ne0$.

38. 38. kártya

    Kérdés

    When is total linear momentum conserved?

    Válasz

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

39. 39. kártya

    Kérdés

    Why avoid memorizing FE handbook page numbers?

    Válasz

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

40. 40. kártya

    Kérdés

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

    Válasz

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

    Independence is not the same as mutual exclusivity.

41. 41. kártya

    Kérdés

    SI unit of frequency in base-unit form?

    Válasz

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

42. 42. kártya

    Kérdés

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

    Válasz

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

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

43. 43. kártya

    Kérdés

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

    Válasz

    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. 44. kártya

    Kérdés

    Work done by a constant force through displacement?

    Válasz

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

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

45. 45. kártya

    Kérdés

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

    Válasz

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

46. 46. kártya

    Kérdés

    SI unit of force in base-unit form?

    Válasz

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

47. 47. kártya

    Kérdés

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

    Válasz

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

48. 48. kártya

    Kérdés

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

    Válasz

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

    This requires $P(B)>0$.

49. 49. kártya

    Kérdés

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

    Válasz

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

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

50. 50. kártya

    Kérdés

    Translational kinetic energy of a particle?

    Válasz

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

    Mass and speed must use a coherent unit system.

51. 51. kártya

    Kérdés

    SI unit of pressure in force-area form?

    Válasz

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

52. 52. kártya

    Kérdés

    Equivalent annual amount for present worth $P$?

    Válasz

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

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

53. 53. kártya

    Kérdés

    May confidential client information be shared for personal benefit?

    Válasz

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

54. 54. kártya

    Kérdés

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

    Válasz

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

55. 55. kártya

    Kérdés

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

    Válasz

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

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

56. 56. kártya

    Kérdés

    Net work-energy relationship for a particle?

    Válasz

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

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

57. 57. kártya

    Kérdés

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

    Válasz

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

    Use this when order matters and selection is without replacement.

58. 58. kártya

    Kérdés

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

    Válasz

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

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

59. 59. kártya

    Kérdés

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

    Válasz

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

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

60. 60. kártya

    Kérdés

    SI unit of energy in force-distance form?

    Válasz

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

61. 61. kártya

    Kérdés

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

    Válasz

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

62. 62. kártya

    Kérdés

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

    Válasz

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

63. 63. kártya

    Kérdés

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

    Válasz

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

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

64. 64. kártya

    Kérdés

    Change in gravitational potential energy near Earth's surface?

    Válasz

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

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

65. 65. kártya

    Kérdés

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

    Válasz

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

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

66. 66. kártya

    Kérdés

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

    Válasz

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

    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. 67. kártya

    Kérdés

    A handbook search for an acronym fails. Next move?

    Válasz

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

68. 68. kártya

    Kérdés

    SI unit of power in energy-time form?

    Válasz

    The watt, $W=J/s$.

69. 69. kártya

    Kérdés

    Logarithm of a product?

    Válasz

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

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

70. 70. kártya

    Kérdés

    Conditions for a binomial model?

    Válasz

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

71. 71. kártya

    Kérdés

    Using another engineer's analysis in your deliverable?

    Válasz

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

72. 72. kártya

    Kérdés

    SI unit of electric charge in current-time form?

    Válasz

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

73. 73. kártya

    Kérdés

    Average power from work over elapsed time?

    Válasz

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

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

74. 74. kártya

    Kérdés

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

    Válasz

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

    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. 75. kártya

    Kérdés

    Logarithm of a positive quantity raised to a power?

    Válasz

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

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

76. 76. kártya

    Kérdés

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

    Válasz

    The volt, $V=J/C$.

77. 77. kártya

    Kérdés

    Instantaneous mechanical power delivered by a force?

    Válasz

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

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

78. 78. kártya

    Kérdés

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

    Válasz

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

79. 79. kártya

    Kérdés

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

    Válasz

    $$E[X]=np$$

80. 80. kártya

    Kérdés

    SI unit of electrical resistance in voltage-current form?

    Válasz

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

81. 81. kártya

    Kérdés

    Moment of a force about a point?

    Válasz

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

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

82. 82. kártya

    Kérdés

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

    Válasz

    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. 83. kártya

    Kérdés

    Inverse relationship between the natural log and exponential?

    Válasz

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

    The second identity requires $x>0$.

84. 84. kártya

    Kérdés

    SI prefix giga?

    Válasz

    $G=10^9$.

85. 85. kártya

    Kérdés

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

    Válasz

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

    Use consistent angular sign convention and radians for angular measures.

86. 86. kártya

    Kérdés

    When should an engineer sign or seal technical work?

    Válasz

    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. 87. kártya

    Kérdés

    Best memory target for returning to a handbook formula?

    Válasz

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

88. 88. kártya

    Kérdés

    SI prefix mega?

    Válasz

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

89. 89. kártya

    Kérdés

    Convert degrees to radians?

    Válasz

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

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

90. 90. kártya

    Kérdés

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

    Válasz

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

91. 91. kártya

    Kérdés

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

    Válasz

    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. 92. kártya

    Kérdés

    Where do licensure and sealing requirements come from?

    Válasz

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

93. 93. kártya

    Kérdés

    Rotational kinetic energy about a fixed axis?

    Válasz

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

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

94. 94. kártya

    Kérdés

    SI prefix kilo?

    Válasz

    $k=10^3$.

95. 95. kártya

    Kérdés

    Right-triangle definition of sine?

    Válasz

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

96. 96. kártya

    Kérdés

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

    Válasz

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

97. 97. kártya

    Kérdés

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

    Válasz

    $$\sum M=I\alpha$$

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

98. 98. kártya

    Kérdés

    SI prefix milli?

    Válasz

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

99. 99. kártya

    Kérdés

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

    Válasz

    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. 100. kártya

     Kérdés

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

     Válasz

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

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

101. 101. kártya

     Kérdés

     Right-triangle definition of cosine?

     Válasz

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

102. 102. kártya

     Kérdés

     Force-displacement relation for an ideal linear spring?

     Válasz

     $$F=-kx$$

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

103. 103. kártya

     Kérdés

     May qualifications or project responsibility be exaggerated in a proposal?

     Válasz

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

104. 104. kártya

     Kérdés

     SI prefix micro?

     Válasz

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

105. 105. kártya

     Kérdés

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

     Válasz

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

106. 106. kártya

     Kérdés

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

     Válasz

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

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

107. 107. kártya

     Kérdés

     Right-triangle definition of tangent?

     Válasz

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

108. 108. kártya

     Kérdés

     Average normal stress under centered axial load?

     Válasz

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

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

109. 109. kártya

     Kérdés

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

     Válasz

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

110. 110. kártya

     Kérdés

     SI prefix nano?

     Válasz

     $n=10^{-9}$.

111. 111. kártya

     Kérdés

     Fundamental Pythagorean trigonometric identity?

     Válasz

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

112. 112. kártya

     Kérdés

     Engineering normal strain?

     Válasz

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

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

113. 113. kártya

     Kérdés

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

     Válasz

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

114. 114. kártya

     Kérdés

     Technical duty to an employer or client?

     Válasz

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

115. 115. kártya

     Kérdés

     How does a length conversion factor apply to area?

     Válasz

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

116. 116. kártya

     Kérdés

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

     Válasz

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

117. 117. kártya

     Kérdés

     When is a Poisson count model reasonable?

     Válasz

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

118. 118. kártya

     Kérdés

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

     Válasz

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

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

119. 119. kártya

     Kérdés

     Linear elastic stress-strain relation in uniaxial loading?

     Válasz

     $$\sigma=E\varepsilon$$

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

120. 120. kártya

     Kérdés

     How does a length conversion factor apply to volume?

     Válasz

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

121. 121. kártya

     Kérdés

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

     Válasz

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

122. 122. kártya

     Kérdés

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

     Válasz

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

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

123. 123. kártya

     Kérdés

     A supervisor directs an illegal engineering action. Proper response?

     Válasz

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

124. 124. kártya

     Kérdés

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

     Válasz

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

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

125. 125. kártya

     Kérdés

     Mass density?

     Válasz

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

     Use mass, not weight, in the numerator.

126. 126. kártya

     Kérdés

     Inches in one foot?

     Válasz

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

127. 127. kártya

     Kérdés

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

     Válasz

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

128. 128. kártya

     Kérdés

     How should subscripts be handled in a retrieved relationship?

     Válasz

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

129. 129. kártya

     Kérdés

     Dot product from vector magnitudes and included angle?

     Válasz

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

     The result is a scalar.

130. 130. kártya

     Kérdés

     Average normal pressure on an area?

     Válasz

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

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

131. 131. kártya

     Kérdés

     Feet in one yard?

     Válasz

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

132. 132. kártya

     Kérdés

     When are two interest rates equivalent?

     Válasz

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

133. 133. kártya

     Kérdés

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

     Válasz

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

134. 134. kártya

     Kérdés

     Expected value of a discrete random variable?

     Válasz

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

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

135. 135. kártya

     Kérdés

     Dot-product test for perpendicular nonzero vectors?

     Válasz

     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. 136. kártya

     Kérdés

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

     Válasz

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

     Depth increases downward and the fluid is at rest.

137. 137. kártya

     Kérdés

     Feet in one statute mile?

     Válasz

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

138. 138. kártya

     Kérdés

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

     Válasz

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

     

     276 kártya

     FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

     Tanulj ingyen ebből a pakliból

     A Nibomo megnyílik, és elkezdheted a tanulást.

139. 139. kártya

     Kérdés

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

     Válasz

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

140. 140. kártya

     Kérdés

     Magnitude of a vector cross product?

     Válasz

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

     The direction follows the right-hand rule.

141. 141. kártya

     Kérdés

     Exact inch-to-metre relationship?

     Válasz

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

142. 142. kártya

     Kérdés

     Volumetric flow rate through a cross-section?

     Válasz

     $$Q=Av_{avg}$$

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

143. 143. kártya

     Kérdés

     Variance from the mean $\mu$?

     Válasz

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

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

144. 144. kártya

     Kérdés

     Future-worth acceptance rule for an independent investment?

     Válasz

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

145. 145. kártya

     Kérdés

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

     Válasz

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

146. 146. kártya

     Kérdés

     Exact foot-to-metre relationship?

     Válasz

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

147. 147. kártya

     Kérdés

     How should important uncertainty be communicated?

     Válasz

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

148. 148. kártya

     Kérdés

     When is the matrix product $AB$ defined?

     Válasz

     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. 149. kártya

     Kérdés

     Steady one-inlet, one-outlet mass continuity?

     Válasz

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     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. 150. kártya

     Kérdés

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

     Válasz

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

151. 151. kártya

     Kérdés

     Square feet in one acre?

     Válasz

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

152. 152. kártya

     Kérdés

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

     Válasz

     $$ad-bc$$

153. 153. kártya

     Kérdés

     Bernoulli relationship along a streamline for ideal steady flow?

     Válasz

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

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

154. 154. kártya

     Kérdés

     May inconvenient measurements be discarded without a technical basis?

     Válasz

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

155. 155. kártya

     Kérdés

     Annual-worth acceptance rule for an independent investment?

     Válasz

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

156. 156. kártya

     Kérdés

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

     Válasz

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

157. 157. kártya

     Kérdés

     Cubic metres in one litre?

     Válasz

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

158. 158. kártya

     Kérdés

     What does a zero determinant mean for a square matrix?

     Válasz

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

159. 159. kártya

     Kérdés

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

     Válasz

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

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

160. 160. kártya

     Kérdés

     Unbiased sample variance for an independent sample from one population?

     Válasz

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

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

161. 161. kártya

     Kérdés

     How should mutually exclusive alternatives be compared?

     Válasz

     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. 162. kártya

     Kérdés

     Cubic centimetres in one millilitre?

     Válasz

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

163. 163. kártya

     Kérdés

     Why keep contemporaneous engineering records?

     Válasz

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

164. 164. kártya

     Kérdés

     Fast check after substituting into a handbook formula?

     Válasz

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

165. 165. kártya

     Kérdés

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

     Válasz

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

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

166. 166. kártya

     Kérdés

     Sensible heat for constant specific heat and no phase change?

     Válasz

     $$Q=mc\Delta T$$

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

167. 167. kártya

     Kérdés

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

     Válasz

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

     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. 168. kártya

     Kérdés

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

     Válasz

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

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

169. 169. kártya

     Kérdés

     Purpose of incremental analysis for mutually exclusive alternatives?

     Válasz

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

170. 170. kártya

     Kérdés

     Physical meaning of $dy/dx$?

     Válasz

     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. 171. kártya

     Kérdés

     One-dimensional steady conduction through a plane wall?

     Válasz

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

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

172. 172. kártya

     Kérdés

     When should you algebraically rearrange a handbook relationship?

     Válasz

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

173. 173. kártya

     Kérdés

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

     Válasz

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

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

174. 174. kártya

     Kérdés

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

     Válasz

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

175. 175. kártya

     Kérdés

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

     Válasz

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

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

176. 176. kártya

     Kérdés

     Convective heat-transfer rate at a surface?

     Válasz

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

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

177. 177. kártya

     Kérdés

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

     Válasz

     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. 178. kártya

     Kérdés

     Internal rate of return?

     Válasz

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

179. 179. kártya

     Kérdés

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

     Válasz

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

180. 180. kártya

     Kérdés

     Convert Celsius temperature to kelvin?

     Válasz

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

     This conversion is for absolute temperature, not temperature difference.

181. 181. kártya

     Kérdés

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

     Válasz

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

182. 182. kártya

     Kérdés

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

     Válasz

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

183. 183. kártya

     Kérdés

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

     Válasz

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

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

184. 184. kártya

     Kérdés

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

     Válasz

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

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

185. 185. kártya

     Kérdés

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

     Válasz

     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. 186. kártya

     Kérdés

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

     Válasz

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

187. 187. kártya

     Kérdés

     Why inspect boundary or initial conditions near a formula?

     Válasz

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

188. 188. kártya

     Kérdés

     Convert Celsius temperature to Fahrenheit?

     Válasz

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

189. 189. kártya

     Kérdés

     Ethical basis for expert technical testimony?

     Válasz

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

190. 190. kártya

     Kérdés

     Meaning of a breakeven value?

     Válasz

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

191. 191. kártya

     Kérdés

     Derivative of $e^x$?

     Válasz

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

192. 192. kártya

     Kérdés

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

     Válasz

     $$\Delta E=Q-W$$

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

193. 193. kártya

     Kérdés

     Frequentist meaning of a 95% confidence procedure?

     Válasz

     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. 194. kártya

     Kérdés

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

     Válasz

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

195. 195. kártya

     Kérdés

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

     Válasz

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

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

196. 196. kártya

     Kérdés

     Relationship between Celsius and kelvin temperature differences?

     Válasz

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

197. 197. kártya

     Kérdés

     How should credit for team engineering work be assigned?

     Válasz

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

198. 198. kártya

     Kérdés

     Main limitation of simple payback period?

     Válasz

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

199. 199. kártya

     Kérdés

     Roles of the null and alternative hypotheses?

     Válasz

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

200. 200. kártya

     Kérdés

     Ideal-gas equation of state?

     Válasz

     $$pV=nRT$$

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

201. 201. kártya

     Kérdés

     First check when reading a handbook table?

     Válasz

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

202. 202. kártya

     Kérdés

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

     Válasz

     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. 203. kártya

     Kérdés

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

     Válasz

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

204. 204. kártya

     Kérdés

     Convert Fahrenheit absolute temperature to Rankine?

     Válasz

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

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. 205. kártya

     Kérdés

     Ohm's law for an ideal resistor?

     Válasz

     $$V=IR$$

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

206. 206. kártya

     Kérdés

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

     Válasz

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

207. 207. kártya

     Kérdés

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

     Válasz

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

208. 208. kártya

     Kérdés

     Is a radian dimensionless?

     Válasz

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

209. 209. kártya

     Kérdés

     Electrical power absorbed under the passive sign convention?

     Válasz

     $$P=VI$$

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

210. 210. kártya

     Kérdés

     Meaning of a p-value?

     Válasz

     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. 211. kártya

     Kérdés

     First check when reading a handbook graph?

     Válasz

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

212. 212. kártya

     Kérdés

     Difference between mass and weight?

     Válasz

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

213. 213. kártya

     Kérdés

     Kirchhoff's current law at a node?

     Válasz

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

214. 214. kártya

     Kérdés

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

     Válasz

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

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

215. 215. kártya

     Kérdés

     Opportunity cost?

     Válasz

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

216. 216. kártya

     Kérdés

     Weight from mass in a gravitational field?

     Válasz

     $$W=mg$$

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

217. 217. kártya

     Kérdés

     Kirchhoff's voltage law around a closed loop?

     Válasz

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

218. 218. kártya

     Kérdés

     Decision rule using significance level $\alpha$?

     Válasz

     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. 219. kártya

     Kérdés

     Can proprietary methods from a former employer be reused freely?

     Válasz

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

220. 220. kártya

     Kérdés

     Pound-force to newtons?

     Válasz

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

221. 221. kártya

     Kérdés

     When does a definite integral equal ordinary geometric area?

     Válasz

     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. 222. kártya

     Kérdés

     Charge-voltage relation for an ideal capacitor?

     Válasz

     $$q=CV$$

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

223. 223. kártya

     Kérdés

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

     Válasz

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

224. 224. kártya

     Kérdés

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

     Válasz

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

225. 225. kártya

     Kérdés

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

     Válasz

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

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

226. 226. kártya

     Kérdés

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

     Válasz

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

227. 227. kártya

     Kérdés

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

     Válasz

     $$\tau=RC$$

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

228. 228. kártya

     Kérdés

     What physical quantity does pound-mass measure?

     Válasz

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

229. 229. kártya

     Kérdés

     Type I error?

     Válasz

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

230. 230. kártya

     Kérdés

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

     Válasz

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

231. 231. kártya

     Kérdés

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

     Válasz

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

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

232. 232. kártya

     Kérdés

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

     Válasz

     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. 233. kártya

     Kérdés

     Recognizable form of a separable first-order differential equation?

     Válasz

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

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

234. 234. kártya

     Kérdés

     Using unverified software output in a safety-relevant calculation?

     Válasz

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

235. 235. kártya

     Kérdés

     Equivalent resistance of ideal resistors in series?

     Válasz

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

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

236. 236. kártya

     Kérdés

     Pressure conversion from psi to pascals?

     Válasz

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

237. 237. kártya

     Kérdés

     Type II error?

     Válasz

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

238. 238. kártya

     Kérdés

     Useful flashcard to make after a failed handbook search?

     Válasz

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

239. 239. kártya

     Kérdés

     Standard form of a first-order linear differential equation?

     Válasz

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

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

240. 240. kártya

     Kérdés

     Equivalent resistance of ideal resistors in parallel?

     Válasz

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

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

241. 241. kártya

     Kérdés

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

     Válasz

     $$BV_k=B-kD$$

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

242. 242. kártya

     Kérdés

     Standard atmosphere in pascals?

     Válasz

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

243. 243. kártya

     Kérdés

     Using AI-generated technical content in engineering work?

     Válasz

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

244. 244. kártya

     Kérdés

     Trial form for a homogeneous linear ODE with constant coefficients?

     Válasz

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

245. 245. kártya

     Kérdés

     Wave-speed relationship among frequency and wavelength?

     Válasz

     $$v=f\lambda$$

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

246. 246. kártya

     Kérdés

     Statistical power?

     Válasz

     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. 247. kártya

     Kérdés

     Bar in pascals?

     Válasz

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

248. 248. kártya

     Kérdés

     How should handbook navigation be practiced before the FE exam?

     Válasz

     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. 249. kártya

     Kérdés

     Is depreciation itself a cash outflow?

     Válasz

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

250. 250. kártya

     Kérdés

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

     Válasz

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

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

251. 251. kártya

     Kérdés

     Relationship between period and frequency?

     Válasz

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

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

252. 252. kártya

     Kérdés

     How should foreseeable environmental harm enter an engineering decision?

     Válasz

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

253. 253. kártya

     Kérdés

     Foot-pound-force in joules?

     Válasz

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

254. 254. kártya

     Kérdés

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

     Válasz

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

255. 255. kártya

     Kérdés

     When should you search instead of relying on recall?

     Válasz

     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. 256. kártya

     Kérdés

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

     Válasz

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

257. 257. kártya

     Kérdés

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

     Válasz

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

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

258. 258. kártya

     Kérdés

     General material balance on a control volume?

     Válasz

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

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

259. 259. kártya

     Kérdés

     Approximate joules in one International Table Btu?

     Válasz

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

260. 260. kártya

     Kérdés

     What is the defender in a replacement analysis?

     Válasz

     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. 261. kártya

     Kérdés

     Speaking publicly about a technical matter outside your expertise?

     Válasz

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

262. 262. kártya

     Kérdés

     Single-interval trapezoidal approximation to an integral?

     Válasz

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

     It is exact for linear $f$.

263. 263. kártya

     Kérdés

     Energy efficiency of a device?

     Válasz

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

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

264. 264. kártya

     Kérdés

     Purpose of sensitivity analysis in engineering economics?

     Válasz

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

265. 265. kártya

     Kérdés

     Can a strong correlation establish causation?

     Válasz

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

266. 266. kártya

     Kérdés

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

     Válasz

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

267. 267. kártya

     Kérdés

     Mechanical horsepower in watts?

     Válasz

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

268. 268. kártya

     Kérdés

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

     Válasz

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

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

269. 269. kártya

     Kérdés

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

     Válasz

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

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

270. 270. kártya

     Kérdés

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

     Válasz

     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. 271. kártya

     Kérdés

     Kilowatt-hour in joules?

     Válasz

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

272. 272. kártya

     Kérdés

     Percent error relative to an accepted nonzero value?

     Válasz

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

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

273. 273. kártya

     Kérdés

     Does legal compliance alone settle an engineering ethics question?

     Válasz

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

274. 274. kártya

     Kérdés

     Does handbook fluency replace discipline-specific problem practice?

     Válasz

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

275. 275. kártya

     Kérdés

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

     Válasz

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

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

276. 276. kártya

     Kérdés

     Dimensional requirement for a physically meaningful additive equation?

     Válasz

     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.