when a nucleus emits a beta particle, the mass number of the nucleus ____________. (2 points) decreases increases remains the same doubles

The net electric force on particle q₂ is determined as -9.86 N.

The net force of particle q₂ is determined by applying Coulomb's law of electrostatic force.

The electric force between particle q₁ and q₂ is the repulsive force and the magnitude is calculated as;

F₁₂ = kq₁q₂ / r²

where;

F₁₂ = -(9 x 10⁹ x 13 x 10⁻⁶ x 7.7 x 10⁻⁶) / (0.25²)

F₁₂ = -14.4 N

The electric force between particle q₃ and q₂ is the attractive force and the magnitude is calculated as;

F₂₃ = kq₃q₂ / r²

F₂₃ = (9 x 10⁹ x 5.9 x 10⁻⁶ x 7.7 x 10⁻⁶) / (0.3²)

F₂₃ = + 4.54 N

The net force on the particle q₂ is calculated as;

F (net) = F₁₂ + F₂₃

F (net) = -14.4 + 4.54

F (net) = -9.86 N

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1. A virtual image is a made-up picture. A light beam that is diverging causes it to happen.

2. Convex lenses are converging lenses, whereas concave lenses are diverging lenses. When parallel rays enter a convex lens, the beams converge to a single point (the focal point), but in the case of a concave lens, the beams diverge.

3. Parallel rays converge to a point at a concave mirror and divert to a convex mirror when they reach it. Convex lenses are analogous to concave mirrors.

4. A concave mirror can indeed be utilized to ignite.

What are concave and convex mirror?

When a hollow sphere's inside surface serves as the reflecting surface and the cut part's outside is painted, the result is a mirror. A concave mirror is the name for this kind of mirror.

If the hollow sphere's cut-out portion is painted from the inside out, then its outside becomes the reflective surface. A convex mirror is the name given to this type of mirror.

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The output voltage is measured across the capacitor in an L-R-C series circuit, and the expression for Vout/vs for a low-pass filter is 1/(1-w^2lc + (wcR)^2. depending on the angular frequency.

A linear shunt regulator's output voltage (LSR) is defined as the difference between the input voltage and the sum of the current flowing through the shunt resistance, and it is denoted by Vo = Vi- (io+Ish)*Rsh or output voltage = input voltage- (output current + shunt field current)*shunt field resistance. The angular frequency, also known as the angular frequency vector, is the size of the vector quantity called angular velocity. The rotational speed of an object is measured by its angular frequency. It is helpful in many scientific and mathematical fields since it makes it possible to comprehend a wide range of physical world objects' qualities.

Vout = Vs/(R+jwl+1/jwc)

Vout/vs = 1/(1-w^2lc + (wcR)^2

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0.12kg of mass, must be added to the object to change the period to 1.8 s.

The period is the amount of time needed for a simple pendulum to swing back and forth (backwards). Seconds (s) are the SI unit of time. A simple pendulum completes one cycle when it swings back and forth.

The amount of matter in a particle or object is represented by its mass, a dimensionless quantity. In the International System, the kilogram serves as the primary unit of mass.

Calculations:

Given

mass suspended from string M = 0.46kg

Oscillating time T = 1.6sec

To find (M') Mass added to change oscillating time to T' = 1.8sec

we know that:

T = 2π/ω

ω = √ (K/M)

T = 2π √ (K/M)

T = 2π ×  √ (M/K)

1.6 = 2 × 3.14 × √ (0.46) /K

1.6/6.28 = √ (0.46) /K

0.254 = √ (0.46) /K

Sq. In both sides

(0.254) ² = {√ (0.46) /K}²

0.645 = 0.46 /K

K= 7.13N/m

Now, for time T'

T' = 2π ×  √ (M'/K)

1.8 = 2 × 3.14 × √(M' /7.13)

1.8/6.28 = √(M' /7.13)

0.286 = √(M' /7.13)

Sq. In both sides

(0.286)²= √(M' /7.13)²

0.0817 = M' /7.13

M'= 0.0817 × 7.13

M' = 0.58kg

To find the added mass

=M' - M

=(0.58 - 0.46) kg

= 0.12kg.

Hence, 0.12kg of mass, must be added to the object to change the time period to 1.8 s.

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The magnitude of the acceleration of the skydiver will be 9.4m/s²

Acceleration is the rate of change in velocity.

It involves a change in speed and direction. When acceleration involves a change in speed only there is; Positive acceleration which occurs when an object speeds up. Negative acceleration occurs when an object slows down. Acceleration is a change of velocity over a period of time, expressed by the equation below.

A=Δv/t

At terminal velocity v, acceleration;

a = g

where,

g = Acceleration due to gravity (9.8m/s²)

ma = mg - m[tex](\frac{1}{2}) ^{2}[/tex]g

a = g(1 - [tex]\frac{1}{25}[/tex])

a = [tex]\frac{24}{25}[/tex]g

a = [tex]\frac{24}{25}[/tex] x 9.8

a = 9.4m/s²

The acceleration of the skydiver who is currently falling at one-fifth his eventual terminal speed is 9.4m/s²

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The phrases that best express separation and movement are those. A. Displacement and distance both have a direction. (Select A).

Transferring unfavorable emotions from one item or person to another is referred to as displacement and is a defensive tactic. To "take out" their rage on a family member, for instance, a person can yell at them if they are upset with their job.

Replace, supersede, and supplant are some frequent alternatives to the word "displace." While all of these phrases refer to "putting out of a normal or suitable position or into the place of another. Thousand had been displaced by fighting.

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The image's size is 1.2 cm.

Given data:

- [tex]$d_0$[/tex] is the distance of the face from the bottom of the bowl

- [tex]$R=40 \mathrm{~cm}$[/tex] is the radius of curvature of the bowl

-[tex]$h_o=5 \mathrm{~cm}$[/tex] is the height of the nose

What is bottom of the bowl acts as a convex mirror?

The focal length of the convex mirror is given by:

[tex]f=-\frac{R}{2}$$[/tex]

or

[tex]f=-\frac{40 \mathrm{~cm}}{2}$$[/tex]

or

[tex]f=-20 \mathrm{~cm}$$[/tex]

Let, [tex]$d_i$[/tex] be the distance of the image of the nose.

The mirror equation is given by:

[tex]\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$$[/tex]

we have:

-[tex]$d_o=64 \mathrm{~cm}$[/tex]

- [tex]$f=-20 \mathrm{~cm}$[/tex]

Let, [tex]$d_i$[/tex] be the distance of the image of the nose.

The mirror equation is given by:

[tex]\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$$[/tex]

we have:

[tex]$\bullet d_o=64 \mathrm{~cm}$[/tex]

- [tex]$f=-20 \mathrm{~cm}$[/tex]

Plugging in the values, we get:

[tex]$$\begin{aligned}& \frac{1}{-20 \mathrm{~cm}}=\frac{1}{64 \mathrm{~cm}}+\frac{1}{d_i} \\& \text { or } \\& \frac{1}{d_i}=-\left(\frac{1}{20 \mathrm{~cm}}+\frac{1}{64 \mathrm{~cm}}\right) \\& \text { or } \\& d_i=-15 \mathrm{~cm}\end{aligned}$$[/tex]

Negative sign indicates that the image is virtual and formed behind the mirror.

Let, [tex]$h_i$[/tex] be the height of the image of the nose.

The magnification formula is given by:

[tex]m=-\frac{d_i}{d_o}=\frac{h_i}{h_o}$$[/tex]

we have

- [tex]$d_o=64 \mathrm{~cm}$[/tex]

- [tex]$d_i=-15 \mathrm{~cm}$[/tex]

- [tex]$h_o=5 \mathrm{~cm}$[/tex]

Plugging in the values, we get:

[tex]$$-\left(\frac{-15 \mathrm{~cm}}{64 \mathrm{~cm}}\right)=\frac{h_i}{5 \mathrm{~cm}}$$[/tex]

or

[tex]$$h_i=\frac{15 \times 5}{64} \mathrm{~cm}$$[/tex]

or

[tex]$$h_i=1.2 \mathrm{~cm}$$[/tex]

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Full range of vertical motion is 4m.

Frequency is 0.6 Hz.

Amplitude is 2m.

What is Oscillation?

Oscillation is the process of any quantity or measure repeatedly varying about its equilibrium value in time. Another definition of oscillation is the periodic variation of a substance between two values or around its core value.

Given,

Amplitude, A = 2m

Time= 6 s

So, the full range of vertical motion is

= 2 × 2= 4m

We know,

Frequency is inversely proportional to time

∴ f = [tex]\frac{1}{T}[/tex] = [tex]\frac{1}{6}[/tex]

= 0.6 Hz

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48.7 m

When a stone is dropped from a cliff, the stone accelerates downwards due to gravity. We investigate the displacement-time using Newton's Second Law-based kinematic equations. When the stone hits the water surface, sound waves travel the same vertical displacement as the stone to reach the ear of the observer. The motion of sound is a constant-speed motion.

Write an equation for the time it takes for the stone  to hit water, PLUS the time for the sound of the splash to come bace. You know the total time; solve for the height, H. Use a suitable speed of sound, such as 340 m/s; you would need to assume a temperature for a more accurate value of the sound speed.

5(seconds) = H/340 + sqrt (2H/g)

[5- (H/340)]^2 = H/4.9

10-(2H/340) = H/4.9

10-0.0058H = H/4.9

H +0.0058H = 10 X 4.9

H(1+ 0.0058) = 49

H = 49/1.0058 =48.7 m

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The second statement is not true.

what is solar system?

We live on a planet that is part of the Milky Way galaxy's outer spiral arm.

Our solar system is made up of the Sun, our star, and everything gravitationally bound to it, such as the moons, planets, and dwarf planets such as Pluto, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.

The way the solar system formed is what determines the positioning of the planets and other celestial objects in our solar system. The solar system's early years saw only stony material capable of withstanding the heat closest to the Sun. Since terrestrial planets, the first four planets in the solar system are also known as these. All of them have stony, sturdy, and tiny exteriors.

Because of how our solar system developed, the planets and other celestial bodies are in a specific sequence and configuration. Only rocky material could tolerate the heat when the solar system was young because it was closest to the Sun. They are all small and have stony, solid surfaces.

A very small fraction of newly formed stars is encircled by gas spinning discs. This statement is not true.

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The amount of fluid the object displaces equals the buoyant force's magnitude.This really is true for any object that is partially or entirely submerged in a fluid.

The object can stay suspended at its current depth if the hydrostatic pressure is equal to its weight.Regardless of whether an object floats, falls, or is held in a liquid, the hydrostatic pressure is constantly at work.

The mass of the fluid that an object displaces determines the size of the buoyancy force acting on it.

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The true statement is that; "Halo stars formed before disk stars, The protogalactic cloud contained essentially no elements besides hydrogen and helium."

We know that a star is a part of the solar system. The solar system is made up of many of the celestial bodies that can be found in the outer space. Some of them are able to produce light while some of the bodies that can be found in the solar system do not produce light.

The  milky way is the star galaxy that has been known to govern the earth and it is known to develop at a slower rate than all the other galaxies that we know.

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Missing parts;

According to present scientific understanding of the Milky Way's formation, which of the following statements are true? Select al that apply. Halo stars are stars that are born in the disk and ejected into the halo by gravitational encounters. The galaxy formed from the collapse of a single, giant protogalactic cloud. Disk stars formed before halo stars. Halo stars formed before disk stars. The protogalatic cloud(s) contained essentially no elements besides hydrogen and helium

a) The change in temperature of water is 0.0084°C.

b) The potential energy is transformed into kinetic energy, which is ultimately transformed into water heat.

c) The metal lost energy as a result of the friction created by the metal's motion inside the water, and this energy was then transformed to heat energy to raise the temperature of the water.

What is kinetic energy?

Kinetic energy is a type of energy that a moving object or particle experiences. When an item undergoes work—the transfer of energy—by being subjected to a net force, it accelerates and acquires kinetic energy. A moving object or particle's kinetic energy, which depends on both mass and speed, is one of its properties. The type of motion could be vibration, rotation on an axis, translation (or travel along a path from one place to another), or any combination of these.

Given,

Potential energy which is lost by the metal through the height, h

= 6m

We know,

PE = mgh

= 0.15 × 9.8 × 6 = 8.82 J

This is the energy used to heat up the water,

So, 8.82 = M × C × dT

Where,

M = 0.25 kg

C = 4186 J/kg/C

dT = Change in temperature of water

= T-22

So,

0.25 × 4186 × (T-22) = 8.82

T = 22.0084°C

Hence, The change in temperature is 0.0084°C.

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Speed of light in Cubic zirconia, v = 1.36 x 10⁸ m/s

Speed of light in sodium chloride  v =1.94 x 10⁸ m/s

Speed of light in polystyrene v =1..89 x 10⁸ m/s,explained clearly in below attached picture.

Zirconium dioxide exists in the cubic crystalline form known as cubic zirconia (CZ) (ZrO2). The synthetic material may be produced in a wide range of hues, although it is typically hard and colorless. Zircon, a zirconium silicate, should not be confused with it (ZrSiO4). It is occasionally mistakenly referred to as cubic zirconium.

Sodium chloride, generally known as salt, is an ionic substance with the chemical formula NaCl, denoting a 1:1 ratio of sodium and chloride ions. Sea salt, however, also contains other chemical salts. The molar weights of 39.34 g Na and 60.66 g Cl in 100 g of NaCl are 22.99 and 35.45 g/mol, respectively.

A synthetic polymer known as polystyrene is created from the monomers of the aromatic hydrocarbon styrene. Solid or foamed polystyrene are both possible. Polystyrene for general use is transparent, rigid, and brittle. Per unit weight, it is a reasonably priced resin. It has a relatively low melting point and a weak barrier to oxygen and water vapor.

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Potential energy lost by block 2 is greater than the potential energy gained by the spring - is true of the energy of the system during this process

Potential energy is stored energy that is affected by the relative location of various components in a system. Stretching or compressing a spring increases its potential energy. A steel ball has higher potential energy when lifted above ground than when it falls to Earth.

Because every item moved from its resting posture has stored energy, it is referred to as potential energy because it has the ability to accomplish work when released.

Thus, potential energy lost by the block 2 = potential energy gained by the spring + energy lost to overcome the friction.

Thus, Potential energy lost by block 2 is greater than the potential energy gained by the spring .

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The complete question is as follows:

Block 1 and Block 2 In the system of two blocks and a spring shown above, blocks 1 and 2 are connected by a string that passes over a pulley. The initially unstretched spring connects block 1 to a rigid wall. Block 1 is released from rest, initially slides to the right, and is eventually brought to rest by the spring and by friction of the horizontal surface. 24. Which of the following is true of the energy of the system during this process? (A) The total mechanical energy of the system is conserved. (B) The total mechanical energy of the system increases. (C) The energy lost to friction is equal to the gain in the potential energy of the spring, (D) The potential energy lost by block 2 is less in magnitude than the potential energy gained by the spring. (E) The potential energy lost by block 2 is greater in magnitude than the potential energy gained by the spring.

Construction and demolition waste management planning is not a credit in the LEED v4.1 BD C MR category.

We are confident that the rating system achieves those objectives because this version of LEED is the result of countless hours of work by our volunteers and staff.

The world's standard for measuring the efficiency of green building design, construction, and operation is called LEED. With more than 93,000 projects registered and certified globally and more than 19 billion square feet of space, different LEED versions have steadily advanced the global green building market over the past 18 years.

Regions and markets develop at different rates, and we want to be sure we can meet the needs of every member of the green building community. LEED v4.1 is the culmination of a number of improvements that will raise the bar for our standards, promote leadership, and make our platform more accessible, user-friendly, and most importantly, collaborative than ever.

The platform for LEED v4.1 will be the most open and transparent one yet.

The question is incomplete. the complete question is 'a) construction and demolition waste management planning b) building life cycle impact reduction c) construction and demolition waste management d) building product disclosure and optimization - sourcing of raw materials'

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The post-collision velocity of miguel and his car turns out to be 10 m/s

determining the collision?

A collision in physics is any situation in which two or more objects rapidly exert force on each other. Despite the fact that the most common usage of the word "collision" refers to situations in which two or more objects collide violently, the scientific usage of the word makes no assumptions. so.

Here are some examples of physical encounters that scientists might classify as collisions:

An insect's leg is said to hit a leaf as it falls on it.

Each contact of a cat's paw with the ground when crossing a lawn is considered a collision, as is every contact of a cat's fur with a blade of grass.

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(a)  If   [tex]R_{G_{2} }[/tex]  is short,  

                            [tex]V_{S} =0.52V[/tex]

                            [tex]V_{P} =8.04V[/tex]

(b) If   [tex]R_{S}[/tex]   is short,

                            [tex]V_{S} =0V[/tex]

                            [tex]V_{P}=1.564V[/tex]

(c) If  [tex]R_{P}[/tex]  is short,

                            [tex]V_{S} =1.764V[/tex]

(d) If   [tex]R_{G_{1} }[/tex]   and   [tex]R_{P}[/tex]   are both short,

                            [tex]V_{S} =5.55V[/tex]

Given,

         [tex]R_{G_{1} } =600K[/tex]                  [tex]R_{G_{2} } =300K[/tex]

          [tex]R_{D} =2.2K[/tex]                    [tex]R_{S} =1.2K[/tex]

          [tex]V_{t} =0.4V[/tex]            

(a)    If   [tex]R_{G_{2} }[/tex]  is short,

            [tex]V_{G} =0V[/tex]          

           [tex]V_{GS} = V_{G} -V_{S}[/tex]

            [tex]V_{GS} =0-I_{P}R_{S}[/tex]

           [tex]V_{P}=9-I_{P}R_{D } = 9-(0.43*10^{-3} )(2.2K)[/tex]

           [tex]V_{P}=8.04V[/tex]          

And,

           [tex]V_{S} = I_{P} R_{S}=(0.43*10^{-3} )(1.2K)[/tex]

           [tex]V_{S} ==0.52V[/tex]

Hence,

                            [tex]V_{S} =0.52V[/tex]

                            [tex]V_{P} =8.04V[/tex]          

(b)  If   [tex]R_{S}[/tex]   is short,

                [tex]V_{G} =\frac{300K}{300K+600K} (9)[/tex]

                [tex]V_{G} =3V[/tex]

∵              [tex]V_{S} =0V[/tex]

∴              [tex]V_{G{S} } =3V[/tex]

               [tex]I_{P} =\frac{K}{2} [3.04]^2=\frac{6.76}{2} mA=3.38mA[/tex]

               [tex]V_{P} =9-({3.38mA} )(2.2K)=1.564V[/tex]

Hence,

                           [tex]V_{S} =0V[/tex]                  

                          [tex]V_{P}=1.564V[/tex]              

(c)   If  [tex]R_{P}[/tex]  is short,

                 [tex]V_{P} =9V[/tex]

                  [tex]V_{S} =I_{P} R_{S }[/tex]

                  [tex]V_{G}=3V[/tex]

                  [tex]I_{P} =\frac{1mA}{2} [(3-(1.2K)I_{P} )-0.4]^{2}[/tex]

                  [tex]I_{P}=1.47mA[/tex]

∴                [tex]V_{S} =I_{P}(1.2K)[/tex]

                  [tex]V_{S} =1.764V[/tex]

Hence,                

                   [tex]V_{S} =1.764V[/tex]            

(d)  If   [tex]R_{G_{1} }[/tex]   and   [tex]R_{P}[/tex]   are both short,

                        [tex]V_{G}=9V[/tex]

                         [tex]V_{S} =I_{P}R_{S}[/tex]

                        [tex]I_{P} =\frac{1mA}{2} [(9-(1.2K)I_{P} )-0.4]^{2}[/tex]

                        [tex]I_{P} =4.63mA[/tex]

∴                       [tex]V_{S} =I_{P}R_{S}=(4.63mA)(1.2K)[/tex]

                        [tex]V_{S} =5.55V[/tex]

Hence,

                      [tex]V_{S} =5.55V[/tex]

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Senen Bacani is an entrepreneur, the CEO of La Fuerta Inc which is one of the largest exporters of bananas in Philippines.

Senen Bacani was the formal sectary of Agriculture to president Corazon Aquino and during that time he visited many Philippines province and realize how poor people struggle to fend for their families and remember how his father who  was a doctor received farm produce from his patient, appreciating him for medical care they received seeing the need of the of the rural people, has compelled him to work for shifts in policy and programs as the secretary and later in 1993 after working for president Aquino administration, he establish a business in agriculture to provide employment and to alleviate poverty in the rural areas Mostly in Mindanao, where he establish business venture that brought about not only employment but peace where there had been years of unemployment, crime and inter-ethnic conflict.

Senen Bacani presently head 9 different companies and presently occupies the position of Chairman for  different Inc., in the Philippines.

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Adaptations acquired during altitude exposure dissipate within 2 -3 weeks after returning to sea level.

High altitude (HA) hikers climb the heights of mountains for a variety of reasons, such as hiking, mountaineering, mining, scientific pursuits, and military duties. The number of visitors to the mountains has increased noticeably in recent years due to improvements in communication, logistics and medical care available at HA sites.

However, in such extreme conditions, the body's normal physiology is altered and consequently the body tends to acclimatize to resume its normal functioning. Normal physiological processes of altitude acclimation usually include hyperventilation, cardioacceleration, and increases in red blood cell count, hemoglobin (Hb), and 2,3-bisphosphoglyceric acid levels. These physiological manifestations assist in the dissociation of oxygen from oxygenated hemoglobin (HbO2), so that more oxygen is delivered to tissues for use by mitochondrial enzymes.

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The Rotation Curve of a Spiral Galaxy animation and click on at various distances from the galactic center to create a graph of the galaxy's rotation curve beginning from the center, speeds in the beginning upward push hastily, after which turn out to be nearly consistent with increasing distance.

Circ = R ∂Φ/∂R. mean orbital motion and their bulk rotational speed can be slightly smaller than the round pace. Spectroscopic radial velocities may be used to determine the rotational velocities of spiral galaxies provided that the galaxies are inclined to the line of sight.

The rotation curve (RC) of our Galaxy, the Milky Way, is built starting from its very internal regions (few hundred parsecs) out to a massive galactocentric distance of ∼2 hundred kpcs the usage of kinematical statistics on an expansion of tracer gadgets shifting in the gravitational potential of the Galaxy, without assuming any theoretical.

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the spring stiffness of the spring for the safe to be hit will be 353 KN-m

A spring's "spring constant" is a property that quantifies the relationship between the force acting on the spring and the displacement it produces. In other terms, it indicates a spring's stiffness and the amount of stretching or compression it can withstand.

BRIEFING:-

The spring's kinetic energy is equivalent to the work the free-falling safe does on it.

[tex]w_{1}[/tex]= [tex]\frac{1}{2}[/tex]k[tex]x^{2}[/tex]

   The spring's potential energy is equal to the work done on the safety by gravity:

[tex]w_{2}[/tex]= mgh

 = 1200*9.81*(2+0.4)

 = 1200*9.81*2.4

 =28252.8N-m

[tex]w_{1} =w_{2}[/tex]

[tex]\frac{1}{2}[/tex]k[tex]x^{2}[/tex]=mgh

[tex]\frac{1}{2}[/tex]k[tex]0.4^{2}[/tex]=28252.8

k=[tex]\frac{28252*2}{0.4^{2} }[/tex]

k=353150N-m

k=353KN-m

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The given statement about EPS (  earnings per share) and FFO (funds from operations) is false. They are not interest deduction.

Net operating income is represented by EPS. Taxes and preferred dividends are factored into FFO (funds from operations), which also leverages them. Cash flow is not a factor in FFO. Net income to the number of outstanding shares is expressed as an EPS ratio. As previously indicated, companies may add FFO per share to their EPS.

Net income divided by the number of outstanding equity shares is earnings per share for a business. The amount of income being produced on a per-share basis is measured by EPS and FFO per share. the income per share. The company's profit, which belongs to the common shareholders, is measured in terms of earnings per share.

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The motion of the object from 0 to 6 seconds is a linear motion; the displacement of the object is zero between 0 to 2 seconds, afterwards between 2 to 6 seconds, the displacement of the object increased with increase in time of motion.

The motion of an object is described as the change in the position of an object with time.

The motion of an object can occur at;

During the motion of an object at a constant velocity, the acceleration of the object for the time period is zero.

If the motion of the object occurs at uniform velocity, the acceleration of the object will be constant.

In the given graph, we can conclude the following based on the object's motion;

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Power is work done by time and rate of doing work the SI unit of power is Watt (W) which is joules per second (J/s).

Sometimes, we want information about how quickly work is done. This is called “power.” The Definition of Power: The rate at which work is done. Power is related to the force or forces that suppy by it.

Mathematically,

The Definition of Power P ≡ dW/dt

The units of power are, 1Joule/1second ≡ 1Watt = 1W. The horsepower is an alternate unit: 1hp=746W.

We weren’t familiar with joules, the unit for work, but you are comfortable with the units of power. For example, a 100W light bulb or a 1200W hair dryer. A 100W bulb uses 100J every second. Similarly, a 1200W hair dryer uses 1200J every second.

The Work-Energy Theorem explains that when net work is done on an object, the object speeds up. The Work-Kinetic Energy Theorem describes what happens when a particular force, such as the one supplied by the catapult, does work to cause only the kinetic energy of the object to change.

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The frequency of its fundamental mode of vibration is 409Hz and the number of the highest harmonic that could be heard by a person who is capable of hearing frequencies up to 1.00x10^4 is 24

Given tension of a steel piano wire (T) = 1070N

Length of wire L = 0.400m

Mass of piano wire M = 4g

We know linear density = mass/length = 4x10-3/0.400 = 0.01 kg/m

fundamental frequency f = 1/2L√T/µ

f = 1/2x0.4x√1070/0.01 = 409Hz

number of loops  is n

n = f'/f = 1x10^4/409 = 24.5 = 24

Hence the frequency of its fundamental mode of vibration is 409Hz and the number of the highest harmonic that could be heard by a person who is capable of hearing frequencies up to 1.00x10^4Hz is 25.

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The  wavelength of light would photosynthesis be at its lowest at 650nm.

The correct option is C.

The wavelength is the spatial period of a periodic wave which is the distance over which the wave's shape repeats.

Since the absorption spectrum for chlorophylls a and b are shown by the graph which indicates that there are two pigments found in plants and green algae that are the main pigments of photosynthesis.

At point 650nm, the wavelength of light would photosynthesis be at its lowest because red has longest wavelength, at around 620 - 780 nanometers with lowest frequency.

In conclusion, the wavelength of light is defined as “the distance between the two successive crests or troughs of the light wave” and is denoted by the Greek letter lambda.

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When force is applied for some distance, it is called work done, and  When force acting on an object moves it across a distance is called work done.

When moving an object over a distance, an external force must direct at least a portion of its force in the direction of the displacement. This is referred to as work done in physics. If the force acting along the path is constant, work can be calculated by multiplying the length of the path by the force's component. The work W is mathematically defined as the product of the force f and the distance h, or W = mgh. The work is W = mas if the force is applied at an angle to the displacement.

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First and Fourth option is correct

Center of mass of an object:

The centroid of a mass distribution in space (also called the equilibrium point) is the unique point where the weighted relative positions of the distribution masses sum to zero. This is the point where force can be applied to produce linear acceleration without angular acceleration. Mechanics calculations are often simplified when formulated in terms of the center of gravity. This is a virtual point at which the entire mass of the object can be assumed concentrated in order to visualize its motion. In other words, the center of mass is the particle equivalent of a particular object for which Newton's laws of motion apply.

Angular momentum:

Angular momentum is the rotational analogue of linear momentum. It is an important physical quantity because it is conserved. The total angular momentum of a closed system remains constant. Angular momentum has both direction and magnitude, both of which are conserved.

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The minimum length of the runway is closer to 167 m. Hence, option (C) is correct.

Acceleration is the rate at which a velocity changes over time. It qualifies as a vector quantity because it possesses both direction and magnitude. Meter/second^2 (m/s^2) is the SI unit of acceleration.

Given that acceleration of the plane: a = 1.2 m/s^2.

Final speed of the plane from rest: v = 20 m/s.

Hence, required minimum length of the runway = v²/2a

= 20²/(2×1.2) m

= 166.67 meter.

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