Propane (C3H8combines with oxygen gas (O2to form carbon dioxide (CO2and water (H2O). Describe the number and type of atoms for a molecule of each substance.

Answers

Answer 1

The balanced equation for the combustion of propane is C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(l), indicating that one molecule of propane reacts with five molecules of oxygen to produce three molecules of carbon dioxide and four molecules of water, keeping the atom count consistent on both sides of the reaction.

Combustion of Propane

To balance the chemical equation for the combustion of propane (C₃H₈), we must account for the number and type of atoms in both the reactants and the products to comply with the law of conservation of mass. The balanced equation is C₃H₈(g) + 5O₂(g)
ightarrow 3CO₂(g) + 4H₂O(l). Each molecule of propane contains 3 carbon atoms and 8 hydrogen atoms. When propane combusts in the presence of oxygen gas, it forms carbon dioxide and water. For carbon dioxide, each molecule contains 1 carbon atom and 2 oxygen atoms, and for water, 2 hydrogen atoms are bonded to 1 oxygen atom.

In the balanced reaction, we can break down the numbers further:

1 molecule of propane (C₃H₈) reacts with 5 molecules of oxygen (O₂).

3 molecules of carbon dioxide (CO₂) are produced.

4 molecules of water (H₂O) are formed.

This ensures that we have the same number of each type of atom on both the reactant and product sides of the equation.


Related Questions

What factor affects the color of a star?

Answers

the temperature and how far it is.

if it has the lowest surface temperature, it is red.

if it has high surface temperature, it is blue.

if you look a the earth science esrt, there is a graph stating the stars in our galaxy, the milky way, and how it far, hot/cold, and howold it is.

plz give me a brainliestt

The temperature of a star affects its color. Hotter stars appear bluish-white, while cooler stars appear reddish. This color variation is due to the relationship between a star's temperature and its emitted light spectrum.

A star's colour depends on its surface temperature. Stars emit a continuous spectrum of light, but temperature varies the intensity distribution across wavelengths. Wien's displacement law indicates that hotter things radiate more energy at shorter wavelengths. Redder stars are cooler, while bluish stars are hotter. Red, orange, yellow, white, and blue are the coldest to hottest star colours.

A star's chemical makeup can also affect its colour. A star's atmosphere absorbs specific wavelengths of light, creating spectral lines that may change its colour. Astronomers can determine a star's temperature, composition, and other properties by analysing its colour and spectrum.

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If you were to walk with a speed if 2m/s for 2 hours how far would you travel

Answers

So simply it to 120m/m for 120 minutes. So then you multiply 120x120 and that equals 14,400

Final answer:

By walking at a speed of 2m/s for 2 hours, you would cover a distance of 14,400 meters, after converting the hours into seconds for compatibility in calculation.

Explanation:

If you were to walk with a speed of 2m/s for 2 hours, you can calculate the distance traveled by using the formula for distance, which is speed × time. In this case, your speed is 2 meters per second (m/s), and your time is 2 hours. However, to use the formula correctly, you need both measurements in compatible units. Since 1 hour equals 3600 seconds, 2 hours equals 7200 seconds. Thus, the calculation should be 2 m/s × 7200 s, which equals 14,400 meters.

2. Which of the following is considered to be a vector? A. Temperature B. Velocity C. Time D. Mass

Answers

Answer: B) Velocity

Explanation:

Velocity is a vector quantity. Velocities have both magnitude and direction.

Velocity is considered to be a vector. Velocity is a vector quantity. it is a time-based component. Option C is correct.

What is a vector?

A vector is a quantity or phenomena with magnitude and direction that are independent of one another.

The change of displacement with respect to time is defined as the velocity.

Velocity is a vector quantity. it is a time-based component. Velocity at any angle is resolved to get its component of x and y-direction.

Hence, option C is correct.

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ANSWER ASAP
Dr. Thakkar was studying a fossil from a dig in a desert when he noticed that the organism had evidence of find. Why would this most likely tell Dr. thakkar

Answers

B the desert was once covered in water

Answer: The answer is B.

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how does wavelength affect the pitch of a sound?

a) the longer the wavelength the longer the sound
b) the shorter the wavelength the lower the sound
c) the taller the wavelength the lower the sound
d) none of these

Answers

The correct answer is (c) The taller the wavelength the lower the sound.

The wavelength of a sound wave affects its pitch by determining the frequency. Longer wavelengths result in lower pitch, while shorter wavelengths result in higher pitch.

Wavelength affects the pitch of a sound by influencing its frequency. Longer sound waves have lower frequency and produce a lower pitch, whereas shorter waves have higher frequency and a higher pitch. This relationship is evident in the correlation between the size of musical instruments and their pitch.

I can’t figure this out!!! Answer what you can , please.

A soccer player kicks a ball from the ground with a speed of 16 m/s at an angle of 63°.

A. What is the horizontal component of the velocity?
B. What is the vertical component of the velocity?
C. How long does it take the ball to reach its highest point?
D. What is the maximum height of the ball?
E. What is the total time that the ball is in the air?
F. How far is the ball from the soccer player when it lands?

Answers

a/b. The ball has velocity vector at time [tex]t[/tex]

[tex]\vec v=(v_x,v_y)=(v_0\cos63^\circ,v_0\sin63^\circ-gt)[/tex]

where [tex]v_0=16\dfrac{\rm m}{\rm s}[/tex] is the ball's initial speed and [tex]g=9.8\dfrac{\rm m}{\mathrm s^2}[/tex].

c. At its highest point, the ball has 0 vertical speed. This occurs when

[tex]v_0\sin63^\circ-gt=0\implies t=1.5\,\mathrm s[/tex]

d. Recall that

[tex]{v_y}^2-{v_{0y}}^2=-2g\Delta y[/tex]

so that at its highest point,

[tex]0^2-(v_0\sin63^\circ)^2=-2g\Delta y\implies\Delta y=10\,\mathrm m[/tex]

e. This is just twice the time it takes for the ball to reach its maximum height, [tex]t=2.9\,\mathrm s[/tex].

f. The ball's horizontal position after time [tex]t[/tex] is

[tex]v_0\cos63^\circ\,t[/tex]

so that after the time found in part (f), the ball has traveled

[tex]v_0\cos63^\circ(2.9\,\mathrm s)=11\,\mathrm m[/tex]

The soccer ball's horizontal and vertical components of velocity are approximately 7.26 m/s and 14.25 m/s, respectively. It takes approximately 1.453 seconds to reach the highest point and the total time in the air is about 2.906 seconds. The maximum height is around 10.35 meters and the ball lands about 21.1 meters from the soccer player.

The student is dealing with a projectile motion problem which can be solved using the kinematic equations of motion and trigonometry. The given initial speed is 16 m/s, and the angle of projection is 63 degrees.

A. Horizontal component of the velocity: Using trigonometry, horizontal component = initial velocity X cos(angle).

[tex]V_{x} = 16 X cos(63^{0})\\ V_{x} = 7.26 m/s[/tex]

B. Vertical component of the velocity: Again using trigonometry, vertical component = initial velocity X sin(angle).
[tex]V_{y}=16 X sin(63^{0} )\\V_{y} = 14.25m/s[/tex]

C. Time to reach the highest point: The time to reach the highest point is calculated using the vertical component of velocity and acceleration due to gravity (g = 9.81 [tex]m/s^2[/tex]).

Using the equation[tex]V_{y} = g X t,[/tex] where t is time, we get [tex]t = \frac{V_{y}}{g}[/tex]
[tex]t = \frac{14.25 m/s}{ 9.81 m/s^2}[/tex]

t = 1.453 seconds.

D. Maximum height of the ball: The maximum height can be computed using the vertical component and time to reach the highest point. Using the equation [tex]H = \frac{Vy X t}{2}[/tex],  we get

[tex]H = \frac{14.25 m/s X 1.453 s}{2}.[/tex]
H = 10.35 m

E. Total time the ball is in the air: The ball takes the same time to go up as to come down, so the total time is twice the time to reach the highest point. T = 2 X 1.453 s = 2.906 seconds.

F. Distance from the player when it lands: Using the horizontal component of velocity and the total time in air, the range can be calculated. [tex]R = Vx X T[/tex]
R = 7.26 m/s X 2.906 seconds

R = 21.1 meters

A sodium vapor lamp emits light waves with a frequency of 5.26 x 1014 Hz. What is the wavelength of the light?

Answers

Answer:

570 nm

Explanation:

The wavelength of an electromagnetic wave is given by:

[tex]\lambda=\frac{c}{f}[/tex]

where

[tex]c=3.0\cdot 10^8 m/s[/tex] is the speed of light (the speed of the electromagnetic waves in a vacuum)

[tex]f=5.26\cdot 10^{14} Hz[/tex] is the frequency of the emitted light

Substituting the numbers into the equation, we can find [tex]\lambda[/tex], the wavelength of the emitted light:

[tex]\lambda=\frac{3\cdot 10^8 m/s}{5.26\cdot 10^{14} Hz}=5.70\cdot 10^{-7} m = 570 nm[/tex]

The Sun's gravitational attraction, along with a planet's _______, keeps the planet moving in a(n) _______ orbit and determines the orbital speed. A. inertia; elliptical B. temperature; linear C. tectonic activity; irregular D. magnetic field; circular

Answers

a- inertia, elliptical

Answer:

Explanation:

a is the answer

What is the period of a wave if the wavelength is 100 m and the speed is 200 m/s?

Answers

0.5 would be your answer >:o)

First answer gets Brainliest!

Which of the following statements describes the difference between physical and chemical weathering?

A. Physical weathering affects rocks, while chemical weathering affects only minerals.

B. Physical weathering is caused by ice, while chemical weathering is caused only by water.

C. Chemical weathering changes the composition of a rock, while physical weathering does not.

D. Chemical weathering affects all kinds of rocks, while physical weathering does not.

Answers

B. Physical weathering is caused by ice, while chemical weathering is caused only by water.

Answer:

Chemical weathering changes the composition of a rock, while physical weathering does not.

Explanation:

Chemical weathering of rocks is a chemical reaction. A chemical change is known to change the composition of a substance. Once a substance is subjected to a chemical reaction, a new substance is automatically formed thereby changing the composition of the original substance.

A physical weathering agent does not affect the composition of rocks. This a major difference between chemical and physical weathering processes. For instance, physical weathering caused by ice has nothing to do with internal rock composition.

which of the following can be used to measure wavelength on a transverse wave

Answers

You measure the distance between crest and crest or trough and trough

A dog walks with a speed of 1.5 m/s. How long will it take the dog to cross a yard of length 8 m? O A. 5.3 s O B. 1.3 s O C. 12s O D. 8s

Answers

Answer is: 8/1.5=5.3 sec

The time taken for the dog to cross a yard of length 8 meters is 5.3 seconds.

What is the time taken for the dog to cover the given distance?

Speed is simply referred to as distance traveled per unit time.

Mathematically, it is expressed as:

Speed = Distance ÷ time

Given the parameters:

Speed of the dog = 1.5 meters per seconds

Distance covered 8 meters

Time taken =?

To determine the time taken by the dog to cover a distance of 8 meters, plug the given values into the above formula and solve for the time.

Speed = Distance ÷ time

1.5m/s = 8m / time

Time × 1.5m/s = 8m

Time = 8 / 1.5

Time = 5.3 seconds

Therefore, the time taken is approximately 5.3 seconds.

Option A) 5.3s is the correct answer.

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When did rock layer H form relative to the other rock layers? In your answers, compare layer H to as many rock layers as you can.

Answers

Final answer:

The formation of rock layer H can be determined relative to other layers using stratigraphy, fossil content, and potentially radiometric dating. Its position in the sequence of layers indicates its relative age while the fossils it contains can correlate it with other layers formed in a similar period. Radiometric dating can provide an absolute age if needed.

Explanation:

In the field of geology, the formation of rock layer H can be understood in relation to other rock layers through the method of stratigraphy. Essentially, the principle of stratigraphy states that in undeformed stratigraphic sequences, the oldest strata will be at the bottom with newer layers deposited on top. Therefore, to understand when layer H formed, one would need to examine the position of rock layer H in the sequence. For instance, if layer H is found below layer G but above layer I, we can tell that rock layer H formed after I but before G.

Fossil content can also provide clues to the relative age of the layers. For example, if rock layer H contains fossils that are found in rock layers G and I, it may indicate that these layers were formed during a similar geological period.

A third way is through the use of radiometric dating, which uses the decay of isotopes in the rocks to determine their age. However, this method is typically used to provide an absolute age to rock layers rather than their relative ages.


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Final answer:

Rock layer H's age relative to other layers can be determined by its position in a stratified formation (archaeological stratification) and the use of radiometric dating. The type of rock also provides clues to its age and formation process.

Explanation:

When considering the formation of rock layer H relative to other rock layers, it's imperative to understand geological concepts like stratification and radiometric dating. For instance, if rock layer H is positioned below another rock layer in a stratified formation, it can be inferred that layer H is older. This technique, called archaeological stratification, uses the relative position of layers to identify their age sequence.

Additionally, the exact age of rock layers can be obtained using radiometric dating methods, which leverage the rate of radioactive decay in certain minerals within the rocks, providing a timeline for their formation. If rock layer H is composed of such minerals, its formation age can be determined, revealing when it was formed in relation to other layers.

Identifying the type of rock is important as well; if layer H is a primitive, sedimentary, or volcanic rock, it provides additional clues to its age and its formation process. For instance, sedimentary rock layers are typically formed in the presence of water, and their positioning can reveal historical water levels.

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How does pressure change as the depth below the surface of a fluid increases?

Answers

Answer:

The pressure increases linearly with the depth below the surface

Explanation:

The pressure at the bottom of a column of fluid is given by:

[tex]p=p_0 + \rho gh[/tex]

where

[tex]p_0[/tex] is the atmospheric pressure

[tex]\rho[/tex] is the fluid's density

g is the gravitational acceleration

h is the depth below the surface of the fluid

As we see from the equation, the pressure is directly proportional to h, the depth below the fluid surface: therefore, as h increases, the pressure increases as well.

An object weighs 30 N on Earth. A second object weighs 30 N on the moon. Which has the greater mass? Question 15 options: The one on the moon The one on Earth Not enough information to say They have the same mass.

Answers

Earth gravity = 9.8 m/s²

Moon gravity = 1.6 m/s²

Weight = (mass) x (gravity)

Divide each side by (gravity) and then it says:

Mass = Weight / gravity

Object on Earth:  Mass = (30N) / (9.8 m/s²)  =  3.06 kg

Object on Moon:  Mass = (30N) / (1.6 m/s²)  =  18.52 kg

If two objects have the same weight on Earth and on the Moon, then the one on the Moon must have more mass.  Six times as much mass, in fact.

a measurement of 152.4 mm has 4 significant figures, because there are 4 digits. What about 152,400 mm? How many significant figures do you think it has

Answers

Answer:

Also  4.

Explanation:

If there was a decimal point after the last zero, you'd count the two zeroes as significant.

The measurement 152,400 mm has three significant figures because the trailing zeros are not significiant in a whole number without a decimal point. This indicates the precision of the measuring tool used for the measurement.

The question asks about the number of significant figures in the measurement 152,400 mm. According to the rules for determining significant figures, trailing zeros in a whole number without a decimal point are not significant. Therefore, only the digits 1, 5, and 2 are significant because they precede the non-significant trailing zeros. However, if the measurement were provided with a decimal point, as in 152,400., all the zeros would be significant due to the presence of the decimal point. Given the fact that there is no decimal point, the number 152,400 mm has three significant figures.

It is important to remember that significant figures are a way of expressing precision in measurement. For instance, if a number is written in scientific notation, all digits in the coefficient are considered significant. For the number 152,400 mm in scientific notation, it would be written as 1.524 x 10⁵ to indicate that there are four significant figures, assuming decimal precision was intended. However, given the original format (152,400), we conclude it has only three significant figures.

If the temperature of a gas is increase by 10 x , what will happen to the volume?

A) It will decrease by -10.

B) It will increase by +10.

C) It will decrease by 1/10.

D) It will increase by 10x.

Answers

I believe it’s D) it will increase by 10x because when temperature increasing particles move faster causing things to expand like when you put a bottle of syrup in the microwave.

-- None of the choices answers the question correctly.  It's not that simple.

The only thing you can say about the result is that the product of (pressure)x(volume) will increase by 10x.

-- You can keep the volume of the gas constant if you want to, while it gets 10x hotter.  (Just keep it in the same bottle and don't let it expand.)  But if you do that, its PRESSURE will increase by 10x.

-- If you want to keep the pressure of the gas constant while it gets 10x hotter, then you'll have to let it expand to 10x its original volume.

Also, by the way, the question doesn't mean you just multiply the Celsius or Fahrenheit temperature by 10.  When you're playing with the pressure, volume, and temperature of a gas, it's the ABSOLUTE temperature you need to look at ... like Kelvins, or (Celsius+273°), or (Fahrenheit+460°).

a ray of light that strikes a surface is known as?

a. incident angle
b. reflection angle
c. reflection ray
d. incident ray

Answers

A ray of light that strikes a surface is known as the incident ray.  (d)

In the physics of optics, it has been defined that the incident rays are the rays which strikes the surface.

Answer : Option D

Explanation:

When the ray of light strikes the surface it is know as ''incident ray''. The angle which it makes with the normal or the perpendicular imagined or drawn to the surface is the ''incident angle''.

According to the ''Law of Reflection'', the incident ray after striking the surface is reflected back, the ray which leaves the surface is called the ''Reflected Ray''. The angle which is made between the same normal and reflected ray is the reflected angle.

Calculate the wavelength of the electromagnetic radiation whose frequency is 7.5 x 10^12 Hz

Answers

velocity of electromagnetic waves=3.0×10^8.

wavelength=velocity/frequency

(3.0×10^8)/(7.5×10^12)

=0.00004

Final answer:

The wavelength of electromagnetic radiation with a frequency of 7.5 x 10^12 Hz is 40 nm.

Explanation:

To calculate the wavelength of electromagnetic radiation with a frequency of 7.5 x 10^12 Hz, we can use the formula c = fλ, where c is the speed of light and f is the frequency. Rearranging the formula, we get λ = c/f. Plugging in the given values, λ = (3.00 x 10^8 m/s)/(7.5 x 10^12 Hz). Calculating this gives us a wavelength of 4 x 10^-5 meters or 40 nm.

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Help please with number 7 !!!!!!! Plz ahhhhhh

Answers

it is the Atlantic ocean

Calculate the electric field strenth between two parallel charged plates, separated by 40cm with a potential difference between them of 1000 V

Answers

Field strength = (1000 v) / (40 cm)

Field strength = (1,000 v) / (0.4 meter)

Field strength = (1,000 / 0.4) (volts/meter)

Field strength = 2,500 volts per meter

The electric field strength between two parallel charged plates, separated by 40 cm is 2500 V/m

How to determine the electric field strength?

The question given above, the following data were obtaines:

Distance between plate (d) = 40 cm = 40 / 100 = 0.40 mPotential difference (V) = 1000 VElectric field strength (E) = ?

The electric field strength can be obtained as shown below:

Electric field strength (E) = Potential difference (V) / Distance apart (d)

= 1000 / 0.40

= 2500 V/m

Thus, the electric field strength between the two plates is 2500 V/m

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Which of the following describes scientists best idea about the formation and expansion of the universe

Answers

A. The big bang theory is how scientists think the world was created.

The Big Bang Theory.

A chemical reaction is the only way to separate a(n) . Mark this and return

Answers

A chemical reaction is the only way to separate a pure substance because in terms of chemical composition, an element can't be broken down any more further, or separated. Some mixtures and solutions can be broken down with physical means, not just chemical reactions.

A Pure substance is only separated by a process of chemical reaction.

What is a Pure Substance?

Pure substances are composed of only one kind of particle and have a constant or unchanging structure.

Elements and compounds are subclasses of pure substances:

An element is a substance that only contains one kind or class of atoms. An element is a pure material if it cannot be broken down or converted into other compounds by physical or chemical mechanisms. Metals, nonmetals, or metalloids make up the vast bulk of elements.

On the other hand, when two or more elements are chemically combined in a specific ratio, compounds can also be considered pure substances. However, these substances can be split up into their component parts through chemical processes.

To break down pure substances (elements and compounds) into their individual atoms or elements, a chemical reaction must take place.

Physical techniques cannot distinguish between pure substances.

Hence, Pure substance is only separated by a process of chemical reaction.

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How can a small human retina detect objects larger than itself?

a. Lenses of the eye change the size of the images.

b. The brain interprets the size of the images.

c. The cells of the retina change the size of the images.

d. The optic nerve interprets the size of the images.

Answers

The correct answer would be A) the lenses of the eye change the size of images

Final answer:

The human retina can detect objects larger than itself through the lenses of the eye and interpretation by the brain.

Explanation:

The small human retina can detect objects larger than itself through a complex process involving the lenses of the eye and the interpretation by the brain. The lenses of the eye focus the incoming light onto the retina, creating an image that is larger than the retina itself. The retina then captures this image and sends signals to the brain, which interprets the size of the image based on the information received from the retina.



So, the correct answer to the question is a. Lenses of the eye change the size of the images. The lenses of the eye help the small retina capture and process larger images, allowing us to see objects that are larger than our retina.

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Electric fuse and a Circuit breaker contains?

Answers

Fuses and Circuit Breakers (CB) are used for the protection of power system. These along with other protective equipment like relays, isolater, switches, are collectively called as switchgear(switching equipment used in power systems).

The basic function is to break the circuit in case of faulty conditions so as to protect the power system equipment and auxiliaries.

FUSE is a low resistance device which is placed in the circuit for protection. Under faulty conditions when the current becomes more than the desired value, then due to the increase in temperature the fuse wire melts and breaks, thus breaking the circuit. These are used for lower power ratings and can be used only once, after that it has to be replaced with a new one.

CIRCUIT BREAKER also solves the same purpose i.e. it breaks the circuit when the fault occurs. These are used for large ratings and in the power systems and auxiliaries. CB also has the capability to re-close after the fault is through i.e. when the system gets healthy. The CB has two parts/contacts one is static and the other is moving(the one responsible for making or breaking the contacts).When the contacts of CB separate, then it said to have tripped. Tripping of the circuit breaker has to be very fast so as to avoid the arc formation between the two contacts, otherwise it will defeat the purpose of installing the CB. The trip signal is given to the CB by an other protective device called as an ELECTRICAL RELAY. CB’s are categorized on the basis of the power ratings and the medium used to extinguish the arc formed during the breaking of the contacts.

mark brainliest  :)

Electric fuse and a Circuit breaker both contain ways to interrupt the flow of electricity.

Hope this helps!

Davinia.

After exercise, your heart rate is ____ and you need to slowly bring it back to normal
A. Lowered
B. Destabilized
C. Elevated
D. Tripled

Answers

Heart rate is the rate at which the heart beats per minute. It is a very important function of the human body. After doing exercise heart rate is elevated you need to gradually get it to normal.

What is heart rate?

The heart rate is the number of times the heartbeats per minute.

During training, the heart will speed up. The highest heart rate is varying which is relying on age.

The role of the heart is to accept blood that is oxygen deficient from veins and pump it to the lungs.Where it gathers up oxygen and gets freed of carbon dioxide.  

The main function of blood is to pump the blood into different portions of the body.

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If one bullet is dropped from a certain height and another is fired from a gun horizontally from the same height which one will hit the ground first or will they hit at the same time?

Answers

If the ground is flat, and both bullets are released at the same time from the same height, then they both hit the ground at the same time.

The horizontal motion of the one from the gun has no effect on its vertical motion.

Succession occurs when environmental factors affecting an ecosystem change. Please select the best answer from the choices provided T F

Answers

The statement given in the question is FALSE.

Ecological Succession refers to the change in the specie structure of an ecosystem over a long period of time. There are two types of succession, primary and secondary succession. A primary success is said to occur when an ecosystem is totally destroyed to the extent that even the soil is wipe out. In this case, the ecosystem development has to start from the scratch. A succession is said to secondary if only part of the ecosystem is destroyed.  

Answer:

The answer is TRUE

Explanation:

got it right on Edge 2023

Pollution and the depletion of _____ may be caused by the production of electric energy.
A.) Resources
B.) Magnets
C.) Electric Fields

Answers

the answer is a resources

The pollution and the depletion of  resources may be caused by the production of electric energy. The power generation might be associated with some atmospheric pollution .

What is electric energy ?

Electric energy is form of energy that can be generated from other forms of energy such as kinetic , mechanical, thermal energy etc. All the electric devices are working by the consumption of electric energy.

Electric energy is usually generated from hydrothermal energy, nuclear energy, wind energy etc. In all these cases, energy is transforming from one form to the other.

Nuclear power plants, coal fields, etc. working for power generation is associated with some pollution that threats the surrounding livings. Depletion of these resources leads to some unwanted products and toxic gases.

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As shown in the diagram, two forces act on an object. The forces have magnitudes F1 = 5.7 N and F2 = 1.9 N. What third force will cause the object to be in equilibrium?

3.8 N at 108° counterclockwise from

6.3 N at 162° counterclockwise from

3.8 N at 162° counterclockwise from

6.3 N at 108° counterclockwise from

Answers

Answer:

Second option 6.3 N at 162° counterclockwise from  F1

Explanation:

Observe the attached image. We must calculate the sum of all the forces in the direction x and in the direction y and equal the sum of the forces to 0.  

For the address x we have:  

[tex]-F_3sin(b) + F_1 = 0[/tex]

For the address and we have:  

[tex]-F_3cos(b) + F_2 = 0[/tex]

The forces [tex]F_1[/tex] and [tex]F_2[/tex] are known  

[tex]F_1 = 5.7\ N\\\\F_2 = 1.9\ N[/tex]

We have 2 unknowns ([tex]F_3[/tex] and b) and we have 2 equations.  

Now we clear [tex]F_3[/tex] from the second equation and introduce it into the first equation.  

[tex]F_3 = \frac{F_2}{cos (b)}[/tex]

Then

[tex]-\frac{F_2}{cos (b)}sin(b)+F_1 = 0\\\\F_1 = \frac{F_2}{cos (b)}sin(b)\\\\F_1 = F_2tan(b)\\\\tan(b) = \frac{F_1}{F_2}\\\\tan(b) = \frac{5.7}{1.9}\\\\tan^{-1}(\frac{5.7}{1.9}) = b\\\\b= 72\°\\\\m = b +90\\\\\m= 162\°[/tex]

Then we find the value of [tex]F_3[/tex]

[tex]F_3 = \frac{F_1}{sin(b)}\\\\F_3 =\frac{5.7}{sin(72\°)}\\\\F_3 = 6.01 N[/tex]

So the answer is 6.3 N at 162° counterclockwise from  F1

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