Three seconds after a gun is fired, the person who fired the gun hears an echo. how far away (in m) was the wall that reflected the sound of the gunshot? assume the speed of sound is 343 m/s.

Answers

Answer 1

The faraway was that reflected the sound of gunshot is 510m.

A sort of energy created by vibrations is sound. The vibration of an object causes the molecules of the air around it to move. These molecules collide with molecules nearby, causing those molecules to vibrate as well. As a result, they collide with more surrounding air molecules. Divide the sound's speed by the amount of time needed to hear the echo to determine how far the surface is. 1020 m/s equals 340 m/s divided by 3 s.

1020/3= 340 m/s

The distance should be divided by 2, though, as the sound is reflected. Received upto

510m that is

1020/2 = 510m

In order to evaluate the exposure to gunfire sound, the peak sound pressure level (SPL), spreading of the pressure wave, and other physical features of the impulse noise from firearms were researched in real-world shooting scenarios

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Related Questions

HELP WILL GIVE BRAINLIEST AND FOLLOW!!!

Answers

Answer:

CO2 and H2O

Explanation:

In order to quadruple the amount of lift created by an airfoil, the air velocity must be?

Answers

In order to quadruple the amount of lift created by an airfoil, the air velocity must be doubled.

What is airfoil?

A wing, a sail, or the blades of a propeller, rotor, or turbine are examples of objects whose motion through a gas can provide significant lift, and an airfoil or aerofoil is the cross-sectional shape of such an item.

By applying a downward push to the air as it passes, an airfoil produces lift. The air must exert an equal and opposite (upward) force on the airfoil, which produces lift, in accordance with Newton's third law.

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You are an engineer in charge of designing a new generation of elevators for a prospective upgrade to the Empire State Building. Before the state legislature votes on funding for the project, they would like you to prepare a report on the benefits of upgrading the elevators. One of the numbers that they have requested is the time it will take the elevator to go from the ground floor to the 102nd floor observatory. They are unlikely to approve the project unless the new elevators make the trip much faster than the old elevators.

If state law mandates that elevators cannot accelerate more than 2.70 m/s2 or travel faster than 14.3 m/s , what is the minimum time in which an elevator can travel the 373 m from the ground floor to the observatory floor?

Answers

Answer:

31.38 s (2 d.p.)

Explanation:

Constant Acceleration Equations (SUVAT)

[tex]\boxed{\begin{array}{c}\begin{aligned}v&=u+at\\\\s&=ut+\dfrac{1}{2}at^2\\\\ s&=\left(\dfrac{u+v}{2}\right)t\\\\v^2&=u^2+2as\\\\s&=vt-\dfrac{1}{2}at^2\end{aligned}\end{array}} \quad \boxed{\begin{minipage}{4.6 cm}$s$ = displacement in m\\\\$u$ = initial velocity in ms$^{-1}$\\\\$v$ = final velocity in ms$^{-1}$\\\\$a$ = acceleration in ms$^{-2}$\\\\$t$ = time in s (seconds)\end{minipage}}[/tex]  

When using SUVAT, assume the object is modeled as a particle and that acceleration is constant.

-----------------------------------------------------------------------------

To find the minimum time in which an elevator can travel the 373 m from the ground floor to the observatory floor, we to accelerate to the maximum allowed velocity as quickly as possible, maintain the maximum velocity for as long as possible, and then decelerate for the shortest period of time in order for the elevator to come to a stop after 373 m.

Therefore, the travel time from the start of the elevator trip to the end will have three phases:

AccelerationConstant velocityDeceleration

Phase 1 - Acceleration

Given information:

[tex]u = 0 \sf \; m/s[/tex][tex]v= 14.3 \sf \; m/s[/tex][tex]a= 2.70 \sf \; m/s^2[/tex]

The time it takes to accelerate from rest to the maximum allowed velocity, where the elevator accelerates at the maximum allowed acceleration:

[tex]\begin{aligned}v & = u+at\\\implies 14.3 & = 0+2.7t\\t & = \dfrac{14.3}{2.7}\\t & = 5.296296296\;\sf s\end{aligned}[/tex]

The distance covered in this time is:

[tex]\begin{aligned}v^2 & = u^2 + 2as\\\implies 14.3^2 & = 0^2 + 2(2.7)s\\204.49 & =5.4s\\s & = \dfrac{204.49}{5.4}\\s & = 37.86851852\; \sf m\end{aligned}[/tex]

Phase 3 - Deceleration

Given information:

[tex]u = 14.3 \sf \; m/s[/tex][tex]v= 0 \sf \; m/s[/tex][tex]a= -2.70 \sf \; m/s^2[/tex]

When the elevator is decelerating from the maximum velocity to being at rest, it will take the same amount of time and cover the same distance as its acceleration phase:

[tex]\begin{aligned}v & = u+at\\\implies 0& = 14.3+(-2.7)t\\2.7t&=14.3\\t & = \dfrac{14.3}{2.7}\\t & = 5.296296296\;\sf s\end{aligned}[/tex]

[tex]\begin{aligned}v^2 & = u^2 + 2as\\\implies 0^2 & = 14.3^2 + 2(-2.7)s\\0 & = 204.49 -5.4s\\5.4s&=204.49\\s & = \dfrac{204.49}{5.4}\\s & = 37.86851852\; \sf m\end{aligned}[/tex]

Phase 2 - constant velocity

The total distance the elevator travels is 373 m.  

Therefore, the distance it travels during phase 2 when it is traveling at a constant (maximum) velocity is the total distance less the distance traveled in phases 1 and 3:

[tex]\begin{aligned}\implies s & =373-2(37.86851852)\\s& = 297.262963\;\sf m\end{aligned}[/tex]

Given information:

[tex]u = 14.3 \sf \; m/s[/tex][tex]v= 14.3 \sf \; m/s[/tex][tex]s = 297.262963\;\sf m[/tex]

Therefore, the time is takes to travel this distance when it is traveling at a constant (maximum) velocity is:

[tex]\begin{aligned}s&=\left(\dfrac{u+v}{2}\right)t\\\implies 297.262963 & = \left(\dfrac{14.3+14.3}{2}\right)t\\297.262963 & = 14.3t\\t & = \dfrac{297.262963}{14.3}\\t & = 20.78761979 \; \sf s\\\end{aligned}[/tex]

Total minimum time

Therefore, the minimum time is the sum of the time calculated for the three phases:

[tex]\begin{aligned}\sf Minimum \: time& = \sf Phase \: 1 + Phase \: 2 + Phase \: 3\\& = 5.296296...+5.296296...+20.78761...\\& = 31.38021...\\& = 31.38\; \sf s\end{aligned}[/tex]

A certain current produces a magnetic field be near the center of the solenoid if the current is:__________

Answers

A certain current produces a magnetic field be near the center of the solenoid if the current is 3B .

Thus, the magnetic field in the core of a solenoid is directly proportional to the product of the current flowing around the solenoid and the number of turns per unit length of the solenoid. This, result is exact in the limit in which the length of the solenoid is very much greater than its diameter.

Now,

Magnetic field due to solenoid

B= u0nI

where n is number of turns per unit length and I is current.

Now I is tripled, hence magnetic field

B' =μon 3I =3B.

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When your car is moving at 3.85 m/s and car has a mass of 881 kg, how much translational kinetic energy does it have?

Answers

The translational kinetic energy does it have  -6,528.21  joule

we have given the values of

v = 3.85m/s

m =  881 kg

kinetic energy = m[tex]v^2[/tex]/2

= 881 [tex]\times[/tex] [tex](3.85)^2[/tex]/ 2

= 881 [tex]\times[/tex]14.82/ 2

= 13,056.42

= 6,528.21  joule

Hence kinetic energy of car is 6,528.21  joule

Units energy is measured in joulesKinetic Energy is the energy of an object's motion due to the object's motion example A rolling ball, a moving rollercoaster, and a toy car.Kinetic energy depends on Mass and speedKinetic Energy is the energy of motion when an object falls It's potential energy is converted into kinetic energy Therefore, potential energy lost = kinetic energy gained mgh = 1/2 m [tex]v^2[/tex]

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Jaycie wants to increase her upper body strength
by doing push-ups. She does one push-up by
applying a force of 10 N to raise her center of
gravity 2 m. How many push-ups must Jaycie
complete to do 200 J of work?
A.
5 push-ups
B. 10 push-ups
C.
15 push-ups
D. 20 push-ups

Answers

The 10 push-ups must Jaycie complete to do 200 J of work. If one push-up is applying a force of 10 N to raise her center of gravity 2 m.

Calculation of work done in one push up

As, we know that

W = F × S

where,

F is the force

W is the work done by the body

S is the distance travelled by the body

Given,

F = 10N

S = 2m

By substituting all the values, we get

W = 10 × 2

W = 20J

So, the 20J work is done by one push up.

Therefore,

200/20

= 10 push ups


Thus, we concluded that the 10 push-ups must Jaycie complete to do 200 J of work. If one push-up is applying a force of 10 N to raise her center of gravity 2 m.

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A constant acceleration means that the speed of the object is __________.

Select all that apply. Please explain your reasoning.

A. constant

B. gradually increasing

C. gradually decreasing

D. null

Answers

A. A constant acceleration means that the speed of the object is constant.

What is constant acceleration?

Constant acceleration is defined as a change in velocity that does not vary over time.

During constant acceleration of an object, the change in velocity of the object with time is the same or constant for all points of the object's motion.

a = Δv/Δt

where;

Δv is change in velocity of the objectΔt is change in time of motion of the object

During constant acceleration, the variable change in velocity (Δv) will be constant with change in time.

Thus, a constant acceleration means that the speed of the object is constant.

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What is the symbol for an atom with three electrons, three protons, and four neutrons?

Answers

Atomic electron arrangement is the only factor that affects how they behave chemically.

The electron arrangement is independent of whether an atom contains three or four neutrons. All that matters is how many protons there are and how many electrons there are to match them, which determines how these atoms will behave chemically. When grouping atoms in the periodic table, we designated a box as an element when all of the atoms have the same number of protons (with a corresponding symbol) Thus, the sole difference between the various forms of an element is its number of neutrons; we refer to these forms as the element's isotopes. Both lithium-6 and lithium-7 have three protons and three neutrons.

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who was newton? who was albert einstein?

Answers

Answer:

Newton discovered gravity and Albert Einstein is a theoretical physics

Explanation

hope it helps have a nice day! :)

BRAINIEST is appreciated

Approximately 1.0 g of caffeine will dissolve in 28 ml of methylene chloride and in 46 ml of water. calculate the distribution coefficient of caffeine in this solvent system.

Answers

The distribution coefficient was found to be 1.61.

First we calculate solubility of caffeine, when dissolved in methylene chloride,

Solubility (in g/ml) = mass of caffeine/volume of solvent

Solubility = 1/28

Now, solubility of caffiene when dissolved in water,

Solubility (in g/mol) = 1/46

Now, we calculate distribution coefficient, (kd) by taking the ratio of the solublities i.e..

Distribution coefficient,(Kd) = solubility of caffeine, when dissolved in methylene chloride / solubility of caffeine when dissolved in water.

Kd= (1/28) / (1/46)

Kd= 1.61

Thus, distribution coefficient was calculated and found to be 1.61.

The distribution coefficient of the solute is defined as the ratio of the concentration of solute dissolved in organic solvent to the concentration of solute dissolved in aqueous phase.

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how do we know that an atom of gold in a ring and an atom of gold in a dental filling are alike

Answers

Gold fillings, also called inlays or onlays, consist of alloys of gold, copper, and other metals. This type of filling is usually the most durable and is considered to last 20 years or more, but it is also the most expensive.

Gold fillings are less common than they used to be, but are still a viable option for obtaining fillings. Gold is durable and resilient, so with proper care, gold fillings can last a lifetime.

Gold is one of the oldest tooth restoration solutions in dentistry and is still used today due to its durability. Gold crowns are rarely used in modern dentistry (except for aesthetic reasons), but gold components are used in combination with other metals such as nickel, chromium, and palladium.

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Jeremy hypothesized that adults with blue eyes are shorter than adults with brown eyes. He collected data by visiting all of the teachers in his school and found that his hypothesis was false. Should Jeremy consider his hypothesis useful?
A.
Yes; now he knows that the exact opposite of his hypothesis must be true.
B.
Yes; a false hypothesis gives a scientist new information to use.
C.
No; a false hypothesis makes a scientist look silly.
D.
No; false hypotheses are a waste of time.

Answers

Answer: B. Yes; a false hypothesis gives a scientist new information to use.

Explanation:

      Let us take a look and break down all the question's answer options.

✗ A.

Yes; now he knows that the exact opposite of his hypothesis must be true.

➜ This is not the case. He must look at this data and decide what is true.

✓B.

Yes; a false hypothesis gives a scientist new information to use.

➜ Yes! We learn from our research and looking back at our hypothesis.

✗ C.

No; a false hypothesis makes a scientist look silly.

➜ This isn't true. You cannot expect to be right all the time, and scientists make incorrect hypotheses frequently.

✗ D.

No; false hypotheses are a waste of time.

➜ Tying back into B and C, this isn't true. We learn from comparing our hypotheses with our data.

A tank is in the shape of an inverted cone, having height h = 3.31 m and base radius r = 0.799 m. of water is poured into the tank at a rate of 11.8 l/s, how long will it take to fill the tank?

Answers

A tank is in the shape of an inverted cone, having height h = 3.31 m and base radius r = 0.799 m. of water is poured into the tank at a rate of 11.8 m/s.

It take to fill the tank

Using the similarity of triangles,

[tex]\frac{0.799}{r} =\frac{3.31}{h} \\r=0.241h[/tex]

Volume of water tank

[tex]V=\frac{1}{3} \pi r^2h\\V=\frac{1}{3} \times 3.14\times (0.241h)^2\times h\\V=0.0608h^3[/tex]

A 2300-kg car slows down at a rate of 3.0 m/s2 when approaching a stop sign. what is the magnitude of the net force causing it to slow down? (numerical value only) *

Answers

The magnitude of the net force causing the car to slow down is 6900 N.

We need to know about force to solve this problem. According to second Newton's Law, the force applied to an object will be proportional to mass and acceleration. Hence, it can be written as

F = m . a

where F is force, m is mass and a is acceleration

From the question above, we know that

m = 2300 kg

a = 3 m/s²

By substituting the given parameters, we can calculate the net force

F = m . a

F = 2300 . 3

F = 6900 N

Hence, the net force causing to slowdown is 6900 N

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Find the net force including its direction of the following: 175n to the left, 234n to the right, 75n to the right, 225n to the left, and 45n to the right

Answers

The net force is 46 N to the left.

We need to know about force resultant to solve this problem. The force resultant is the total net force applied to the object according to the direction. It can be written as

R = F1 + F2 + ... + Fn

where R is force resultant (net force)

From the question above, we know that

(Assume that the right direction is positive and left direction is negative)

F1 = -175 N

F2 = 234 N

F3 = 75 N

F4 = -225 N

F5 = 45 N

By substituting the following parameters, we can calculate the net force

R = F1 + F2 + F3 + F4 + F5

R = -175 + 234 + 75 - 225 + 45

R = -46 N

Hence, the net force is -46 N

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Create a hypothesis using If, then and because.

Answers

Hypothesis: If I lower the amount of prey, then the frog population would lower, because the frogs would not have any food and then they would die.

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A person is on a paddleboard. The person exerts a force on the water with
the paddle, causing the water to move. The paddleboard also moves, but in
the opposite direction. Which statement best explains why this happens?
O Inertia
O Action and reaction forces
Newton's 2nd Law of motion
O Law of Conservation of Momentum

Answers

Answer:

action and reaction forces

Explanation:

An motion pressure is a pressure that is utilized to an object. A response pressure is a outcome of an action force which is opposite in direction.

Calculate the amount of water (in grams) that must be added to (a) 5.80 g of urea [(nh2)2co] in the preparation of a 6.40 percent by mass solution:

Answers

The amount of water (in grams) that must be added to 5.80 g of urea [(nh2)2co] in the preparation of a 6.40 percent by mass solution is 84.83g.

How to calculate the amount of water added?

When the masses of a solute and a solution are provided, the concentration of the solution is expressed using the mass percent:

Mass% = Mass of Solvent 100% of Solution's Mass

The percent by mass solution = the grams of solute in 100 g. of solution.

(A) So, 6.40 g of urea are contained in 100 g of solution.

So, 93.6 water was added to make a 6.40 g solution.

Thus for, 5.80 g of urea,

(5.8*93.6)/6.4 = 84.83g

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I need help ASAP
You need to match each thing to it’s place I’m not sure

Answers

Answer:

1st box: 2

2nd box: 1

3rd box: 4

4th box: 3

Explanation:

Kinetic energy the energy an object has due to its being in motion.  Potential energy is energy held by an object because of its position relative to another object.

5.when an object is weighed in air, its weight is wair=10.8 n. when completely immersed in water, however, it has a weight of wwater=1.00 n. what is the (a) volume and (b) density of the object?

Answers

According to Archimedes' principle, (a) the submerged volume is 1 liter and (b) the density of object is 1102 kg/m³.

We need to know about Archimedes' principle to solve this problem. Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid is proportional to the volume and density of the fluid. It can be determined as

Fb = ρ . g . V

where Fb is buoyant force, ρ is the density of the fluid, g is the gravitational acceleration (9.8 m/s²) and V is submerged volume.

The buoyant force also can be calculated by measuring the change in weight in air and water

Fb = Wa - Ww

where Wa is weight in air and Ww is weight in water.

From the question above, we know that

Wa = 10.8 N

Ww = 1 N

ρ = 1000 kg/m³

Find the buoyant force

Fb = Wa - Ww

Fb = 10.8 - 1

Fb = 9.8 N

Determine the submerged volume

Fb = ρ . g . V

9.8 = 1000 . 9.8 . V

V = 1/1000 m³

V = 1 dm³ = 1 liter

Determine the density of the object

Wa = m . g

10.8 = m . 9.8

m = 1.102 kg

ρ = m/V

ρ = 1.102 / 1

ρ = 1.102 kg / liter

ρ = 1102 kg/m³

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Answer in units of m/s.

Answers

Answer:

The metre per second (m/s) is the unit of both speed (scalar quantity) and velocity in the International System of Units (SI).

At any instant, how many water molecules are ionized in 1 l of pure water at ph 7.0? (b) express this number as a percentage of the total water molecules

Answers

The number of water molecules which are ionized in 1L of pure water at pH 7.0 is equivalent to 6×10¹⁶ molecules.

The number as a percentage of the total water molecules is 1.8×10⁻⁷ % .

At pH 7.0, [H⁺]=10⁻⁷ M, so 10⁻⁷  moles of water molecules have ionized. This is almost equal to (10⁻⁷  mol)(6×10²³ molecules. mol⁻¹) = 6×10¹⁶ molecules.

For the second part of the question let the concentration of water be 55.5 M, then there are (55.5 mol)(6×10²³ molecules.mol⁻¹) = 3.3×10²⁵ molecules of water in 1L. The fraction of ionized molecules is 6×10¹⁶ molecules)/(3.3×10²⁵ molecules) = 1.8×10⁻⁹ or 1.8×10⁻⁷ %.

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If a cheetah can reach speeds of 33 m/s, how long will it take to travel 1 km? Best answer will be mark Brainliest!

Answers

Answer: 30.3 seconds

Explanation:

1000 m=1 km

33m * 1 km/1000 m=

33 * 1/1000=

33/1000=0.033 km

1/0.033=30.3030...

30.3030=30.3 seconds

The density of sugar is 1.58 g/cm3 what is its density in pounds per cubic inch (lb/in3)?

Answers

The density of sugar, which is in 1.58 g/cm³, is equivalent to 0.05708 in/in³.

What is Density?

Density is a measure of the mass of matter contained by a unit volume.

Density is a function of mass and density, hence, it is measured in units of grams (g) and cubic centimeters (cm³).

However, cubic centimeters can be converted to pounds per cubic inch as follows:

1 gram / cubic centimetre = 0.0361 pound / cubic inch

According to this question, the density of sugar is 1.58 g/cm³. This value is equivalent to;

= 1.58 × 0.0361 = 0.05708

Therefore, the density of sugar, which is in 1.58 g/cm³, is equivalent to 0.05708 in/in³.

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You stand on a scale that rests on the floor of an elevator that is accelerating upward. what is the relationship between the force due to gravity (mg) and the normal force (n) exerted by the scale?

Answers

The relationship between the force due to gravity (mg) and the normal force (n) exerted by the scale

due to upward accelaration.

N = mg + ma , here N MEANS normal force

here now, N > mg  realtionship between normal force and force

whilst an item sits on a surface, the floor exerts a force on that object. This force is called the normal pressure, ordinary method "perpendicular" no longer "regular". The everyday force is always perpendicular to the floor.The everyday force is equal to the load of the item (for this class) = mg .The regular force is the "same and opposite response pressure" to the items weight. It continues the object from falling thru the floorForce is measured in Newtons.  N

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During stage 3 of star formation, the dense, opaque region at the center of the cloud is called a:_____.

Answers

During stage 3 of star formation, the dense, opaque region at the center of the cloud is named a:Herbig-Haro object.

What is Herbig-Haro object?

Bright nebulosity patches known as Herbig-Haro (HH) objects are linked to young stars. They are created when fast-moving, nearby clouds of gas and dust meet with narrow jets of partly ionized gas released by stars. Typical Herbig-Haro objects can contain up to 20 Earth masses of material and have temperatures of about 10,000 Kelvin.

They also have densities of a few thousand to a few hundred thousand particles per cubic centimeter. Over 600 have been discovered so far, all in star-forming regions and typically connected to Bok globules. They were once extremely rare. A brilliant cloud that stretches away from a star in the process of formation is known as a Herbig-Haro object (or HH object). The gravitational agglomeration of clouds produces protos tars.

Hence, During stage 3 of star formation, the dense, opaque region at the center of the cloud is named a:Herbig-Haro object.

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A particle is moving at 0.86c. by what magnitude percentage is the newtonian expression for momentum in error?

Answers

The calculated magnitude percentage is 125 %.

The Heisenberg Principle has a significant impact on how science is done and how experiments are created. This will transfer some of the momentum from the second particle to the electron being measured, changing it. A particle with a shorter wavelength and higher energy would be needed to measure the electron's position with more accuracy, but this particle would also change the momentum of the collision even more.

Pi is P Pf plus 50/100. P = 3/2 P

E = P2/2m describes how kinetic energy and momentum are connected.

E2 = (E2 - E 1)/E1 [E1 = E, E2 =?

100 = Pi 2/ 2m/ (Pf 2/2m - Pi 2/2m)

×100 = {(3/2) ² - 1} ×100 = (2.25-1) ×100 = 125%

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What is the identity of a metal that has a mass of 27.0 g and a volume of 10.0 cm3?

Answers

The metal with a mass of 27.0 g and a volume of 10.0 cm3 has a density of: 2.70 g/cm3

The density formula and the procedure we will use is:

d = m/v

Where:

v= volumed= densitym= mass

Information about the problem:

m = 27.0 gv = 10.0 cm3d= ?

Applying the density formula, we get:

d = m/v

d = 27.0 g/ 10.0 cm3

d = 2.70 g/cm3

What is density?

It is a physical quantity that expresses the ratio of the body mass to the volume it occupies.

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Moving from the element with atomic number 10 to atomic number 11 on the periodic table, there is a change in reactivity. Which of the following are true? You MUST select ALL correct answers to earn full credit for this question.

reactivity increases
reactivity decreases
neon has another shell (energy level, orbit), meaning the atom will be larger
sodium has another shell (energy level, orbit), meaning the atom will be larger
valence electrons in sodium are farther from the nucleus
atomic number 11 does not have a full electron shell.

Answers

Moving from the element with atomic number 10 to atomic number 11 on the periodic table changes observed are :

Reactivity increases,

Sodium has more shell,

Valence electrons in sodium are farther from the nucleus,

Atomic number 11 does not have a full electron shell

Atomic number in periodic table :

In increasing order of atomic number, the elements are listed. The amount of protons in an atom's nucleus is indicated by its atomic number. An element's identity is determined by its proton count. The number of protons determines an element's identity.

What is relativistic effect in periodic table?

The indirect relativistic effect amplifies the decreases in the binding energies of the valence d and f electrons as they move down the periodic table. As a result, the d electrons in the heavier coinage metals become more chemically active, leading to higher oxidation states in these elements.

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Aristarchus measured the angle between the sun and the moon when exactly half of the moon was illuminated. he found this angle to be:_________

Answers

Aristarchus measured the angle between the sun and the moon when exactly half of the moon was illuminated, he found this angle to be 90 degree.

The Moon exhibits a circular motion around the Earth as well as the relative position occupied by the sun, the earth, and the moon results in the creation of the lunar phases.

Aristarchus realized the fact that the Moon was exactly half illuminated as it forms a right triangle with the Sun and the Earth. As by knowing the distance occupied between the Earth and the Moon, the one and only thing he needed was the angle that existed between the Moon and Sun to compute the distance of the Sun itself at that present moment

In this case, whenever the Sun is illuminating half of the Moon, the angle between the sun and the moon must be at 90°. Actually, this angle changes according to the movement of the moon as there it will be zero degrees for the new moon as well as 180° for the full moon.

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