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Soru 1Soru →

Evaluate whether the following statement is true or false:

The only positive integer solutions to the linear inequality −35(103x−15)+4(x−2)≥−52(−2x+4)+2-\frac{3}{5}\left(\frac{10}{3}x - 15\right) + 4(x - 2) \geq -\frac{5}{2}(-2x + 4) + 2 are 1, 2, and 3.
Cevabı ve açıklamayı göster

Cevap: True

Cevap

The statement is True.
By successfully distributing the fractional negative coefficients and combining like terms, the inequality simplifies to −3x≥−9-3x \geq -9. Dividing by −3-3 requires reversing the inequality to x≤3x \leq 3. The positive integers in this solution set are exactly 1, 2, and 3, meaning the statement is factually correct.

Adım Adım Çözüm

1
Distribute the negative fractions and constants on the left side of the inequality.
(−2x+9)+(4x−8)(-2x + 9) + (4x - 8)
Multiplying −35-\frac{3}{5} by 103x\frac{10}{3}x gives −2x-2x, and −35-\frac{3}{5} by −15-15 gives +9+9. Multiplying 44 by (x−2)(x-2) gives 4x−84x - 8.
2
Distribute the negative fraction on the right side of the inequality.
(5x−10)+2(5x - 10) + 2
Multiplying −52-\frac{5}{2} by −2x-2x gives 5x5x, and −52-\frac{5}{2} by 44 gives −10-10.
3
Combine the like terms on both sides.
2x+1≥5x−82x + 1 \geq 5x - 8
On the left side, −2x+4x=2x-2x + 4x = 2x and 9−8=19 - 8 = 1. On the right side, −10+2=−8-10 + 2 = -8.
4
Isolate the variable xx by subtracting 5x5x and 11 from both sides.
−3x≥−9-3x \geq -9
Grouping all variables on one side and constants on the other prepares the equation for the final division.
5
Divide both sides by −3-3 and reverse the inequality symbol.
x≤3x \leq 3
Dividing an inequality by a negative number requires flipping the inequality direction. Since x≤3x \leq 3, the only integers greater than zero that satisfy this are 1, 2, and 3.

Anahtar Kavram

Solving complex linear inequalities by distributing negative fractions, combining like terms, and properly applying the inequality sign flip rule.

Alternatif Yöntem

You can verify the statement by plugging the boundary values into the original inequality. Substitute x=3x=3 (which evaluates to 7≥77 \geq 7, a true statement), x=4x=4 (which evaluates to 9≥129 \geq 12, a false statement), and recognize that since it is a linear relation, solutions are valid downwards. Zero is not a positive integer, leaving 1, 2, and 3 as the only valid positive integers.
Tahmini Süre:2m 30s
Soru 2Soru →

Striking the faces of two hardened steel hammers directly against each other is an acceptable shop technique to increase driving force when freeing a seized component.

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False
The statement is false because hammer striking faces are tempered to a high level of hardness. Striking two hardened faces together creates a severe risk of brittle chipping, which can send sharp metal fragments flying into the workspace.

Adım Adım Çözüm

1
Identify the metallurgical properties of hammer striking faces.
Striking faces are induction-hardened or heat-treated to resist mushrooming and denting during standard striking tasks.
Hardened tool steel gains wear resistance at the cost of ductility, making it brittle under steel-on-steel shock loading.
2
Assess the risk of impacting two hardened steel striking faces together.
The collision between two hard, brittle surfaces creates high localized stress that causes spalling, chipping, and flying metal shards.
Shop safety standards strictly prohibit striking one hardened hammer face against another to prevent severe eye and body injuries.

Anahtar Kavram

Hammer Hardness and Face-to-Face Impact Safety
Tahmini Süre:45s
Soru 3Soru →

A vertical column in a building framework is primarily designed to resist tensile forces that attempt to stretch it.

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False
The statement is false because vertical columns bear the downward weight of a structure, subjecting them to compressive forces (pushing or squeezing) rather than tensile forces (pulling or stretching). Structural members primarily designed for tension are typically known as ties or cables.

Adım Adım Çözüm

1
Identify the structural component and its primary function.
The component in question is a vertical column, which supports the heavy weight of the building framework directly above it.
Understanding the component's physical role dictates the type of force it experiences.
2
Determine the type of internal force caused by this load.
Weight pushing down on a vertical support creates compression (pushing the material together), not tension (pulling the material apart).
Tensile forces stretch a material, while compressive forces squeeze it.

Anahtar Kavram

Tension vs. Compression in Structural Members
Tahmini Süre:30s
Soru 4Soru →

For the linear inequality −34(8x−12)+2x>−3(x−4)−2x-\frac{3}{4}(8x - 12) + 2x > -3(x - 4) - 2x, the value x=3x = 3 is included in the solution set.

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False, because the solution set is x>3x > 3, which strictly excludes the boundary value of 3.
Simplifying both sides of the inequality yields −4x+9>−5x+12-4x + 9 > -5x + 12. Isolating xx provides the solution set x>3x > 3. Because the inequality is strictly 'greater than', it does not include the boundary value of 3, making the statement false.

Adım Adım Çözüm

1
Distribute the negative fraction −34-\frac{3}{4} on the left side of the inequality.
−34(8x)−(−34)(12)+2x=−6x+9+2x-\frac{3}{4}(8x) - (-\frac{3}{4})(12) + 2x = -6x + 9 + 2x
To clear the parentheses and prepare the left side for combining like terms.
2
Distribute the negative integer −3-3 on the right side of the inequality.
−3(x)−(−3)(4)−2x=−3x+12−2x-3(x) - (-3)(4) - 2x = -3x + 12 - 2x
To clear the parentheses on the right side of the inequality.
3
Combine the like xx terms on both sides of the inequality.
Left side: −6x+2x+9=−4x+9-6x + 2x + 9 = -4x + 9. Right side: −3x−2x+12=−5x+12-3x - 2x + 12 = -5x + 12. The simplified inequality is −4x+9>−5x+12-4x + 9 > -5x + 12.
To simplify the expression before isolating the variable.
4
Isolate the variable xx by adding 5x5x and subtracting 99 on both sides.
−4x+5x>12−9-4x + 5x > 12 - 9, which simplifies to x>3x > 3.
To determine the final solution set for the inequality.
5
Evaluate whether x=3x = 3 satisfies the solution set x>3x > 3.
Since 33 is not greater than 33, the value is not included in the solution set.
To definitively determine if the original statement is true or false.

Anahtar Kavram

Solving multi-step linear inequalities and determining boundary value inclusion
Soru 5Soru →

The smooth endoplasmic reticulum is studded with ribosomes that synthesize polypeptides, whereas the rough endoplasmic reticulum lacks ribosomes and specializes in lipid synthesis and detoxification.

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False. The statement reverses the structural characteristics and primary functions of the rough and smooth endoplasmic reticulum.
The statement is false because it swaps the structural definitions and cellular functions of the two types of endoplasmic reticulum. In eukaryotic cells, the rough endoplasmic reticulum is named for the ribosomes attached to its cytoplasmic surface, which synthesize proteins destined for membranes or secretion. In contrast, the smooth endoplasmic reticulum is tubular, lacks ribosomes, and primarily synthesizes lipids, phospholipids, and steroid hormones while detoxifying metabolic byproducts and drugs.

Adım Adım Çözüm

1
Analyze the structural characteristics described for the rough and smooth endoplasmic reticulum.
The statement asserts that the smooth endoplasmic reticulum possesses ribosomes and the rough endoplasmic reticulum lacks them.
Identifying the physical markers of each organelle confirms whether the structural definitions are accurate.
2
Evaluate the cellular functions attributed to each organelle against established biological principles.
Ribosomes are attached to the rough endoplasmic reticulum to synthesize proteins, whereas the smooth endoplasmic reticulum synthesizes lipids and handles detoxification.
Matching each organelle to its correct metabolic role determines the overall truth value of the assertion.
3
Formulate the final evaluation.
The statement is false because it inverts both the presence of ribosomes and the functional duties between the rough and smooth endoplasmic reticulum.
A direct comparison proves the statement is factually incorrect.

Anahtar Kavram

Endoplasmic Reticulum Structure and Function (Rough vs. Smooth ER)
Soru 6Soru →

Passage:
In ultrasonic testing of pipeline weld seams, high-frequency sound waves are directed into the steel to detect internal voids. When these acoustic pulses encounter a boundary between solid metal and an internal discontinuity, a portion of the wave reflects back to the transducer rather than passing through. By measuring the time interval between the initial pulse transmission and the arrival of the reflected echo, technicians can precisely determine the depth of the flaw beneath the pipe surface.

Statement: Based on the passage, inspectors calculate how deep a structural defect lies within a weld by tracking the elapsed time required for reflected acoustic signals to return to the sensor.

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True
The statement is true because it accurately restates the passage's explanation using synonymous terms. The text explains that measuring the time interval between sending a sound pulse and receiving the reflected echo allows technicians to determine flaw depth. The statement preserves this exact functional relationship using equivalent phrases such as 'tracking the elapsed time' and 'depth a structural defect lies.'

Adım Adım Çözüm

1
Analyze the assertion in the statement to identify the key relationship.
The statement asserts that the depth of a defect is determined by measuring how long it takes for a reflected acoustic signal to return to the sensor.
Establishes the exact factual claim that must be verified against the text.
2
Locate the relevant factual detail in the passage.
The passage states that technicians determine the depth of a flaw by measuring the time interval between pulse transmission and the arrival of the reflected echo.
Extracts the source evidence concerning how depth is calculated.
3
Compare the statement's vocabulary and syntax with the passage's wording.
The statement restates 'depth of the flaw' as 'how deep a structural defect lies,' 'transducer' as 'sensor,' and 'time interval between initial pulse transmission and arrival of the reflected echo' as 'elapsed time required for reflected acoustic signals to return.'
Confirms that the statement is an accurate, fully supported paraphrase of the passage detail.

Anahtar Kavram

Paraphrased Fact Recognition
Tahmini Süre:1m 0s
Soru 7Soru →

Read the following passage:

Modern industrial dry-type transformers are increasingly replacing traditional liquid-filled units in commercial facilities primarily because their solid-cast epoxy resin insulation eliminates severe fire and environmental contamination hazards. Unlike oil-immersed transformers, dry-type systems contain no combustible fluids that could ignite or rupture during severe electrical fault conditions. While liquid units offer slightly superior thermal dissipation and lower initial purchase costs, dry-type units reduce facility insurance premiums, eliminate the need for exterior containment dikes, and permit direct indoor placement close to electrical loads. Consequently, despite higher manufacturing costs, heightened fire safety and reduced structural regulations make dry-type transformers the preferred choice for indoor commercial power distribution.

Statement: The assertion that dry-type transformers eliminate the need for exterior containment dikes represents the central main idea of the passage.

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False. The referenced statement functions as a supporting detail rather than the overarching main idea.
The correct response is False because the statement isolates a specific supporting detail rather than the central thesis. The main idea of the passage is that dry-type transformers are increasingly preferred for commercial indoor power distribution because their safety benefits and reduced regulatory demands outweigh their higher initial costs. Mentioning the elimination of containment dikes merely serves as supporting evidence illustrating one regulatory and cost advantage.

Adım Adım Çözüm

1
Identify the primary thesis and scope of the entire passage.
The text explains that commercial facilities favor dry-type transformers over liquid-filled units because safety and installation advantages outweigh higher equipment costs.
The main idea must synthesize the introductory claim and the concluding summary of the entire paragraph.
2
Analyze the functional role of the referenced statement in the passage.
The mention of eliminating exterior containment dikes is one of several specific examples demonstrating how dry-type units reduce auxiliary structural costs and regulatory burdens.
Distinguishing between a thesis and evidence requires evaluating whether a statement acts as an umbrella concept or a subordinate supporting point.
3
Compare the scope of the statement against the scope of the full text.
The statement focuses narrowly on a single civil engineering feature, making it too limited in scope to serve as the main idea.
A main idea must cover all major elements of the passage rather than a single factual detail.

Anahtar Kavram

Distinguishing the central thesis from supporting factual details
Tahmini Süre:1m 15s
Soru 8Soru →

Read the passage below and determine whether the following statement is True or False based strictly on the text.

During sub-zero operations below -30°F, tracked utility vehicles require MIL-PRF-5606 hydraulic fluid rather than standard synthetic oils to prevent pump cavitation. Before engine turnover, operators must activate the primary manifold heater for exactly 15 minutes; if ambient temperatures fall below -45°F, auxiliary glow plugs must also cycle for two consecutive 30-second intervals. Technicians are prohibited from engaging the power take-off (PTO) unit until the reservoir sight glass confirms a minimum core fluid temperature of 40°F, regardless of engine operating duration.

Statement: When operating at temperatures below -45°F, technicians may engage the power take-off (PTO) unit as soon as the auxiliary glow plugs complete two consecutive 30-second cycles.

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False. Power take-off (PTO) engagement is prohibited until the reservoir sight glass confirms a core fluid temperature of at least 40°F, not upon the completion of glow plug cycles.
The statement directly contradicts the facts provided in the text. The passage explicitly restricts power take-off (PTO) engagement to when the reservoir sight glass verifies a minimum core fluid temperature of 40°F. The completion of two 30-second glow plug cycles applies only to engine pre-turnover at temperatures below -45°F.

Adım Adım Çözüm

1
Scan the passage for the specific terms mentioned in the statement: 'power take-off (PTO)' and 'auxiliary glow plugs'.
Located two separate conditions: glow plugs pertain to engine turnover below -45°F, while the PTO unit is governed by reservoir fluid temperature.
Direct fact retrieval requires isolating the exact clause that defines the rules for the action in question.
2
Examine the explicit requirement governing PTO engagement in the final sentence.
The text states: 'Technicians are prohibited from engaging the power take-off (PTO) unit until the reservoir sight glass confirms a minimum core fluid temperature of 40°F, regardless of engine operating duration.'
This establishes the sole prerequisite stated in the text for engaging the PTO.
3
Compare the statement's claim with the retrieved factual condition.
The statement incorrectly claims PTO engagement is allowed directly after glow plug cycles finish, which conflates pre-starting steps with PTO operation requirements.
Because the statement contradicts the explicit text, it must be evaluated as false.

Anahtar Kavram

Direct Fact Retrieval of Technical Operating Constraints
Tahmini Süre:1m 15s
Soru 9Soru →

Read the following passage:

Modern aviation turbofan engines operate at combustion temperatures exceeding the melting thresholds of high-strength nickel-base superalloys. To protect high-pressure turbine blades, manufacturers deposit thin ceramic thermal barrier coatings, predominantly yttria-stabilized zirconia, onto metallic components via electron-beam physical vapor deposition. Rather than directly cooling the underlying metal, this ceramic layer exhibits extremely low thermal conductivity, creating a steep temperature drop across its thickness while internal compressor bleed air circulates through cast cooling passages within the blade core. Consequently, the ceramic insulation permits elevated combustor discharge temperatures without subjecting the supporting structural metal to thermal deformation.

Based on the passage, the ceramic coating prevents structural distortion of turbine components by resisting heat transmission and establishing a sharp thermal gradient across its depth.

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True: The passage directly supports the claim that the ceramic layer prevents thermal deformation by acting as a low-conductivity insulator that creates a steep temperature drop across its thickness.
The statement is fully substantiated by the text. The passage confirms that the ceramic layer's low thermal conductivity produces a steep temperature drop across its thickness, protecting the structural substrate from heat-induced deformation.

Adım Adım Çözüm

1
Analyze the assertion in the stem to isolate the key causal mechanisms and factual claims.
The statement claims that ceramic coatings avert structural distortion by impeding heat flow and creating a significant temperature difference across their thickness.
Isolating the core claims allows direct cross-referencing against explicit details in the reading passage.
2
Locate and extract the corresponding factual evidence from the passage.
The text notes that the ceramic coating 'exhibits extremely low thermal conductivity, creating a steep temperature drop across its thickness,' which ensures engine operation 'without subjecting the supporting structural metal to thermal deformation.'
Finding the specific textual reference confirms the exact physical process described by the author.
3
Evaluate the paraphrase mapping between the statement and the textual evidence.
'Resisting heat transmission' accurately paraphrases 'extremely low thermal conductivity,' 'sharp thermal gradient across its depth' accurately restates 'steep temperature drop across its thickness,' and 'prevents structural distortion' restates 'without subjecting the supporting structural metal to thermal deformation.'
Confirming semantic equivalence establishes that the statement is an accurate paraphrase and therefore factually true.

Anahtar Kavram

Paraphrased Fact Recognition in Technical Passages
Soru 10Soru →

In a direct current (DC) circuit, electrical current periodically reverses its direction of flow at a fixed frequency measured in hertz (Hz\text{Hz}).

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False. Direct current (DC) flows in a single constant direction, while alternating current (AC) periodically reverses its direction of flow.
The statement is false because direct current (DC) flows in one fixed direction without reversing. The periodic reversal of direction and polarity over time at a frequency measured in hertz (Hz\text{Hz}) is the defining attribute of alternating current (AC).

Adım Adım Çözüm

1
Define the fundamental behavior of direct current (DC).
Direct current is characterized by the unidirectional flow of electric charge, maintaining a constant polarity with a frequency of 0 Hz0\text{ Hz}.
Establishing the baseline definition of DC.
2
Analyze the characteristic described in the statement.
Periodic reversal of current flow at a measurable frequency in hertz (Hz\text{Hz}) defines alternating current (AC).
Distinguishing between AC and DC waveform characteristics.
3
Evaluate the accuracy of the statement.
The statement incorrectly assigns the periodic reversal and frequency properties of AC to DC, making the statement false.
Determining the correct truth value.

Anahtar Kavram

Direct Current (DC) flows continuously in one direction with zero frequency, whereas Alternating Current (AC) periodically reverses direction at a specified frequency.
Tahmini Süre:30s
Soru 11Soru →

An electrical current whose magnitude periodically fluctuates over time without ever reversing its polarity or direction of electron flow is classified as an alternating current (AC).

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False
The statement is false because the defining characteristic of alternating current (AC) is a periodic reversal in the direction of current flow and voltage polarity. Current that varies in magnitude while remaining strictly unidirectional is pulsating direct current (DC).

Adım Adım Çözüm

1
Analyze the fundamental definition of alternating current (AC).
Alternating current requires that electrons periodically change direction, moving back and forth across a zero reference axis.
AC is defined by periodic reversal of polarity and current direction, not merely changing magnitude.
2
Analyze the characteristics of direct current (DC) and its variations.
Direct current is any current that flows continuously in a single direction; when its amplitude varies over time without crossing zero to reverse direction, it is termed pulsating DC.
Unidirectional current flow remains DC regardless of whether the magnitude is constant or time-varying.
3
Evaluate the statement based on electrical classification principles.
The statement incorrectly classifies a unidirectional pulsating current as alternating current.
Because polarity never reverses, the current is DC, making the statement false.

Anahtar Kavram

Classification of DC vs. AC based on polarity reversal versus magnitude variation
Soru 12Soru →

A transistor can use a small electrical signal at one terminal to control a much larger current flowing through its other terminals.

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True
The statement is true because the defining characteristic of a transistor is its ability to govern a large current path using a relatively weak electrical control signal, making it effective for both amplification and switching.

Adım Adım Çözüm

1
Identify the primary operational functions of a transistor in electronic circuits.
Transistors are solid-state components designed to act as electronic switches and signal amplifiers.
Recalling the basic definition and purpose of semiconductor devices establishes the core functional criteria.
2
Evaluate the relationship between the input control signal and the output circuit current.
Applying a relatively small signal to the control terminal modulates and directs a much larger current between the power terminals.
This control mechanism allows small electronic signals to switch heavy loads on or off and amplify weak audio or radio signals.

Anahtar Kavram

Transistor amplification and electronic switching principle
Tahmini Süre:30s
Soru 13Soru →

When a bipolar junction transistor operates in its cutoff region, the collector-to-emitter path behaves as an open switch, preventing significant current flow through the output circuit.

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True
In the cutoff region, the control junction receives negligible bias voltage, preventing base current from flowing. Consequently, the output conduction path between the collector and emitter remains non-conductive, functioning electrically like an open switch.

Adım Adım Çözüm

1
Identify the specified operating state of the transistor
The statement specifies operation in the cutoff region.
A transistor's conductivity between its output terminals depends directly on its operating state: cutoff, active, or saturation.
2
Evaluate the current conduction characteristics in cutoff
Without base drive voltage, base current is zero, which halts collector current and creates an open-circuit condition.
In electronic switching applications, cutoff represents the 'off' or open-switch state where current cannot pass to the load.

Anahtar Kavram

Transistor Cutoff Region and Switching Operation
Tahmini Süre:45s
Soru 14Soru →

In an alternating current (AC) circuit, the direction of electron flow periodically reverses, whereas in a direct current (DC) circuit, electrons flow in only one continuous direction.

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True
The statement is true because the defining characteristic distinguishing AC from DC is the direction of current flow: direct current flows in a single direction with constant polarity, whereas alternating current regularly reverses direction over time.

Adım Adım Çözüm

1
Analyze the fundamental definition of direct current (DC).
Direct current is characterized by electric charges flowing exclusively in a single, constant direction through a circuit.
Direct current power sources, such as chemical batteries, provide a fixed polarity across their terminals.
2
Analyze the fundamental definition of alternating current (AC).
Alternating current periodically cycles between positive and negative polarities, causing charge carriers to oscillate back and forth.
AC generators produce an alternating sinusoidal voltage waveform that regularly inverts direction.
3
Compare the definitions against the provided statement.
The statement accurately reflects the defining behavioral distinction between alternating and direct current.
Both halves of the statement describe standard electrical principles correctly.

Anahtar Kavram

Directional characteristics of alternating current (AC) versus direct current (DC)
Soru 15Soru →

Unlike current-driven bipolar devices, an enhancement-mode metal-oxide-semiconductor field-effect transistor (MOSFET) conducts significant current between its drain and source terminals when its gate-to-source voltage is zero.

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False. Enhancement-mode MOSFETs are normally-off devices that require a gate-to-source voltage exceeding the threshold voltage to establish a channel and conduct current.
The evaluation 'False' is correct because enhancement-mode MOSFETs are normally-off solid-state devices. Without an applied gate-to-source voltage exceeding the device's threshold voltage (VthV_{th}), the channel between the drain and source remains non-conductive, preventing drain current from flowing.

Adım Adım Çözüm

1
Identify the component classification and operating archetype specified in the statement.
The statement specifies an enhancement-mode metal-oxide-semiconductor field-effect transistor (MOSFET).
Different transistor families (bipolar vs. field-effect) and operational modes (enhancement vs. depletion) exhibit distinct default conduction states.
2
Analyze the channel status of an enhancement-mode device at zero gate-to-source voltage (VGS=0 VV_{GS} = 0\text{ V}).
At VGS=0 VV_{GS} = 0\text{ V}, no conductive channel connects the drain and source regions across the substrate, resulting in an open circuit where drain current (IDI_D) is approximately zero.
Enhancement-mode devices are manufactured without a pre-formed channel and operate as normally-off switches.
3
Determine what electrical condition is required to initiate conduction.
An electric field created by applying a gate-to-source voltage greater than the threshold voltage (VGS>VthV_{GS} > V_{th}) is mandatory to enhance/induce a channel.
Because current does not flow at zero bias, the assertion that it conducts significant current at zero gate voltage is incorrect.

Anahtar Kavram

Default conduction state and threshold voltage mechanics of enhancement-mode field-effect transistors

Alternatif Yöntem

Recall the root word 'enhance': the channel must be actively enhanced (created) by gate voltage, meaning at zero gate voltage, no channel exists and no current flows.
Tahmini Süre:45s
Soru 16Soru →

The value x=2x = 2 is a valid solution for the inequality 5−2(3x+1)<4x−175 - 2(3x + 1) < 4x - 17.

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False
Substituting x=2x = 2 into both sides of the inequality results in −9<−9-9 < -9. Because −9-9 is equal to −9-9 and not strictly less than it, the mathematical statement is false. Alternatively, fully solving the inequality yields x>2x > 2, which does not include 22 as a solution.

Adım Adım Çözüm

1
Substitute x=2x = 2 into the left side of the inequality.
5−2(3(2)+1)=5−2(6+1)=5−2(7)=5−14=−95 - 2(3(2) + 1) = 5 - 2(6 + 1) = 5 - 2(7) = 5 - 14 = -9
To evaluate the numerical value of the left expression for the given test value.
2
Substitute x=2x = 2 into the right side of the inequality.
4(2)−17=8−17=−94(2) - 17 = 8 - 17 = -9
To evaluate the numerical value of the right expression for the given test value.
3
Compare the two evaluated sides using the strict inequality symbol (<<).
−9<−9-9 < -9
To determine if the resulting mathematical relationship is true.
4
Evaluate the truth of the final statement.
Since −9-9 is exactly equal to −9-9, it is not strictly less than −9-9. The statement is therefore false.
A strict inequality requires the left side value to be genuinely smaller than the right side value.

Anahtar Kavram

Solving One-Variable Inequalities
Soru 17Soru →

The solution set for the linear inequality 2(3x−5)−4x>8x−222(3x - 5) - 4x > 8x - 22 is x>2x > 2.

Cevabı ve açıklamayı göster

Cevap: False

Cevap

The statement is false. The correct solution set is x<2x < 2.
The statement is false because solving the inequality gives x<2x < 2. The inequality symbol must be flipped when dividing the final term −6x>−12-6x > -12 by the negative coefficient −6-6.

Adım Adım Çözüm

1
Distribute the 22 across the terms inside the parentheses.
6x−10−4x>8x−226x - 10 - 4x > 8x - 22
To eliminate the parentheses and prepare the terms for combining.
2
Combine like terms on the left side of the inequality.
2x−10>8x−222x - 10 > 8x - 22
To simplify the expression on the left side (6x−4x=2x6x - 4x = 2x).
3
Subtract 8x8x from both sides.
−6x−10>−22-6x - 10 > -22
To gather all the variable terms on one side of the inequality.
4
Add 1010 to both sides.
−6x>−12-6x > -12
To isolate the variable term completely.
5
Divide both sides by −6-6 and reverse the inequality sign.
x<2x < 2
Dividing an inequality by a negative number requires flipping the inequality symbol to maintain a mathematically true statement.

Anahtar Kavram

Solving multi-step linear inequalities and reversing the inequality symbol when dividing by a negative number.
Soru 18Soru →

For a silicon PNP bipolar junction transistor to operate correctly in the active region as a linear amplifier, the DC biasing circuit must ensure that the collector terminal is maintained at a higher positive voltage relative to the emitter terminal.

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False
The statement is false because in a PNP transistor, the emitter must be at a higher positive potential than the collector to ensure current flows correctly (from emitter to collector) and the junctions are properly biased for the active region.

Adım Adım Çözüm

1
Identify the specific transistor type and its intended operating state.
The device is a PNP bipolar junction transistor operating in the active region (as a linear amplifier).
Different transistor types (NPN vs. PNP) require completely opposite voltage polarities for the same operating state.
2
Recall the structural composition of a PNP transistor.
A PNP transistor consists of a P-type emitter, an N-type base, and a P-type collector.
Understanding the semiconductor materials (P or N) dictates how junctions must be biased.
3
Determine the required junction biasing for the active region.
For any BJT to act as a linear amplifier (active region), its emitter-base junction must be forward-biased, and its collector-base junction must be reverse-biased.
This specific biasing arrangement allows a small base current to control a larger collector current without entering saturation or cutoff.
4
Apply the biasing rules to the PNP terminal voltages.
To forward-bias the P-N emitter-base junction, the P-type emitter must be more positive than the N-type base. To reverse-bias the P-N collector-base junction, the P-type collector must be more negative than the N-type base.
Forward biasing requires connecting positive potential to P-type material; reverse biasing requires connecting negative potential to P-type material.
5
Evaluate the statement based on the deduced voltage potentials.
The emitter is the most positive terminal in a properly biased PNP amplifier circuit. Therefore, the collector is at a lower voltage relative to the emitter, making the original statement false.
The statement claims the collector is at a higher positive voltage, which incorrectly describes an NPN transistor's biasing.

Anahtar Kavram

Transistor Biasing and Polarity Configuration
Tahmini Süre:1m 30s
Soru 19Soru →

Unlike a steady DC power system where individual electrons physically drift through the entirety of the closed conductive path over time, the electrons in a standard 60 Hz60\text{ Hz} AC household system only vibrate back and forth within a localized region of the wire and never complete a full lap around the circuit.

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Cevap: True

Cevap

True. DC causes a continuous physical progression of electrons, while AC causes localized oscillation.
The statement is true because the constant unidirectional electric field in a DC system allows for a continuous physical progression of electrons around the circuit loop. In an AC system, the rapidly alternating electric field causes the electrons to simply wiggle back and forth locally, transferring energy without requiring a full physical transit of the circuit.

Adım Adım Çözüm

1
Analyze the nature of electron movement in a steady DC system.
DC maintains a constant voltage polarity, which forces electrons to slowly drift in one continuous direction around the circuit.
Understanding DC electron drift establishes the baseline for comparison.
2
Analyze the nature of electron movement in an AC system.
AC voltage constantly reverses polarity, which in a 60 Hz60\text{ Hz} system occurs 120 times per second.
This rapid reversal determines how the electric field influences the electrons.
3
Evaluate the distance an electron can travel in an AC system before reversing.
Because electron drift velocity is incredibly slow, the rapid polarity reversal forces them to merely vibrate in place rather than completing a circuit lap.
Comparing the slow drift speed to the high AC frequency proves that AC electrons cannot traverse the entire circuit.

Anahtar Kavram

Electron Drift and Oscillation in AC vs. DC
Soru 20Soru →

An alternating current (AC) sinusoidal voltage with a peak value of 10 V10\text{ V} delivers the same electrical power to a resistive heating element as a steady 10 V10\text{ V} direct current (DC) supply.

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Cevap: False

Cevap

False. An alternating current (AC) sine wave with a peak voltage of 10 V10\text{ V} delivers an effective (RMS) voltage of approximately 7.07 V7.07\text{ V}, which provides less electrical power to a resistor than a constant 10 V10\text{ V} direct current (DC) supply.
Direct current (DC) maintains a continuous, constant voltage and unidirectional current flow over time. In contrast, sinusoidal alternating current (AC) fluctuates, reaching its maximum peak voltage only momentarily and crossing zero volts twice per cycle. The effective value of an AC voltage—representing the DC voltage that would deliver the exact same average heating power across an identical resistor—is defined by its Root-Mean-Square (RMS) value (VRMS=0.707×VpeakV_{\text{RMS}} = 0.707 \times V_{\text{peak}}). For a 10 V10\text{ V} peak AC supply, the effective voltage is only 7.07 V7.07\text{ V}, resulting in half the power output of a steady 10 V10\text{ V} DC supply.

Adım Adım Çözüm

1
Identify the relationship between peak voltage and effective (RMS) voltage for alternating current.
VRMS=Vpeak2≈0.707×Vpeak=0.707×10 V=7.07 VV_{\text{RMS}} = \frac{V_{\text{peak}}}{\sqrt{2}} \approx 0.707 \times V_{\text{peak}} = 0.707 \times 10\text{ V} = 7.07\text{ V}.
Direct current supplies a continuous, constant potential, whereas alternating current oscillates, meaning the effective power output of AC must be calculated using its RMS value.
2
Compare the power dissipated by the 10 V10\text{ V} DC source and the 10 V10\text{ V} peak AC source across a resistor RR.
PDC=(10 V)2R=100RP_{\text{DC}} = \frac{(10\text{ V})^2}{R} = \frac{100}{R}, whereas PAC=(VRMS)2R=(7.07 V)2R=50RP_{\text{AC}} = \frac{(V_{\text{RMS}})^2}{R} = \frac{(7.07\text{ V})^2}{R} = \frac{50}{R}.
Power delivered to a resistor is proportional to the square of the applied voltage; the 10 V10\text{ V} peak AC source delivers only 50%50\% of the power delivered by the 10 V10\text{ V} DC source.
3
Evaluate the truth value of the stem statement.
The statement is false.
Equal peak and DC voltage values do not result in equal power output due to the cyclic nature and lower effective RMS value of AC.

Anahtar Kavram

AC RMS Voltage vs. DC Equivalent Heating Power
Tahmini Süre:35s
Sayfa 1 / 13Sonraki