You are given the equation(s) used to solve a problem. write a realistic problem for which this is the correct equation(s) number 72

The rate at which the height is changing is ( 5 / x ) m / hr

We know that,

Area of an equilateral triangle A = [tex]\sqrt{3}[/tex] [tex]x^{2}[/tex] / 4

h = [tex]\sqrt{3}[/tex] x / 2

Where,

x = Side

h = Height

Given that,

dA / dt = 5 [tex]m^{2}[/tex] / hr

h = [tex]\sqrt{3}[/tex] x / 2

Differentiate both sides with respect to t

dh / dt = ( [tex]\sqrt{3}[/tex]  / 2 ) ( dx / dt )

dx / dt = ( 2 /  [tex]\sqrt{3}[/tex] ) ( dh / dt )

A = [tex]\sqrt{3}[/tex] [tex]x^{2}[/tex] / 4

Differentiate both sides with respect to t

dA / dt = ( [tex]\sqrt{3}[/tex] / 4 ) ( 2x ) ( dx / dt )

5 =  ( [tex]\sqrt{3}[/tex] / 4 ) ( 2x ) ( 2 /  [tex]\sqrt{3}[/tex] ) ( dh / dt )

dh / dt = ( 5 / x ) m / hr

Rate of change of height is defined as the rate at which height of an object changes with respect to time. It is represented as dh / dt

Therefore, the rate at which the height is changing is ( 5 / x ) m / hr

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The Mole fraction of Water in this solution is 0.34

We know that,

Mole Fraction of Water = No. of moles of Water / Total number of moles of the solution

No. of moles = Mass / Molar mass

Given that,

Mass of Water = 11g

Mass of Acetic acid = 72g

Molar mass of Water = 18.015 g/mol

Molar mass of Acetic acid = 60.052 g/mol

No. of moles of Water= 11 / 18.015= 0.611 moles

No. of moles of Acetic acid = 72 / 60.052= 1.199 moles

Total no. of moles = 0.611+ 1.199 = 1.81 moles

Mole fraction of chloroform = 0.611 / 1.81 = 0.338

In a solution containing at least 2 components, the number of moles of one component divided by total number of moles in that solution is called  Mole fraction.

Therefore, the Mole fraction of Water in this solution is 0.34

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When a new path of lesser resistance is made for an existing circuit a(n) short circuit occurs.

An electrical circuit short circuit is when two nodes that are supposed to be connected at different voltages make an improper connection. This leads to an electric current that can damage circuits, cause overheating, fire, or explosions, and is only constrained by the network's remaining nodes' equivalent Thevenin resistance. While short circuits are typically the result of a failure, they can occasionally be brought on purpose, such as when voltage-sensing crowbar circuit protectors are being installed.

An electrical connection that requires two nodes to have the same voltage is known as a short circuit in circuit analysis. Since there is no resistance and hence no voltage drop across the link in a "perfect" short circuit, there is no short circuit.

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The momentum change is 125440 kg.m/s.

We need to know about momentum to solve this problem. Momentum can be defined as the degree of difficulty to stop a moving object. It can be determined by

P = m . v

where P is momentum, m is mass and v is velocity.

Momentum also can be defined by kinetic energy

KE = 1/2 . m . v²

KE = P² / 2m

where KE is kinetic energy

From the question above, we know that:

m = 80 kg

h = 1 m

g = 9.8 m/s²

By conservation of energy, the initial kinetic energy is zero because of the person is in static condition. Hence, the initial momentum is

KEo = Po² / 2m

Po = 0 kgm/s

After the jump, the person will have maximum kinetic energy before landing which can be written

KE = PE

P² / 2m = m . g . h

P² = 2m² . 9.8 . 1

P² = 2.80² . 9.8 . 1

P² = 125440 kg.m/s

The momentum change is

ΔP = P - Po

ΔP = 125440 - 0

ΔP = 125440 kgm/s

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Valid line of code for displaying the twenty-eighth element of some array is System.out.println(somearray[27]).

Arrays are among the most well-known and essential data structures, and they are utilized by practically all programs. A wide variety of additional data structures, including lists and strings, are likewise implemented using them. They successfully take advantage of computers' addressing systems. The memory is a one-dimensional array of words whose indices are their addresses in the majority of contemporary computers and many external storage devices. Array operations are frequently optimized for by processors, especially vector processors.

The main reason why arrays are helpful is that the element indices may be calculated in real time. This feature, among other things, enables a single iterative statement to process an array's items in any number.

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The coefficient of kinetic friction is 0.255.

The ratio of the friction force to the normal force felt by a body moving on a dry, uneven surface is known as the kinetic friction coefficient (k).

Wb = Mg = 12 X 9.8 = 117.6 N. = Normal

force, Fn.

Fx-Ff = Ma.

Since the velocity is constant, the acceleration is zero.

Fx-Ff = MX0 = 0.

Ff = Fx = 30 N.

Ff = uXFn.

u = Ff/Fn = 30/117.6 = 0.255.

The coefficient of kinetic friction is 0.255

Kinetic friction is a force that exists between moving surfaces. A body moving on the surface feels a force in the reverse direction of its movement. The magnitude of the force is determined by the kinetic friction coefficient of the two materials.

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A toy car is given an initial velocity of 5.0 m/s east and experiences a constant acceleration of 2.0 m/s2 east. As a result, the toy car's final velocity is 17m/s

Velocity (v) is a vector quantity that represents displacement (or change in position, s) over time (t) via the equation v = s/t. Speed (or rate, r) is a scalar number that represents the distance travelled (d) divided by the change in time (t) by the equation r = d/t.

When an automobile begins at rest, its initial velocity is zero. When a projectile is launched into space, its initial velocity will be greater than zero. When a car comes to a halt after using the brakes, the starting velocity is greater than zero, but the end velocity is zero.

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This is an exercise on the density of liquids and gases.

The data provided in the exercise are:

Density (d) = ?

Mass (m) = 64g

Volume (v) = 8cm³

To calculate the density of the cube when it is placed on the balance, divide the mass divided by the volume. We apply the following formula:

We substitute our data in the formula and solve:

Answer: The density of the cube placed on the three-beam balance is 8 g/cm³. ✅

Answer: 25000 milligrams are in 25 grams

Explanation:

Answer:

25,000

Explanation:

Since 1 gram is 1,000 milligrams, multiply 25 x 1,000 to get the answer.

If a scientist wanted to determine the amount of space occupied by an object, she would measure its Volume

Volume in simple words can be called as a three dimensional area which is nothing but a measure of space occupied. Technically volume is the calculated by dividing the object's mass by its density.

V = m / ρ

The reason it cannot be mass or density is because a small amount of these quantities can occupy a larger space and a large amount of these quantity can occupy a smaller area. But in case of volume the space occupied is not based on matter present inside of it rather the physical appearance which is constant.

Therefore, if a scientist wanted to determine the amount of space occupied by an object, she would measure its Volume

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Scalar is a physical quantity  having only magnitude. (amount)

scalar quantity : The physical quantity which are specified with the magnitude are known as scalar quantities.

For example :

length - 5m

speed - 10 m/s , 10km/h etc

Mass - 6kg , 20g etc

energy - 30 joule

density - 56kg/m³

There is another quantity known as vector quantity.

vector quantity : The physical quantity which are specified by its magnitude and direction also.

For example, velocity, acceleration, force etc.

Scalar is a physical quantity  having only magnitude. (amount)

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The burning of fossil fuels is a threat to the environment.

The term pollution has to do with the introduction of harmful material and energy into the environment. We know that the burning of fossil fuels is one of the chief sources of pollution in the environment. This is can be seen from the images attached.

The burning of fossil fuels introduces carbon dioxide into the environment which in turn causes the temperature of the earth to rise. This is the situation that we call global warming.

The greatest concern of the earth is to ensure that the carbon burden is reduced and that the emission of the carbon to the atmosphere is mitigated in order to reduce the impact of this carbon on the earth.

Thus, the burning of fossil fuels is a threat to the environment.

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A frame of reference is just a set of coordinates that are used in the study of physics to calculate things like position and velocity. Axes that specify the three dimensions of space within the frame of reference are often included in such a frame.

A railway platform is an illustration of an inertial frame of reference. The platform doesn't move, hence it satisfies the requirement for not accelerating. The platform's objects move according to the law of inertia.

An acceleration with respect to an inertial frame characterizes a non-inertial reference frame. In general, an accelerometer at rest in a non-inertial frame will pick up a non-zero acceleration. While all inertial frames share the same laws of motion, non-inertial frames have different laws of motion depending on the acceleration. For example, let's imagine you are driving through a stop signal in an automobile. The automobile has stopped moving. The automobile accelerates when the light turns green. The car is not an inertial frame of reference when it is accelerating. You will feel yourself "pushed" into the seat if the acceleration is significant enough.

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The final velocity of the ball, given the data is –13.8 m/s

This is defined as the rate of change of velocity which time. It is expressed as

a = (v – u) / t

Where

The final velocity of the ball can be obtained as follow:

a = (v – u) / t

–2 = (v – 0.2) / 7

Cross multiply

v – 0.2 = –2 × 7

v – 0.2 = –14

Collect like terms

v = –14 + 0.2

v = –13.8 m/s

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7.4304*10²⁴ molecules water molecules are present in 222.22 ml sample of water ( molar mass =18.01 g/mol).

Mass of water = density * volume

=1.00gm/mμ*222.22mol

=222.22gn

No of moles of water = mass/molar mass

no of water molecules/Avogadro  no.=12.34 mol

no of water molecules= 12.34 mol * 6.022*10²³ mol

=74.304*10²³ molecules

=7.4304*10²⁴ molecules

so, 7.4304*10²⁴ molecules are present in 222.22 ml of water sample

7.4304*10²⁴ molecules.

One or more atoms make up molecules. They may have the same atoms (for example, an oxygen molecule has two oxygen atoms) or different atoms if they have more than one (a water molecule has two hydrogen atoms and one oxygen atom). Proteins and DNA are examples of biological compounds that can contain thousands of atoms.

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The radius is equal to the Earth’s radius. You can find this information online by computing the Earth’s surface area while assuming that it is a perfect sphere, then multiplying the result by the percentage of the planet that is covered in water.

Actually, you can demonstrate this without knowing the radius.

P/A = e•s•T4

Water has an emissivity, e, of roughly 0.96. And 5.67108 W/m2 K4 is the Stefan-Boltzmann constant.

The power radiated from a black body is described by the Stefan-Boltzmann law in terms of its temperature. The Stefan-Boltzmann constant, often known as the proportionality constant, is derived from several well-known physical constants.

Where k is the Boltzmann constant, h is the Planck’s constant, and c is the speed of light in a vacuum, the constant has the value since 2019

When compared to a black body, a body that does not completely absorb incident radiation (sometimes referred to as a grey body) emits less total energy.

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The correct answer 27 mm^3 is the volume of the cube measureing 3 mm x 3 mm x 3 mm.

The cube's volume is 3 in x 3 in x 3 in = 27 mm ^3

The volume of a cube is calculated by multiplying its side by three. Thus, the volume of a cube can be expressed as Volume of cube = s ^3, where s is the cube's side length. A cube's volume is the space enclosed by its six faces. In contrast to 2d shapes, it has additional dimensions in addition to length and width, which are known as height and thickness. As a result, the volume of a cube equals the product of its length, width, and height.

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A solar eclipse when the moon is at its far end of orbit, leaving a ring of light around the black circle of the moon is called a ring of fire.

When the moon passes in front of the sun and casts a shadow on Earth, there is a solar eclipse. Only during the new moon phase, when the moon travels squarely between the sun and Earth and casts shadows on its surface, can a solar eclipse occur.

The North and South Poles are unable to view total solar eclipses. Solar eclipses that are nearly identical occur every 18 years and 11 months. There can be two to five solar eclipses per year, depending on the Sun, Moon, and Earth's geometry. One to two years can pass between complete solar eclipses.

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A high-mass star has layers that are arranged in order of b. Temperature for fusion.

The temperature at which a substance transforms from a solid to a liquid is known as its melting point. The solid and liquid phases are in equilibrium at the melting point. Pressure affects a substance's melting point, which is typically reported at a standard pressure such 1 atmosphere or 100 kPa. There are two main categories of fusion reactions: those that maintain the ratio of protons to neutrons and those that convert protons to neutrons. The solid-liquid and liquid-to-gas transitions are connected with the typical heats of fusion and vaporization, respectively, for each substance.

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The velocity of the eagle relative to the air = 42.0 miles/hour

Vwp = Velocity of wind wrt person = 27 miles/hour

Vew = velocity of eagle wrt wind = 15 miles/hour

Vep = velocity of eagle wrt person

= Vew + Vwp

= 27 + 15 = 42 miles/hour

Then,

Vap = velocity of air relative to the person = Vwp = 27

Vap = Vwp = 27 miles/hour

Vea = Velocity of eagle relative to air

= Vea = 15 miles/hour

Vep = Vea + Vap

= 15 + 27 = 42 miles/hour

Any kind of motion that is perceived from or related to a material system that serves as a frame of reference (such as two neighboring walls and the floor of a room) is called as relative motion.

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Comparing these two values, Fgav is much greater than Fr.

First, calculate the force produced by the radiation pressure:

The radiation pressure produces a force equal to,

Fr=pr(πRe2)

=(I/c) ( πRe2)

Given that

I= Intensity of sun = 1370 W/m²

c = speed of light = 2.998×108m/s

Re = Radius of the earth=  6.37×106m

Ms= mass of sun = 2.0×1030kg

Me= mass of earth = 5.98×1024kg

des2 = distance of earth and sun apart =1.5×1011m

Substituting the given values according to the question

Fr= π (1.37 × 103 kW/m2) (6.37×106m)2/2.998×108m/s

=6.0×108N

(b) The gravitational pull of the Sun on the Earth is,

Fgav= GMsMe/ des2

putting values according to question

Fgav= (6.67×10−11 N⋅m2/kg2) (2.0×1030kg) (5.98×1024kg) / (1.5×1011m)2

=3.6×1022N.

Comparing these two values, it is obvious that Fgav is much greater than Fr.

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The weight of the fuel when the tank is filled is 2.13 kip.

The density of the fuel of the jet engine= 1.32 slug/ft³

The total volume of the fuel that can be filled in the fuel tank of a jet engine = 50 ft³

The specific weight of the fuel when the tank is filled is,

[tex] \gamma = p \times g[/tex]

[tex] \gamma = 1.32 \times 32.2[/tex]

[tex] \gamma = 42.504 \: ib/ft ^{3} [/tex]

The specific weight of the fuel when the tank is filled is 42.504 ib/ft ³.

The weight of the fuel when the tank is filled is,

[tex]w = \gamma \times ∀[/tex]

[tex]w = 42.5.4 \times 50[/tex]

[tex]w = 2.13 \: kip[/tex]

The weight of the fuel is 2.13 kip.

Therefore, the weight of the fuel when the tank is filled is 2.13 kip.

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Unshielded twisted-pair cable capable with a specification of 100 MHz/100 maps is also called category of switch.

The unshielded turned pair link is 100-ohm copper link that is constitutive of unshielded curved matches which range somewhere in the range of two to 1,000 and 800. They have no metallic covering on top of the contorted wires. This enjoys the benefit of making the link more modest in distance across. One normal use for protected wound pair links is to involve it in outrageous cold circumstances. Many individuals know that critical exploration is being led in very chilly region of the world. Truth be told, turned pair links have tracked down a great deal of utilizations in the media communications industry prior to getting well known in the PC organizing industry.

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The work w (in j) done by the force in moving an object is 222.4 J

We know that,

[tex]M_{n}[/tex] = ∑[tex]_{i = 1}^{n}[/tex] f ([tex]m_{i}[/tex] ) Δ

where,

i = [tex]i^{th}[/tex] rectangle

n = Number of rectangles

f ([tex]m_{i}[/tex] ) = Function of the curve evaluated at the midpoint of the [tex]i^{th}[/tex]   rectangle

[tex]m_{i}[/tex] = Midpoint of [tex]i^{th}[/tex] interval

Δ = Width of each rectangle

Given that,

x     5    9    13     17   21   25  29   33   37

f(x)  5  5.5  6.8  8.8  9.8  8.1  6.7  5.4  4.2

n = 4

Δ = ( 37 - 5 ) / 4

Δ = 8

∫[tex]_{5} ^{37}[/tex] f (x) dx = ∑[tex]_{i = 1}^{4}[/tex] f ([tex]m_{i}[/tex] ) Δ

∑[tex]_{i = 1}^{4}[/tex] f ([tex]m_{i}[/tex] ) Δ = 8 ( 5.5 +8.8 + 8.1 + 5.4 )

∑[tex]_{i = 1}^{4}[/tex] f ([tex]m_{i}[/tex] ) Δ = 222.4

∫[tex]_{5} ^{37}[/tex] f (x) dx = 222.4 J

The midpoint rule, also known as the midpoint Riemann sum is used to estimate integral of a function or area under a curve.

Therefore, the work w (in j) done by the force in moving an object is 222.4 J

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Answer:

1568 km/hr

Explanation:

First convert from ft/s to km/s

Do this by using a conversion rate.

3280 ft/km

(1429 ft/s)/(3280 ft/km) = 0.4355 km/s

Then convert from km/s to km/hr

Conversion rate 3600 s/hr

(0.4355 km/s)(3600 s/hr) = 1568 km/hr

The correct answer for the density of silver in kilograms per cubic meter is 10500 kg/m^3.

Silver has a density of 10.8103 kg/m3.Pure silver is nearly white, lustrous, soft, very ductile, and malleable, and it is an excellent heat and electricity conductor. Although it is not a chemically active metal, it is attacked by nitric acid (which forms nitrate) and hot concentrated sulfuric acid.

Atomic weight: 107.87 g.mol-1

At 20°C, the density is 10.5 g.cm-3.

962 °C melting point

2212 °C is the boiling point.

Silver has long been used in the manufacture of coins, ornaments, and jewelry due to its relative scarcity, brilliant white color, malleability, ductility, and resistance to atmospheric oxidation. Silver, along with gold and the platinum-group metals, is one of the so-called precious metals.

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True the total torque on the loop is the same regardless of what is chosen as the position of the vertical axis of rotation.

The term torque may also refer to the moment, moment of force, rotating force, or turning effect, depending on the topic of study.

In physics and mechanics, torque is the rotational equivalent of a force. It serves as an example of how a force can alter a body’s rotational motion.

Archimedes, who investigated the use of levers, is credited with creating the saying, “Give me a lever and a place to stand, and I shall move the Earth.”

Similar to how a linear force is either a push or a pull, a torque may be thought of as a twisting of an object about a specific axis. The sum of the force times its magnitude is the definition of torque.

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The airplane lands with a velocity of 150 m/s and its rate of deceleration is constant at -3 m/s^2,

[tex]u = 150 m/s[/tex]

[tex]a = -3 m/s^{2}[/tex]

[tex]v = 0[/tex]

According to the Equation of motion , [tex]v^{2} = u^{2} + 2as[/tex]

s = 3750 m

Equations of motion are the mathematical formula that describes the position, velocity, or acceleration of a body relative to a given frame of reference.

The airplane will have to travel 3750 m until it stops if its rate of deceleration is constant at -3 m/s^2.

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The force exerted by the pump is 4533.33 N

Force can be define as, that it is an external agent capable of changing an object's state of rest or motion. In a very simple word i.e. a push or pull upon an object resulting from the object's interaction with another object is also known as force and it is vector quantity . The unit of force F is Newton (N) .

F = ma

Here, F  is force, m is mass and a is acceleration of the object.

We are given that ,

The power of water pump = P = 3.4 × 10² watts

The rate of water to lift up = v = 7.5 ×10⁻²  m/s

Thus, to get the value of force F exerted by the pump to lift water up can be given as,

P = F × V

Where, p is the power , F is the force and V is the velocity of the pump. Since, the above equation can be express as,

F = P/V

F = (3.4 × 10² watts)/ (7.5 × 10⁻² )m/s

F = 4533.33 N

Therefore, the force exerted by the pump to lifted up water would be 4533.33N

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Tides are strongest when the earth, moon and sun are in line.

A tidal wave is a periodically occurring shallow water wave brought on by the ocean's gravitational interactions with the Sun, Moon, and Earth. Despite the fact that tides have nothing to do with tsunamis, the phrase "tidal wave" is frequently used to describe them. A storm surge, storm flood, tidal surge, or storm tide is a tsunami-like occurrence of rising water that frequently occurs along coastlines during low-pressure weather systems like cyclones. It is calculated as the increase in water level over the average tidal level and excludes waves.

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