TOLC-Med 2024 July Worked Solution

Full explanation

The title Decameron comes from the Greek words déka ("ten") and hēméra ("day"), meaning "ten days." In Boccaccio's work, ten young people flee the plague in Florence and spend ten days telling stories.

Each day, every member of the group tells one story, resulting in a total of 100 stories (10 storytellers × 10 days).

Although the work contains one hundred stories, the title refers to the ten-day framework in which the storytelling takes place, not to the number of stories or characters.

Therefore, the correct answer is option A.

Full explanation

The passage explains that animals are heterotrophic, meaning they obtain already-formed organic substances (such as proteins, sugars, and fats) from food.

Before these nutrients can enter cells, food must be mechanically and chemically broken down so that its constituent organic molecules are isolated and can cross the cell membrane.

Option E accurately summarizes this idea: animals process food to isolate its organic molecules so they can be absorbed and used by cells.

Why the other options are incorrect:

A) Incorrect.

Proteins, sugars, and fats are already organic substances; they do not need to become organic.

B) Incorrect.

Cell membranes allow nutrients to enter cells, but they do not provide the energy that satisfies animals' energy needs.

C) Incorrect.

The comparison is reversed.

Plants build organic substances (e.g., by photosynthesis), whereas animals obtain and break down pre-existing organic substances.

D) Incorrect.

While animals break down organic substances, they do not feed exclusively on plants—many are carnivores or omnivores.

Full explanation

The passage describes the evolution of 20th-century art as a process of increasing expressive freedom, innovation, and independence.

Compared with the previous century, art becomes more detached from sensory experience and from Western artistic tradition, explores every kind of reality (psychic, rational, unconscious, existential, and even random), and gradually asserts itself as an autonomous domain, eventually reaching the level of "behavioral values." Option B captures all the main ideas without adding information that is not in the passage: art is presented as an ongoing search for new forms of expression that becomes progressively independent of other fields.

Why the other options are incorrect:

A) Incorrect.

The passage does not portray science and technology as enemies of art; initially, art is in dialogue or competition with them before asserting its independence.

C) Incorrect.

The blurring of painting and sculpture is mentioned, but it is only one aspect of a much broader transformation and is not presented as its defining feature.

D) Incorrect.

The passage never states that 20th-century art expresses anguish.

E) Incorrect.

"Behavioral values" are the culmination of the process, not its starting point, and the passage does not suggest that art takes space away from science and technology.

Full explanation

The events occurred in the following order: Congress of Vienna (1814–1815) – Redrew the political map of Europe after Napoleon's defeat.

Mazzini founds Young Italy (1831) – A movement promoting Italian unity and independence.

First War of Independence against the Austrian Empire (1848–1849) – The first military attempt to achieve Italian unification.

Expedition of the Thousand (1860) – Garibaldi's campaign that conquered the Kingdom of the Two Sicilies.

Proclamation of the Kingdom of Italy (1861) – Official birth of the unified Kingdom of Italy.

Only Option C follows this historical sequence.

Full explanation

Translate each instruction into a positional relationship: C is immediately to the right of T → T C N is between E and C → C N E E is to the right of C and immediately to the left of G → C N E G Z is to the right of G, and X is between G and Z → G X Z

Combining all the conditions gives the sequence: T C N E G X Z

The question asks for the sequence read from right to left, so we reverse it: Z X G E N C T This corresponds to Option B.

Full explanation

First, convert the given weight: F = 0.04 kg = 40 g Since E weighs 10 g less than F: E = 40 − 10 = 30 g Now calculate their sum: E + F = 30 + 40 = 70 g D weighs four times this sum: D = 4 × 70 = 280 g Finally, convert grams to hectograms: 1 hg = 100 g 280 g = 2.8 hg

Therefore, the correct answer is Option B.

Full explanation

Let: G = Giacomo's age A = Alessia's age R = Romina's age

We know: G + R = 62 A + G = 43 A + R = 55

Add the three equations: (G+R)+(A+G)+(A+R)=62+43+55=160 So: 2(A+G+R)=160 A+G+R=80 Now subtract A + G = 43: R=80-43=37 Therefore, Romina is 37 years old.

Full explanation

Draw four seats around a table.

Start with the information that Cristina and Giacomo sit next to each other.

Next, use the profession clues: The surgeon sits immediately to the left of Maria.

The neurologist sits opposite Antonio.

A woman sits immediately to the left of the orthopedist.

Testing the possible arrangements while respecting the circular seating shows that there is only one assignment of professions satisfying every condition:

Therefore, the pediatrician is Antonio.

Full explanation

Represent the statements as sets: All CUZ are CW ⟹ CUZ ⊆ CW No DE is CW ⟹ DE and CW do not overlap Some DE are DR ⟹ There is at least one element that belongs to both DE and DR.

Now evaluate each option.

A) No DE can be CUZ Since all CUZ are CW and no DE is CW, DE cannot contain any CUZ. Certainly true.

B) Some DR can be CW We only know that some DR are DE (and therefore not CW).

Other DR may or may not be CW. Can be true.

C) No DR can be CUZ This is not certain.

We know that some DR belong to DE, but we are not told that all DR are DE. It is possible that other DR are outside DE and belong to CUZ (and therefore CW).

Not certainly true.

D) Not all DR are certainly also DE The premises only state that some DE are DR. They do not imply that every DR is DE. Certainly true.

E) Some CW might not be CUZ Since CUZ is a subset of CW, it is possible that CW contains elements that are not CUZ. Might be true.

Therefore, the statement that is not certainly true is:

C) no DR can be CUZ

Full explanation

Bioelements are the chemical elements that make up living organisms, including both plants and animals.

The six major bioelements—carbon (C), hydrogen (H), oxygen (O), nitrogen (N), phosphorus (P), and sulfur (S)—account for about 99% of the mass of living matter.

Bioelements are classified according to their abundance: Major elements (high concentration), Minor elements (low concentration), Trace elements (very small amounts, but often essential).

Therefore, it is false to say that bioelements are not the basic chemical elements of plants.

Why the other options are incorrect:

B) True.

Some bioelements (e.g., carbon and oxygen) are abundant.

C) True.

Others occur in lower concentrations.

D) True.

Trace elements such as iron and zinc are present in minute amounts.

E) True.

CHONPS make up approximately 99% of living matter.

Full explanation

Approximate sizes Ribosome: 20-30 nm Mitochondrion: 1-10 μm Platelet: 2-3 μm Red blood cell: 7-8 μm Ovum: ~100 μm Therefore, the ribosome is the smallest structure among the listed.

Full explanation

The fungal cell wall is composed mainly of chitin, a strong structural polysaccharide that also forms the exoskeleton of arthropods.

This distinguishes fungi from: Plants, whose cell walls are mainly made of cellulose.

Bacteria, whose cell walls contain peptidoglycan.

Why the other options are incorrect:

A) Peptidoglycan is characteristic of bacterial cell walls.

B) Cellulose is the main component of plant cell walls.

D) Phospholipids form the cell membrane, not the cell wall.

E) Glycogen is the storage polysaccharide of fungi and animals, not a structural component of the cell wall.

Full explanation

Prokaryotic cells lack membrane-bound organelles, one of the main features distinguishing them from eukaryotic cells.

Among the structures listed: Ribosomes are present in all cells.

Capsules are found in many bacteria and provide protection.

Cell walls are present in most prokaryotes.

Pili help bacteria attach to surfaces or exchange genetic material.

Mitochondria are membrane-bound organelles found only in eukaryotic cells.

Therefore, mitochondria are not present in prokaryotic cells.

Full explanation

Most eukaryotic cells have a diameter between 10 and 100 micrometres (µm).

Examples: Animal cells: about 10–30 µm Plant cells: often 20–100 µm By comparison: Prokaryotic cells are much smaller, typically 1–5 µm.

Ribosomes are measured in nanometres (nm).

Therefore, the correct range is 10–100 µm.

Full explanation

In eukaryotic cells, the genomic DNA is enclosed within the nucleus and is wrapped around histone proteins, forming chromatin.

This packaging: allows long DNA molecules to fit inside the nucleus, regulates gene expression, condenses into chromosomes during cell division.

Unlike bacteria, eukaryotes do not have a nucleoid, and their nuclear DNA is linear, not circular.

Why the other options are incorrect:

A) Eukaryotic nuclear DNA is linear, not a single circular molecule.

B) Nuclear DNA is not free in the cytoplasm.

C) The nucleoid is found only in prokaryotes.

D) Circular DNA in the cytoplasm is characteristic of bacteria (and of mitochondria/chloroplasts, not the genome).

Full explanation

Mitochondria contain their own DNA (mtDNA), which is: small compared with nuclear DNA, circular, double-stranded, inherited almost exclusively from the mother.

Human mitochondrial DNA contains 37 genes, far fewer than the approximately 20,000 protein-coding genes in the nuclear genome.

According to the endosymbiotic theory, mitochondria evolved from an aerobic bacterium.

The main supporting idea behind this theory is the shared characteristics with bacteria.

One of these is the structure of DNA. Therefore, we can also remember that mitochondria have a DNA structure similar to that of prokaryotes (bacteria).

Therefore, the correct statement is that mitochondrial DNA is smaller than nuclear DNA.

Full explanation

Prokaryotic ribosomes are 70S ribosomes, composed of two subunits: 50S (large subunit) 30S (small subunit)

By contrast, eukaryotic ribosomes are 80S, made of 60S and 40S subunits.

Full explanation

The nuclear envelope consists of two membranes perforated by nuclear pores.

These pores regulate the exchange of materials between the nucleus and the cytoplasm.

Although very small molecules can diffuse passively, most transport occurs through nuclear pore complexes, making Option B the best answer.

Full explanation

According to the fluid mosaic model, the plasma membrane is mainly composed of: Phospholipids, forming the lipid bilayer.

Proteins, many of which are glycoproteins.

Glycolipids, involved in cell recognition.

Sterols (mainly cholesterol in animal cells), which regulate membrane fluidity.

Nitrogenous bases (adenine, thymine, cytosine, guanine, and uracil) are components of DNA and RNA, not structural components of cell membranes.

Full explanation

Enzymes are biological catalysts.

They increase the speed of chemical reactions by lowering the activation energy, allowing reactions to occur more rapidly.

Enzymes: act on specific substrates, are not consumed during the reaction, can be reused many times, are effective even in very small amounts.

Therefore, the false statement is that enzymes decrease the rate of a reaction.

In reality, they increase the reaction rate.

Full explanation

A naked virus consists of only two basic components: Genetic material (DNA or RNA) A capsid, a protein coat that surrounds and protects the viral genome.

Unlike cells, viruses do not possess organelles such as mitochondria, lysosomes, the endoplasmic reticulum, or the Golgi apparatus.

Some viruses also have a lipid envelope, but naked viruses lack this envelope and consist only of the nucleic acid enclosed within the capsid.

Therefore, the only structure present in all naked viruses is the capsid.

Full explanation

Passive transport moves substances down their concentration gradient, from an area of higher concentration to one of lower concentration, without requiring cellular energy (ATP).

Diffusion is the simplest example of passive transport.

The other mechanisms require membrane proteins or vesicles and are classified as active transport or vesicular transport.

Other options

A) Uniport simply means a transporter moves one type of molecule.

It may be passive (facilitated diffusion) or active, so the term alone does not identify passive transport.

B) Endocytosis requires energy to bring material into the cell.

D) Symport is generally a form of secondary active transport.

E) Exocytosis is an ATP-dependent vesicular transport process.

Full explanation

The adult vertebral column has four physiological curves: Cervical lordosis Thoracic kyphosis Lumbar lordosis Sacral kyphosis These alternating curves help distribute body weight, maintain balance, and absorb mechanical shocks during movement.

Therefore, the vertebral column has: 2 lordoses 2 kyphoses

Full explanation

The division of the cell nucleus is called karyokinesis, more commonly known as mitosis in somatic cells.

During mitosis, one nucleus divides to produce two genetically identical nuclei.

Mitosis is followed by cytokinesis, the division of the cytoplasm, which completes cell division.

The stages of mitosis are: Prophase Metaphase Anaphase Telophase Interphase is not part of mitosis; it is the phase during which the cell grows and replicates its DNA before division.

Full explanation

Crossing-over is the reciprocal exchange of corresponding DNA segments between non-sister chromatids of homologous chromosomes.

It occurs during prophase I of meiosis, when homologous chromosomes pair up in a process called synapsis.

This exchange creates new combinations of alleles, increasing the genetic variation of the gametes and, consequently, of the offspring.

Why the other options are incorrect:

B) Cytoplasmic division is called cytokinesis, not crossing-over.

C) The nuclear envelope disappears during prophase, but this is not crossing-over.

D) Chromatin condensation also occurs during prophase, but it is a separate event.

E) Chromosome decondensation occurs at the end of cell division, not during crossing-over.

Full explanation

Mitosis is the process by which one somatic (body) cell divides to produce two genetically identical daughter cells.

If the parent cell is diploid (2n), each daughter cell is also diploid (2n) because the chromosome number is maintained.

Mitosis is essential for: growth, tissue repair, replacement of damaged or worn-out cells.

Full explanation

The S phase ("S" for Synthesis) is the stage of interphase during which the cell replicates its DNA. As a result: every chromosome is duplicated, each chromosome now consists of two sister chromatids joined at the centromere.

DNA replication prepares the cell for mitosis, ensuring that each daughter cell receives a complete copy of the genome.

Why the other options are incorrect:

A) Quiescence occurs in the G₀ phase, not the S phase.

B) Nuclear division occurs during mitosis (M phase).

C) Cell division (cytokinesis) occurs after mitosis.

E) RNA and proteins are mainly synthesised during the G₁ and G₂ phases; the defining event of the S phase is DNA replication.

Full explanation

The limbic system is a network of brain structures involved in: emotion, memory, learning, motivation.

Key components include: the hippocampus, which plays a central role in forming new memories, the amygdala, which processes emotions such as fear and anxiety.

Because of these functions, the limbic system is often called the brain's "emotional centre." Why the other options are incorrect:

A) The corpus callosum connects the two cerebral hemispheres.

B) The spinal cord conducts nerve impulses and mediates reflexes.

C) The pituitary gland is an endocrine gland that secretes hormones.

E) The brainstem regulates vital functions such as breathing, heart rate, and blood pressure.

Full explanation

Familial hypercholesterolaemia is stated to have dominant inheritance.

Let's use: H = disease allele (dominant) h = normal allele (recessive) Since the woman is healthy, she must be hh.

The couple has both: affected children, and healthy children.

If the father were HH (homozygous dominant): HH×hh→100%Hh (affected) All children would be affected, which contradicts the information.

Therefore, the father must be Hh (heterozygous).

Recheck: Hh x hh → 50% Hh (affected), 50% hh (healthy) This matches the family described.

The fact that both sons and daughters are affected also supports autosomal (not sex-linked) inheritance.

Full explanation

Water enters vascular plants mainly through root hairs, which are thin extensions of root epidermal cells.

Root hairs: greatly increase the surface area available for absorption, take up water primarily by osmosis, also absorb dissolved mineral ions.

The absorbed water then moves into the xylem and is transported throughout the plant.

Why the other options are incorrect:

A) The ligule is a small structure found in grasses and is not involved in water absorption.

B) The root apex contains the growing tip but is not the main absorption zone.

D) Stem hairs do not absorb water from the soil.

E) Hydathodes release excess water (guttation); they do not absorb it.

Full explanation

A backcross (test cross) is performed by crossing an individual showing the dominant phenotype with a homozygous recessive individual.

Let: A = long tail (dominant) a = short tail (recessive) If the dominant parent is heterozygous (Aa):

Aa x aa

Offspring: 50% Aa → long-tailed 50% aa → short-tailed This is exactly the observed ratio.

Therefore, the cross is Aa x aa

Full explanation

The systemic circulation begins when the left ventricle pumps oxygen-rich blood into the aorta.

The blood travels through arteries to all body tissues, where oxygen and nutrients are delivered.

It then returns as deoxygenated blood to the right atrium via the venae cavae.

This circulation supplies the body's organs with oxygen and nutrients.

Why the other options are incorrect:

A) The right ventricle pumps deoxygenated, not oxygenated, blood.

C) Blood travelling to the lungs belongs to the pulmonary circulation.

D) The right ventricle initiates the pulmonary circulation, not the systemic circulation.

E) The systemic circulation begins in the left ventricle, not the left atrium.

Full explanation

At the same temperature and pressure, gas volumes are proportional to the number of moles (Avogadro's law).

From the balanced equation: CH₄ + 2O₂ → CO₂ + 2H₂O 1 volume of CH₄ reacts with 2 volumes of O₂.

Therefore: 2 L CH₄ requires 2×2=4 L O₂

Full explanation

Nitrogen exists as N₂, meaning each molecule contains 2 nitrogen atoms.

Since: Molar mass of N₂ = 28 g/mol Then each nitrogen atom has atomic mass: 28/2=14 u (a.m.u.) Check the other options:

B) Wrong.

At STP, 1 mole occupies 22.4 L, not 224 L.

C) Wrong.

One molecule weighs approximately 28/6.022×10⁽²³⁾ g, not 28 g.

D) Wrong.

Atomic mass is 14, not 28.

E) Wrong.

One mole of N₂ weighs 28 g, not 14 g.

Full explanation

First ionization energy is the energy needed to remove the first electron.

Across Period 3, ionization energy generally increases from left to right: Na < Mg < Al < Si < P > S < Cl < Ar There are two small exception: Al < Mg S < P (because of electron pairing) Among the options given: Na, Mg, Al, Si, S Sulfur still has the highest first ionization energy of this list, despite being slightly lower than phosphorus (which isn't an option).

Full explanation

Determine the formula using ionic charges.

Calcium ion: Ca²⁺ Phosphate ion: PO₄^3- To make the compound electrically neutral: 3 Ca²⁺ gives +6 2 PO₄^3- gives −6 So the formula is: Ca₃(PO₄)₂

Full explanation

To determine whether an ionic formula is possible, check that the total positive and negative charges balance.

A) KMnO₄ K⁺ + MnO₄^- → Neutral (potassium permanganate)

B) Ca(BO₃)₂ Ca²⁺ If the ion is BO₃^3- (borate), then: Total charge = +2 + 2(−3) = −4 (Not neutral) A neutral compound would require Ca₃(BO₃)₂.

C) NaClO₄ Na⁺ + ClO₄^- (Neutral)

D) Ca(H₂PO₄)₂ H₂PO₄^- has a −1 charge.

Ca²⁺ + 2(H₂PO₄^-) (Neutral)

E) PbCO₃ Pb²⁺ + CO₃^2- (Neutral)

Full explanation

Boiling point elevation is a colligative property, meaning it depends only on the number of dissolved particles, not on their identity.

The equation is: ΔT_b=iK_bm where: i = van't Hoff factor (number of particles produced) m = molality K₍b₎ = boiling-point elevation constant So the more dissolved particles there are, the greater the boiling point increase.

Why the others are wrong:

A) Osmotic pressure is another colligative property but does not directly determine boiling point elevation.

B) The chemical identity of the solute is not the determining factor.

D) Van der Waals forces are not the primary factor in this context.

E) Latent heat is unrelated to the definition of boiling point elevation.

Full explanation

Aluminium has: Atomic number = 13 Electron configuration: 1s² 2s² 2p⁶ 3s² 3p¹ Its valence shell contains 3 electrons.

By losing these three electrons, aluminium forms: Al⁽³⁺⁾ which has the electron configuration of Neon, a stable noble gas with a complete octet.

Full explanation

A decomposition reaction occurs when one compound breaks down into two or more simpler substances.

Let's classify each reaction:

A) Combination (synthesis): two reactants combine to form one product.

B) Single displacement (Mg displaces Si).

C) Redox reaction.

D) One compound (NaHCO₃) decomposes into three products.

E) Double displacement followed by gas evolution.

Therefore: 2NaHCO₃→Na₂CO₃+CO₂+H₂O is the decomposition reaction.

Full explanation

The mole fractions of all components in a solution must add up to 1: X_(glucose)+X_(sucrose)+X_(water)=1

Given: X_(glucose)=0.07 Check each option:

A) Incorrect.

Water + sucrose = 1-0.07=0.93, not 1.

B) Incorrect. 0.07+0.07+0.70=0.84, not 1.

C) Incorrect.

The solvent is usually the largest component, but its mole fraction is not necessarily 1.

D) Incorrect.

Being a disaccharide has nothing to do with mole fraction.

Mole fraction depends only on the number of moles present.

E) Check: 0.07+0.08+0.85=1.00 This is the only option consistent with the definition of mole fraction.

Full explanation

Ethane has the formula: C₂H₆ Structure: H₃C-CH₃ The carbon-carbon bond is: single bond (σ bond) covalent between two identical carbon atoms Since both atoms have the same electronegativity, the bond is nonpolar.

Why the others are wrong:

A) Triple bond → found in alkynes (e.g., ethyne).

B) Double bond → found in alkenes (e.g., ethene).

D) Hydrogen bond → intermolecular force, not the C–C bond.

E) Ionic bond → formed between metals and nonmetals.

Full explanation

In traditional nomenclature: -ous → lower oxidation state -ic → higher oxidation state Examples: FeO → ferrous oxide (Fe²⁺) Fe₂O₃ → ferric oxide (Fe³⁺) Likewise: Cu₂O → cuprous oxide (Cu⁺) CuO → cupric oxide (Cu²⁺) Therefore, "-ic" always refers to the higher oxidation state.

Why the others are wrong:

B) Not always +1.

C) Oxygen content is not the naming criterion.

D) Oxides obviously contain oxygen.

E) Bond type is irrelevant to this nomenclature.

Full explanation

Hund's rule states: Electrons occupy orbitals of equal energy (degenerate orbitals) singly, with parallel spins, before pairing up.

Example: Nitrogen (1s² 2s² 2p³) The three 2p electrons are arranged as: ↑ ↑ ↑ rather than ↑↓ ↑ _ This minimizes electron-electron repulsion and gives the most stable arrangement.

Therefore, the correct answer is

B) The progressive filling of degenerate orbitals

Full explanation

An ionic bond is typically formed between: a metal (which loses electrons to form a cation), and a non-metal (which gains electrons to form an anion).

Chlorine (Cl) is a non-metal that forms the chloride ion: Cl^- Let's examine the options:

A) C (Carbon) → Non-metal; forms covalent bonds with chlorine (e.g., CCl₄).

B) P (Phosphorus) → Non-metal; forms covalent compounds such as PCl₃ and PCl₅.

C) Mg (Magnesium) → Metal; loses two electrons to form Mg²⁺, producing the ionic compound: MgCl₂

D) Se (Selenium) → Non-metal; generally forms covalent chlorides.

E) F (Fluorine) → Another non-metal; does not form a typical ionic compound with chlorine.

Full explanation

Saponification is the alkaline hydrolysis of esters, especially triglycerides (fats and oils).

General reaction: Triglyceride+3NaOH→Glycerol+3Soap (fatty acid salts) The ester bonds are broken by hydroxide ions.

Why the others are wrong:

A) No bases are synthesized; a base (NaOH or KOH) is used.

B) Triglycerides are broken down, not synthesized.

D) This is hydrolysis, not reduction.

E) Phospholipids are not formed during saponification.

Full explanation

Some common phosphorus oxoacids

Full explanation

Use Ohm's law: R=V/I

Given: V=1.5 V I=30 mA=0.03 A Substitute the values: R=1.5/0.03=50 Ω Therefore, the resistance is 50 Ω.

Full explanation

The volumetric flow rate is: Q=V/t Convert the given quantities to SI units: Volume: 200 L=0.2 m³ Time: 20 min=1200 s Now calculate: Q=0.2/1200=1.67×10^-4 m³/s Q~0.00017 m³/s

Therefore, the correct answer is about 0.00017 m³/s.

Full explanation

Impulse is given by: J=FΔt

Given: F=30 N Δt=10 s Substitute the values: J=30×10=300 N⋅s Therefore, the impulse is 300 N·s.

Full explanation

For perpendicular components, use the Pythagorean theorem: ∣V∣=√(V_x²+V_y²)

Given: V_x=3 V_y=4 Calculate: ∣V∣=√(3²+4²)=√(9+16)=√(25)=5 Therefore, the magnitude of the vector is 5.

Full explanation

The rules for equivalent resistance and capacitance are: Resistors in series: R_(eq)=R₁+R₂+⋯ Resistors in parallel: R_(eq)=R₁R₂/(R₁+R₂) (for two resistors) Capacitors in parallel: C_(eq)=C₁+C₂+⋯ Capacitors in series: C_(eq)=C₁C₂/(C₁+C₂) (for two capacitors) Therefore, the statement that capacitors in series add directly is incorrect.

Full explanation

Kirchhoff's first law, also called the current law (KCL), states that the algebraic sum of currents at a junction (node) is zero.

In other words, I=0 or equivalently, Total current entering a node=Total current leaving the node.

This expresses the conservation of electric charge.

Full explanation

The magnitude of the electric field produced by a point charge is given by E=k₀Q/r², where: k₀ is Coulomb's constant, Q is the charge, r is the distance from the charge.

The electric field is directly proportional to the charge and inversely proportional to the square of the distance.

Full explanation

A horizontal hyperbola centred at the origin has the form x²/a²-y²/b²=1, where: vertices are at (±a, 0), foci are at (±c, 0), c²=a²+b².

From the question: vertex: (3, 0) => a=3, so a²=9, focus: (4, 0) => c=4, so c²=16.

Thus, b²=c²-a²=16-9=7.

The equation is x²/9-y²/7=1.

Therefore, the correct answer is A.

Full explanation

The four points lie on the same circle, forming a cyclic quadrilateral.

The angles α and β are opposite angles of the cyclic quadrilateral, so they satisfy: α+β=180°.

Since α=130°, we get β=180°-130°=50°.

So the correct answer is E.

Full explanation

Use the identity (A-B)²=A²-2AB+B².

Let A=3ax, B=5ay.

Then (3ax-5ay)²=(3ax)²-2(3ax)(5ay)+(5ay)².

Simplifying, =9a²x²-30a²xy+25a²y².

Therefore, the correct answer is E.

Full explanation

Rewrite each equation in slope-intercept form: y=mx+b.

For option B, 3y-6x-4k=0 3y=6x+4k y=2x+4k/3.

The slope is always m=2, while the intercept changes with k.

Therefore, the lines are parallel.

Hence, the correct answer is B.

Full explanation

Volume: V=πr²h=π(6)²(12)=432π.

Total surface area: A=2πr(r+h)=2π(6)(6+12)=216π.

Therefore, V/A=432π/216π=2 cm.

So the correct answer is C.

Full explanation

First simplify the product: (1/2-x)(1/2+x)=(1/2)²-x²=1/4-x².

Since (-1)²=1, the inequality becomes -6x+1/4-x²-9<0.

Simplify: -x²-6x-35/4<0.

Multiply both sides by -4, remembering to reverse the inequality: 4x²+24x+35>0.

Factor: (2x+5)(2x+7)>0.

A product is positive when both factors have the same sign, so x<-7/2 or x>-5/2.