All practice questions

Question 12661Question →

A field surveyor starts at point $P$ and walks $10\text{ km}$ due East to point $Q$ . From point $Q$ , she changes direction and walks $10\text{ km}$ on a bearing of $210^\circ$ to reach point $R$ . What is the bearing of point $P$ from point $R$ ?

330^\circ

060^\circ

150^\circ

300^\circ

Show answer & explanation

Answer: $330^\circ$

Answer

The bearing of point

P

from point

R

is

330^\circ

.

Point

Q

lies

10\text{ km}

East of

P

(bearing

090^\circ

). From

Q

, moving

10\text{ km}

on bearing

210^\circ

forms an interior angle of

60^\circ

with the line

QP

(which has bearing

270^\circ

). Because

PQ = QR = 10\text{ km}

and the included angle is

60^\circ

,

\triangle PQR

is equilateral, making

\angle QRP = 60^\circ

. The back bearing from

R

to

Q

is

030^\circ

. Subtracting the

60^\circ

interior angle from

030^\circ

yields a bearing of

330^\circ

for point

P

from point

R

.

Step-by-Step Solution

1

Determine the interior angle

\angle PQR

at point

Q

.

\angle PQR = 60^\circ

Since

P

is due West of

Q

, the bearing of

P

from

Q

is

270^\circ

. The bearing of

R

from

Q

is

210^\circ

. The interior angle between these two lines is

270^\circ - 210^\circ = 60^\circ

.

2

Analyze the properties of triangle

PQR

.

Triangle

PQR

is an equilateral triangle with side lengths

10\text{ km}

and interior angles of

60^\circ

.

Given

PQ = 10\text{ km}

and

QR = 10\text{ km}

,

\triangle PQR

is isosceles. Since the vertex angle

\angle PQR = 60^\circ

, the remaining two angles are also

60^\circ

each.

3

Calculate the back bearing of

Q

from

R

.

Bearing of

Q

from

R

is

030^\circ

.

The bearing of

R

from

Q

is

210^\circ

. The back bearing is

210^\circ - 180^\circ = 030^\circ

.

4

Compute the bearing of

P

from

R

.

Bearing of

P

from

R

is

330^\circ

.

From line

RQ

(bearing

030^\circ

), line

RP

lies

60^\circ

counter-clockwise (since

\angle QRP = 60^\circ

). Thus,

030^\circ - 60^\circ = -30^\circ \equiv 330^\circ

.

Key Concept

Bearings and Triangle Geometry

Question 12662Question →

Match each trade policy mechanism or commercial geography concept listed on the left with its defining economic role or structural function on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Customs Union matches with establishing internal free trade alongside a shared external tariff; Entrepôt Trade matches with importing commodities specifically for transit storage and re-exportation; Import Quota matches with setting explicit physical quantitative restrictions on imports; Currency Devaluation matches with purposefully reducing a nation's exchange rate to enhance export competitiveness.

Each concept aligns directly with its core functional mechanism in commercial geography: A Customs Union eliminates internal tariffs while adopting a Common External Tariff; Entrepôt Trade centers on transshipment and re-exportation of commodities; an Import Quota restricts the physical quantity of imported items; and Currency Devaluation lowers official exchange rates to make national exports cheaper internationally.

Step-by-Step Solution

1

Analyze trade integration frameworks

Identify that economic blocs which eliminate internal tariffs and adopt a common external tariff define a Customs Union.

This structural feature distinguishes a customs union from a basic free trade area or common market.

2

Evaluate transshipment port functions in commercial geography

Recognize that handling imported goods exclusively for redistribution and re-exportation constitutes Entrepôt Trade.

Entrepôt centers specialize in global logistics, storage, and re-exporting without altering the core nature of the goods.

3

Distinguish non-tariff trade control measures

Match the setting of explicit physical limits on import volumes to an Import Quota.

Unlike tariffs which alter price via taxes, quotas restrict the physical availability of foreign goods.

4

Examine macroeconomic trade adjustment mechanisms

Associate deliberate currency exchange rate reductions with Currency Devaluation.

Lowering currency value alters price ratios by making exports foreign-market cheap and foreign imports domestically expensive.

Key Concept

Trade barriers, economic integration stages, commercial port operations, and exchange rate policies in commercial geography

Question 12663Question →

Arrange the following stages of regional economic integration in Africa in order from the lowest level of economic integration to the highest level.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from lowest to highest level of economic integration is: Free Trade Area, Customs Union, Common Market, and Economic Union.

Regional economic integration progresses sequentially starting from a Free Trade Area (internal tariff removal), followed by a Customs Union (common external tariff), advancing to a Common Market (free movement of labor and capital), and culminating in an Economic Union (harmonized fiscal and monetary policy).

Step-by-Step Solution

1

Identify the foundational stage where internal trade barriers are eliminated.

Free Trade Area is the starting point of regional economic integration.

Countries first remove tariffs on trade among themselves before coordinating external trade rules.

2

Identify the stage that establishes unified external trade policies.

Customs Union is the second stage.

It builds upon the Free Trade Area by instituting a common external tariff against non-member nations.

3

Identify the stage allowing mobility of production factors across borders.

Common Market is the third stage.

It extends integration beyond physical trade to permit free movement of labor, capital, and services.

4

Identify the stage requiring institutional policy harmonization and monetary alignment.

Economic Union is the final and highest stage.

It requires member states to harmonize macro-economic policies and often adopt a unified currency.

Key Concept

Stages of Regional Economic Integration

Question 12664Question →

A radio station located at longitude $10^\circ\text{W}$ begins a live news broadcast at $2:15\text{ p.m.}$ local solar time. What is the local solar time at a receiving station located at longitude $35^\circ\text{E}$ when the broadcast is heard?

11:15\text{ a.m.}

3:55\text{ p.m.}

5:15\text{ p.m.}

12:35\text{ p.m.}

Show answer & explanation

Answer: $5:15\text{ p.m.}$

Answer

5:15\text{ p.m.}

The correct response of

5:15\text{ p.m.}

is derived by calculating the total longitudinal distance of

45^\circ

(

10^\circ\text{W} + 35^\circ\text{E}

), converting it to a 3-hour difference (

45^\circ / 15^\circ = 3\text{ hours}

), and adding 3 hours to the transmitting local time (

2:15\text{ p.m.}

) because the destination lies to the east.

Step-by-Step Solution

1

Calculate the total angular distance between the transmitting and receiving longitudes.

10^\circ\text{W} + 35^\circ\text{E} = 45^\circ

Since the two positions are in opposite hemispheres (West and East), their longitudinal values must be added together.

2

Convert the total angular distance into a time difference.

\frac{45^\circ}{15^\circ\text{ per hour}} = 3\text{ hours}

The Earth rotates

360^\circ

in 24 hours, which equals

15^\circ

of longitude per hour.

3

Adjust the initial local solar time according to relative direction.

2:15\text{ p.m.} + 3\text{ hours} = 5:15\text{ p.m.}

Because Earth rotates from west to east, locations situated further east experience solar time ahead of locations to the west.

Key Concept

Longitude and Local Solar Time Calculation

Estimated Time:1m 30s

Question 12665Question →

A mining corporation operating in a landlocked region needs to transport large volumes of heavy, low-value iron ore to a distant inland processing plant across terrain where navigable waterways are absent. Based on transport cost principles (terminal versus line-haul costs), which mode of transport is economically most suitable for this long-distance overland freight movement?

Rail transport

Road transport

Air transport

Pipeline transport

Show answer & explanation

Answer: Rail transport

Answer

Rail transport is economically most suitable because of its low line-haul costs per unit over long distances for heavy bulk freight.

Rail transport is designed for long-distance haulage of heavy, bulky, non-perishable goods. Although building tracks and terminals requires high initial capital, its line-haul cost per tonne-kilometer drops significantly over long distances, adhering to the tapering rate principle.

Step-by-Step Solution

1

Analyze cargo characteristics and distance constraints

The cargo is heavy, low-value bulk solid material (iron ore) moving over long overland distances without water routes.

Transport selection depends on matching cargo bulk/value ratio with distance and modal cost curves.

2

Evaluate transport cost structure (Terminal vs. Line-haul costs)

Road has low terminal but high line-haul costs. Rail has high terminal but low line-haul costs for long overland distances.

Over long distances, low line-haul costs outweigh high fixed terminal setup costs.

3

Select the optimal transport mode

Rail transport offers the lowest cost per tonne-kilometer for heavy bulk solids across long inland distances.

Rail provides high carrying capacity and energy efficiency over long distance land corridors.

Key Concept

Tapering cost principle and modal suitability for freight transport

Question 12666Question →

In triangle $PQR$ , the side lengths are $p = 8\text{ cm}$ and $q = 15\text{ cm}$ , and the included angle $\angle R = 60^\circ$ . What is the length of side $r$ in centimeters?

Show answer & explanation

Answer: 13

Answer

The length of side

r

is

13\text{ cm}

.

Using the Cosine Rule formula

r^2 = p^2 + q^2 - 2pq \cos R

with

p=8

,

q=15

, and

R=60^\circ

, we calculate

r^2 = 64 + 225 - 240(0.5) = 169

. Taking the square root gives

r = 13\text{ cm}

.

Step-by-Step Solution

1

Identify the given values and appropriate trigonometric rule

Givens:

p = 8\text{ cm}

,

q = 15\text{ cm}

,

\angle R = 60^\circ

. Since two sides and the included angle (SAS) are given, use the Cosine Rule:

r^2 = p^2 + q^2 - 2pq \cos R

.

The Cosine Rule is required to find the third side when two sides and their included angle are known.

2

Substitute the values into the Cosine Rule formula

r^2 = 8^2 + 15^2 - 2(8)(15) \cos 60^\circ

Replacing variables with their numerical equivalents sets up the algebraic calculation.

3

Calculate the terms and evaluate

r^2

r^2 = 64 + 225 - 240 \times 0.5 = 289 - 120 = 169

Since

\cos 60^\circ = 0.5

, simplify the arithmetic operations.

4

Solve for side length

r

r = \sqrt{169} = 13\text{ cm}

Take the square root of both sides to obtain the length of side

r

.

Key Concept

Applying the Cosine Rule to find an unknown side given two sides and the included angle (SAS)

Question 12667Question →

In satellite remote sensing, sensor performance and data utility are defined by distinct resolution dimensions. Match each resolution type on the left with its correct definition on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Spatial Resolution matches the minimum ground area dimensions per pixel; Spectral Resolution matches the number and width of electromagnetic wavelength bands; Radiometric Resolution matches sensor sensitivity to variations in energy intensity; Temporal Resolution matches satellite revisit frequency over the same location.

Each resolution type targets a specific dimension of remote sensing data: spatial for ground distance/pixel size, spectral for waveband detail, radiometric for signal energy sensitivity, and temporal for revisit frequency.

Step-by-Step Solution

1

Identify spatial measurement characteristics in remote sensing.

Spatial resolution determines ground cell size (pixel resolution).

Pixel dimensions govern spatial detail.

2

Identify spectral characteristics.

Spectral resolution relates to electromagnetic band sampling.

It defines how spectral bands are isolated.

3

Identify radiometric characteristics.

Radiometric resolution relates to energy levels and bit depth.

It measures sensitivity to subtle signal differences.

4

Identify temporal characteristics.

Temporal resolution defines time between successive satellite imaging passes.

Temporal relates directly to time frequency.

Key Concept

Four Resolution Dimensions in Remote Sensing

Estimated Time:45s

Question 12668Question →

Match each thermometer type on the left with its corresponding physical thermometric property on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Constant-volume gas thermometer matches variation of gas pressure at constant volume; Thermocouple matches variation of electromotive force (e.m.f.); Platinum resistance thermometer matches variation of electrical resistance; Liquid-in-glass thermometer matches variation of liquid column length/volume.

Each thermometer is paired with its corresponding thermometric property: constant-volume gas thermometer relies on gas pressure variation, thermocouple relies on thermoelectric e.m.f. variation, resistance thermometer relies on electrical resistance variation, and liquid-in-glass thermometer relies on liquid thermal expansion.

Step-by-Step Solution

1

Identify the thermometric property for a constant-volume gas thermometer.

Gas pressure at constant volume.

Pressure varies linearly with temperature for an ideal gas at constant volume.

2

Identify the thermometric property for a thermocouple.

Electromotive force (e.m.f.).

The thermoelectric effect generates an e.m.f. proportional to the temperature difference between two junctions.

3

Identify the thermometric property for a platinum resistance thermometer.

Electrical resistance.

The electrical resistance of platinum increases continuously and predictably with temperature.

4

Identify the thermometric property for a liquid-in-glass thermometer.

Liquid column length/volume.

The liquid expands linearly along the capillary stem as temperature rises.

Key Concept

Thermometric Properties of Thermometers

Question 12669Question →

On a regional planning map drawn to a Representative Fraction (R.F.) scale of $1 : 80,000$ , a proposed bypass road between two industrial hubs measures $16.5\text{ cm}$ . What is the actual ground distance of the bypass road in kilometers?

13.2\text{ km}

132.0\text{ km}

4.85\text{ km}

26.4\text{ km}

Show answer & explanation

Answer: $13.2\text{ km}$

Answer

The actual ground distance of the bypass road is

13.2\text{ km}

.

Multiplying the map distance of

16.5\text{ cm}

by the scale denominator

80,000

yields

1,320,000\text{ cm}

. Converting centimeters to kilometers by dividing by

100,000

correctly yields

13.2\text{ km}

.

Step-by-Step Solution

1

Calculate the ground distance in centimeters using the Representative Fraction scale.

\text{Ground Distance (cm)} = 16.5\text{ cm} \times 80,000 = 1,320,000\text{ cm}

The R.F. scale of

1 : 80,000

indicates that

1\text{ cm}

on the map represents

80,000\text{ cm}

on the ground.

2

Convert the ground distance from centimeters to kilometers.

\text{Ground Distance (km)} = \frac{1,320,000\text{ cm}}{100,000\text{ cm/km}} = 13.2\text{ km}

There are

100,000\text{ cm}

in

1\text{ km}

(

100\text{ cm/m} \times 1,000\text{ m/km}

).

Key Concept

Ground distance calculation from Representative Fraction (R.F.) map scale

Question 12670Question →

The establishment and spatial concentration of major cement manufacturing complexes at Ewekoro and Sagamu in Ogun State, Gboko in Benue State, and Nkalagu in Ebonyi State demonstrate a specific principle of industrial location. Which factor primarily determined the choice of these industrial sites?

Proximity to heavy, weight-losing raw material deposits

High market demand in adjacent densely populated metropolitan centers

Direct access to major coastal seaport facilities for importing clinker

Abundant supply of agricultural crop resins used as binding agents

Show answer & explanation

Answer: Proximity to heavy, weight-losing raw material deposits

Answer

The primary factor determining the location of cement plants at Ewekoro, Sagamu, Gboko, and Nkalagu is their proximity to heavy, weight-losing raw material deposits (limestone quarries).

The correct answer highlights proximity to heavy, weight-losing raw material deposits. Cement manufacturing requires vast quantities of limestone. Because limestone loses substantial weight during high-temperature processing to form clinker, locating factories directly at limestone quarry sites minimizes overall freight costs.

Step-by-Step Solution

1

Identify the primary raw materials used in cement manufacturing in Nigeria.

Cement manufacturing requires limestone, clay/shale, and gypsum, with limestone constituting over 75% of the total raw material mass.

Understanding the input requirements is essential for analyzing industrial orientation.

2

Apply industrial location principles (Weber's Least Cost Theory) to weight-losing materials.

Limestone loses significant weight and bulk during calcination and clinker formation. Moving raw limestone long distances incurs prohibitive transport charges compared to transporting finished bagged cement.

Weight-losing raw materials attract manufacturing plants to the source of the raw material rather than the market.

3

Correlate the physical geological sites with the plant locations.

Ewekoro/Sagamu (Ewekoro formation), Gboko (Lower Benue Trough), and Nkalagu (Asu River group) are all situated directly atop extensive limestone and marble deposits.

Validates that quarry proximity was the key location determinant.

Key Concept

Raw Material Orientation of Weight-Losing Heavy Industries

Question 12671Question →

Match each elementary surveying instrument listed on the left with its primary fieldwork function on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Gunter's Chain matches measuring linear distances for land area units; Abney Level matches measuring vertical slope angles; Surveying Arrows match marking completed full chain lengths; Plumb Bob matches centering instruments precisely over ground station pegs.

Each instrument is correctly paired based on standard practical geography fieldwork procedures: Gunter's chain is calibrated for land area (acreage) calculations; the Abney level measures vertical slope angles; surveying arrows tally completed chain intervals along the baseline; and the plumb bob provides precise vertical centering of equipment over ground station pegs.

Step-by-Step Solution

1

Identify the primary structural design and historical purpose of Gunter's Chain

Gunter's chain measures

66\text{ ft}

(

4\text{ rods}

), providing a direct link between linear chaining and land area units in acres.

It was specifically constructed so that

10\text{ square chains} = 1\text{ acre}

.

2

Determine the operational function of an Abney Level

The instrument is used for vertical angle measurement and slope determination during field reconnaissance.

It incorporates a handheld sighting tube with a index arm and spirit level attached to a vertical arc.

3

Distinguish between auxiliary chain survey tools (Arrows vs. Plumb Bob)

Surveying arrows mark completed chain intervals, while a plumb bob ensures vertical alignment over a ground mark.

The follower collects arrows inserted by the leader to tally chain lengths, whereas a plumb bob uses gravity for accurate station centering.

Key Concept

Elementary Surveying Instruments and Fieldwork Functions

Estimated Time:2m 0s

Question 12672Question →

Given the matrix $A = \begin{pmatrix} 3 & 1 \\ 4 & 2 \end{pmatrix}$ , what is the determinant of the matrix $3A$ ?

6

18

30

54

Show answer & explanation

Answer: $18$

Answer

The determinant of the matrix

3A

is

18

.

For any

2 \times 2

matrix, scaling the matrix by a factor

k

scales its determinant by

k^2

. Since

\det(A) = (3)(2) - (1)(4) = 2

, multiplying the matrix by

3

yields

\det(3A) = 3^2 \times 2 = 9 \times 2 = 18

. Alternatively, computing

3A = \begin{pmatrix} 9 & 3 \\ 12 & 6 \end{pmatrix}

directly gives

\det(3A) = (9)(6) - (3)(12) = 54 - 36 = 18

.

Step-by-Step Solution

1

Calculate the determinant of matrix

A

.

\det(A) = (3)(2) - (1)(4) = 6 - 4 = 2.

The determinant of a

2 \times 2

matrix

\begin{pmatrix} a & b \\ c & d \end{pmatrix}

is given by

ad - bc

.

2

Apply the determinant scalar multiplication property for an

n \times n

matrix.

\det(3A) = 3^2 \det(A) = 9 \times 2 = 18.

For any

n \times n

square matrix

A

and scalar

k

, the identity

\det(kA) = k^n \det(A)

holds. Here,

k=3

and

n=2

.

Key Concept

Scalar Multiplication Property of Determinants

Estimated Time:1m 15s

Question 12673Question →

An energy board in West Africa is evaluating power sources to ensure sustainable long-term development. Which of the following best explains why geothermal energy is classified as a renewable natural resource, whereas coal deposits are classified as non-renewable?

Geothermal energy is continuously naturally replenished on a human timescale, whereas coal forms over geological periods far exceeding human rate of consumption.

Geothermal heat originates from inorganic Earth processes, whereas coal originates from ancient organic matter.

Geothermal plants cause no environmental degradation, whereas coal extraction severely disrupts topsoil and vegetation.

Geothermal energy can be recycled after consumption, whereas thermal energy from coal combustion is permanently lost.

Show answer & explanation

Answer: Geothermal energy is continuously naturally replenished on a human timescale, whereas coal forms over geological periods far exceeding human rate of consumption.

Answer

Geothermal energy is classified as renewable because it is naturally replenished on a human timescale, whereas coal forms over geological timeframes far exceeding its rate of consumption.

Renewability is defined by the rate at which a natural resource naturally replenishes relative to human consumption. Geothermal heat is continuously supplied by the Earth's interior processes on a human timeframe, whereas coal is a fossil fuel whose geological formation process requires millions of years, making it finite and exhaustible.

Step-by-Step Solution

1

Define the criterion for natural resource classification (renewable vs. non-renewable).

Classification depends primarily on the rate at which the resource is naturally replenished relative to human rate of utilization.

Renewable resources naturally regenerate fast enough to be sustained indefinitely under proper management.

2

Analyze geothermal heat as an energy source.

Geothermal energy draws on continuous subsurface heat flows generated by planetary thermal decay, providing ongoing replenishment.

This heat flux is functionally infinite and self-renewing on human time horizons.

3

Analyze coal deposits as a fossil fuel resource.

Coal forms from compressed organic matter under heat and pressure over millions of years.

Because its formation rate is millions of times slower than current extraction rates, coal reserves are finite and exhaustible.

Key Concept

Resource Classification by Rate of Replenishment

Estimated Time:1m 0s

Question 12674Question →

Which of the following instruments is specifically used to measure wind speed at a weather station?

Anemometer

Wind vane

Barometer

Hygrometer

Show answer & explanation

Answer: Anemometer

Answer

The instrument specifically used to measure wind speed is the anemometer.

An anemometer is designed with cups or vanes that rotate as wind passes across them; the rotation rate directly corresponds to wind speed.

Step-by-Step Solution

1

Identify the weather element specified in the question stem.

The target weather element to measure is wind speed.

Different atmospheric parameters require specific recording instruments.

2

Match the targeted element (wind speed) to its corresponding standard measuring instrument.

The anemometer (commonly a cup anemometer) is the standard instrument that measures wind speed in meters per second or knots.

The rotating cups of an anemometer spin at a rate proportional to wind speed.

Key Concept

Weather Elements and Instruments

Question 12675Question →

Arrange the following Nigerian towns in order of decreasing duration of the rainy season, starting from the town with the longest wet season to the town with the shortest wet season.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from longest to shortest rainy season duration is Calabar, followed by Enugu, then Kaduna, and finally Maiduguri.

The duration of the wet season in Nigeria depends primarily on latitude and proximity to the Atlantic Ocean, as moisture is brought by the maritime Tropical (mT) air mass. Coastal Calabar in the south receives the longest rainy period (9–10 months), followed by sub-coastal Enugu (7–8 months), interior Kaduna (5–6 months), and far northern Maiduguri in the Sahel zone (3–4 months).

Step-by-Step Solution

1

Analyze the latitudinal movement of the Inter-Tropical Discontinuity (ITD) across Nigeria.

The rain-bearing maritime Tropical (mT) air mass moves northward behind the advancing ITD from south to north, and retreats southward from north to south.

Duration of the rainy season in Nigeria decreases progressively from the southern coast to the far northern interior.

2

Determine the relative geographic locations and climatic belts of each town.

Calabar is coastal (South), Enugu is southern interior, Kaduna is northern middle-latitude (Sudan belt), and Maiduguri is far northeast (Sahel belt).

Latitudinal positioning directly correlates with annual rainfall duration.

3

Sequence the towns from highest annual rainy season duration to lowest.

Calabar (9–10 months) > Enugu (7–8 months) > Kaduna (5–6 months) > Maiduguri (3–4 months).

Southern coastal areas stay under the influence of moisture-bearing winds longest, while northern continental fringes receive brief seasonal rainfall.

Key Concept

Rainfall gradient and seasonality driven by ITD movement across Nigeria

Estimated Time:1m 0s

Question 12676Question →

If the determinant of the matrix $A = \begin{pmatrix} k & 1 & 2 \\ 3 & -1 & 0 \\ 2 & 4 & 1 \end{pmatrix}$ is equal to $17$ , what is the value of $k$ ?

Show answer & explanation

Answer: 8

Answer

The value of

k

is

8

.

Expanding the matrix determinant along the first row gives

\det(A) = k(-1) - 1(3) + 2(14) = -k + 25

. Setting

-k + 25 = 17

leads to

-k = -8

, so

k = 8

.

Step-by-Step Solution

1

Perform cofactor expansion along the first row of matrix

A

.

\det(A) = k((-1)(1) - (0)(4)) - 1((3)(1) - (0)(2)) + 2((3)(4) - (-1)(2))

Expanding along the first row uses the formula \det(A) = a_{11}C_{11} + a_{12}C_{12} + a_{13}C_{13}.

2

Evaluate the products and simplify the algebraic expression for the determinant.

\det(A) = -k - 3 + 28 = -k + 25

Simplifying each sub-determinant term yields a linear expression in

k

.

3

Equate the expression to

17

and solve for

k

.

-k + 25 = 17 \implies k = 8

Subtracting 25 from both sides gives

-k = -8

, which simplifies to

k = 8

.

Key Concept

Determinant of a 3x3 Matrix

Question 12677Question →

A point charge $Q = +6.0 \times 10^{-9}\text{ C}$ is fixed in a vacuum. A small test charge $q = +2.0 \times 10^{-9}\text{ C}$ is placed at a distance of $0.30\text{ m}$ from $Q$ . What is the magnitude of the electric field intensity produced by $Q$ at the location of the test charge? [Take $k = 9.0 \times 10^9\text{ N m}^2\text{ C}^{-2}$ ]

1.8 \times 10^2\text{ N C}^{-1}

6.0 \times 10^2\text{ N C}^{-1}

8.0 \times 10^2\text{ N C}^{-1}

1.2 \times 10^{-6}\text{ N C}^{-1}

Show answer & explanation

Answer: $6.0 \times 10^2\text{ N C}^{-1}$

Answer

6.0 \times 10^2\text{ N C}^{-1}

The magnitude of the electric field intensity

E

created by a point charge

Q

at a distance

r

is given by

E = \frac{k Q}{r^2}

. Substituting

k = 9.0 \times 10^9\text{ N m}^2\text{ C}^{-2}

,

Q = 6.0 \times 10^{-9}\text{ C}

, and

r = 0.30\text{ m}

yields

E = \frac{54}{0.09} = 600\text{ N C}^{-1}

, which equals

6.0 \times 10^2\text{ N C}^{-1}

. The test charge magnitude does not affect the electric field produced by the source charge.

Step-by-Step Solution

1

Identify the formula for electric field intensity due to a point charge

E = \frac{k Q}{r^2}

The electric field intensity depends solely on the magnitude of the source charge

Q

and the square of the distance

r

from it.

2

Substitute the given values into the formula

E = \frac{(9.0 \times 10^9\text{ N m}^2\text{ C}^{-2}) \times (6.0 \times 10^{-9}\text{ C})}{(0.30\text{ m})^2}

Insert

k = 9.0 \times 10^9

, source charge

Q = 6.0 \times 10^{-9}\text{ C}

, and distance

r = 0.30\text{ m}

.

3

Simplify the arithmetic

E = \frac{54}{0.09} = 600\text{ N C}^{-1} = 6.0 \times 10^2\text{ N C}^{-1}

Squaring

0.30

gives

0.09

, and dividing

54

by

0.09

yields

600\text{ N C}^{-1}

.

Key Concept

Electric Field Intensity of a Point Charge

Question 12678Question →

The primary economic and ecological rationale for environmental conservation is that natural ecosystems provide essential life-support services whose degradation creates long-term socio-economic costs that far exceed the short-term profits of unsustainable resource exploitation.

True

False

Show answer & explanation

Answer: True

Answer

The statement is TRUE.

The statement correctly highlights the core need for environmental conservation: preserving ecological services that serve as the foundational infrastructure for human health, food security, and sustained economic welfare.

Step-by-Step Solution

1

Examine the fundamental definition and necessity of environmental conservation.

Conservation involves the wise management and sustainable use of environmental resources to satisfy present needs without compromising future generations.

Determining the truth of the statement requires identifying why environmental management is essential for human societies.

2

Analyze the economic and ecological trade-offs mentioned in the statement.

Unsustainable activities generate fast economic returns but collapse essential natural infrastructure, resulting in severe long-term financial, health, and environmental crises.

Evaluating cost-benefit dynamics confirms that conserving ecosystem services prevents catastrophic future losses.

Key Concept

Concept and Need for Environmental Conservation

Question 12679Question →

Match each urban land-use model or settlement phenomenon listed on the left with its defining geographical characteristic or urban outcome on the right.

Click a left item, then click its matching right item

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Answer

Burgess Concentric Zone Model matches urban growth in successive concentric rings from the core; Hoyt Sector Model matches expansion along transport corridors forming wedge-shaped sectors; Urban Heat Island matches elevated microclimatic temperatures in built-up centers relative to rural margins; Peripheral Slum Proliferation matches substandard informal housing growth on city outskirts caused by rapid rural-urban influx.

Each urban term correctly aligns with its spatial or environmental characteristic: the Burgess model describes concentric expansion, the Hoyt model describes wedge-shaped transport sectors, the Urban Heat Island describes urban thermal elevation, and peripheral slum proliferation describes informal settlement growth from unmanaged migration.

Step-by-Step Solution

1

Analyze urban land-use structure models

Differentiate between circular ring expansion (Burgess model) and corridor/wedge-shaped expansion (Hoyt model).

Burgess focuses on radial distance rings from the CBD, while Hoyt emphasizes transport routes directing linear sectoral growth.

2

Analyze microclimatic urban environmental problems

Identify the Urban Heat Island effect as atmospheric warming in dense downtown zones due to thermal mass and waste heat.

Urban infrastructure absorbs heat during the day and re-radiates it at night, elevating urban temperatures above rural surroundings.

3

Analyze social and housing settlement problems

Link peripheral slum proliferation with rapid urban migration exceeding municipal planning capacity.

Low-income migrants build informal, unserviced shelters on vacant peripheral land when formal urban housing is unavailable.

Key Concept

Urban Land-Use Models and Environmental/Social Settlement Problems

Question 12680Question →

Arrange the following levels of settlement hierarchy found in Nigeria in ASCENDING order based on their typical population size and complexity of economic functions, starting from the lowest level.

Drag items to arrange them in the correct order

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Answer

The correct ascending sequence of Nigerian settlement hierarchy levels is Isolated Farmstead / Homestead, Rural Hamlet, Nucleated Agricultural Village, and Metropolitan Urban Center.

Settlement hierarchy categorizes human habitations from smallest to largest based on population threshold, land coverage, and the range of central functions provided. The isolated farmstead/homestead is the smallest unit (single family), followed by a rural hamlet (small cluster of homes), then a nucleated agricultural village (larger rural population with periodic markets), and finally a metropolitan urban center (large population, high density, and specialized non-agricultural services).

Step-by-Step Solution

1

Identify the lowest functional unit of habitation in rural Nigeria.

The Isolated Farmstead / Homestead is the smallest unit, typical of dispersed agricultural areas such as parts of the Benue Valley.

It contains only a single housing structure or family compound with minimal land footprint.

2

Identify the next tier above an isolated homestead.

The Rural Hamlet forms the second tier.

It clusters several homesteads together to form a small hamlet with a low population threshold.

3

Determine the rural community center level.

The Nucleated Agricultural Village forms the third tier.

Villages aggregate larger populations capable of supporting periodic local markets, primary schools, and health centers.

4

Identify the highest settlement order in the given list.

The Metropolitan Urban Center occupies the highest tier.

Metropolitan cities like Ibadan, Kano, and Lagos serve as major economic, commercial, and administrative hubs with high population density and secondary/tertiary functions.

Key Concept

Settlement Hierarchy and Population Distribution in Nigeria

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