What differentiable functions have an arc length on the interval [a,b] given by the following integrals? note that the answers are not unique. give all functions that satisfy the conditions.

Answers

Answer 1

The functions such as non-vertical, continuously differentiable, non-vertical tangent satisfy the conditions.

What are differentiable functions?

In mathematics, a differentiable function of one real variable is a function that has a derivative at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain.

A smooth, differentiable function lacks any breaks, angles, or cusps (it is locally well approximated as a linear function at each interior point).

If the derivative f'(x 0) exists, a function f is said to be differentiable at x0 if x0 is an inner point in the domain of the function.

In other words, the point (x0, f(x0)) on the graph of f has a non-vertical tangent line. If f is differentiable at every point along U, then U is said to be differentiable.

If the derivative off is also a continuous function over the domain of the function ff, then f is said to be continuously differentiable.

In general, if f’s initial k derivatives are f prime (x), f prime (x), and lots, f(k)(x), then f is said to be of class Ck. f prime (x), f prime (x), lots, and f (k) prime (x) exist and are continuous across the function’s domain.

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Related Questions

Johnny Hotfoot slams on the brakes of his car mov- ing at 60 mph (26.7 m/s) and skids to a stop in 4 s. (a) What is the deceleration of the car? (b) How far does it skid?

Answers

At 60 mph (26.7 m/s), Johnny Hotfoot slams on the brakes of his car and skids to a stop in 4 s. (A) How fast is the car slowing down? (b) The extent of the skid.

If the car had been traveling at 40.0 m/s, it would have slid 27.2 m.

The frictional force opposes the linear force pulling on the automobile. Consequently, m is the vehicle's mass, an is its acceleration, and c is its coefficient of friction.

The normal force is R.

given the aforementioned variables

Find the length of the skid if the vehicle had been traveling at 40.0 m/s.

The car would have skidded 27.2 meters if it had been driving at 40.0 meters per second.

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In parabolic solar cooker a cooking vessel is not kept at the radius of the curved surface

Answers

In parabolic solar cooker, the container of cooking is placed at the focal point of mirror of parabolic shape so that all rays that are falling on solar cooker can converge to one point and produce large amount of heat energy.

A parabolic solar cooker is a cooking device that works on the energy generated from solar panel.

Though solar cookers are slow to cook, they are green sources of energy utilizer as well as renewable source of energy.

Parabolic solar cookers make the use of a reflector which is parabolic in shape to concentrate sunlight into a smaller area in order to generate heat for cooking. They are able to reach high temperatures, which allows them to be used for grilling and frying. These temperatures are significantly higher than what can be reached by a solar box cookers or solar panel cookers .

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Signal at least ____ before making a turn.
a) 2 blocks
b) 10 feet
c) 20 feet
d) 100 feet

Answers

The correct option is (d) 100 feet

Signal at least 100 feet before making a turn.

Before stopping, turning, or changing lanes, signal to other drivers so they are aware of your impending action. You can signal with your hand, arm, or your car's turn signals and brake lights. You should signal at least 100 feet before your turn so that other vehicles have time to adjust. You should turn from the lane that is closest to the direction you wish to go and into the lane that is closest to the one you came from if there are no signs or lane markers to restrict turning. You'll cross the fewest number of lanes of traffic in this manner. When making turns, switch lanes as smoothly as you can without going over the lane lines or obstructing the flow of traffic.

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Acceleration is obtained of 6 m/s2 with a force of 36 n. what is the mass of the object accelerating?

Answers

The mass of the object is 6 kg.

Any push or pull applied to an object is termed a force. In other words, force is defined as the product of the mass of the object and its acceleration. SI unit of force is Newton and that is denoted by the symbol N. Force is termed as a vector quantity because it has both magnitude and direction.

[tex]Force = Mass × Accleration [/tex]

[tex] F = m × a[/tex]

Acceleration is defined as the rate at which velocity changes an object over time.

Si unit of the acceleration is a meter per second square.

[tex]Accleration = \frac{Velocity}{ Time}[/tex]

[tex]a = \frac{v}{t} [/tex]

Acceleration = 6 m/s²

Force = 36 N

The mass of the object is,

[tex]F = m × a[/tex]

[tex]36 = m \times 6[/tex]

[tex]m = \frac{36}{6} [/tex]

[tex]m = 6 \: kg[/tex]

Therefore, the mass of the object is 6 kg.

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In which environment(s) is a population of seed-eating birds likely to undergo adaptive radiation? check all that apply.

Answers

a relatively recent volcanic island with a wide variety of vegetation.

Adaptive radiations can be caused by intrinsic variables (also known as "important adaptive innovations") that improve the availability of niches to a diverging lineage, or by external factors (such as the creation of new ecological opportunities through the emergence of fresh environments). existence of populations of recently diverged closely related species. The first half of this century's naturalists believed that three ecological processes led to adaptive radiation: phenotypic differentiation of populations through resource-based divergent natural selection, phenotypic differentiation through resource competition (ecological opportunity), and phenotypic differentiation through divergent character.

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Speed limit signs on expressway exit ramps are generally colored __________ .

Answers

Answer:

White with black lettering

Explanation:

Generally they are yellow with black lettering but that's for highways at least the state I live in.

Hope this helps!

In an inductive circuit with an uncorrected power factor of 40 percent to 60 percent, the power factor can be corrected to within 5 percent of unity by the addition of a(n) ____

Answers

In an inductive circuit with an uncorrected power factor of 40 percent to 60 percent, the power factor can be corrected to within 5 percent of unity by the addition of a(n) capacitor.

What is capacitor?

A capacitor is a gadget that stores electrical energy in an electric field. It is an inactive electronic part with two terminals. The impact of a capacitor is known as capacitance. A capacitor is a gadget that stores electrical energy in an electric field. It is an uninvolved electronic part with two terminals. The impact of a capacitor is known as capacitance. While some capacitance exists between any two electrical conduits in closeness in a circuit, a capacitor is a part intended to add capacitance to a circuit. The capacitor was initially known as a condenser or compensator. This name and its cognates are still generally utilized in numerous dialects, yet seldom in English, one eminent exemption being condenser mouthpieces, likewise called capacitor receivers.

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Consider a stage doing batch processing with a required setup. if the batch size increases 2 times, how would the stage capacity be affected?

Answers

The correct answer for the affect in the stage capacity is that it will increase.

The stage's capacity will increase .

The capacity formula is as follows:

Capacity = (Batch size) / (Total setup time + processing time x batch size) 

Clearly, increasing the batch size twice will increase capacity, but not in the same proportion because the batch size is the same in the numerator and denominator. Increasing the batch size will increase the capacity but in very small proportions. Furthermore, if the batch size is too large, goods will be produced even if there is no demand, and if the batch size is too small, capacity will be lost. As a result, there is a trade-off between batch size and capacity.

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A particle has an acceleration of 6.14 m/s2 for 0.300 s. at the end of this time the particle's velocity is 9.41 m/s. part a what was the particle's initial velocity? chefggg

Answers

The initial velocity of particle is 7.568 m/s

Given:

Acceleration = a = 6.14 m/s2

Time = t = 0.300 s.

final velocity = v = 9.41 m/s.

To Find:

initial velocity = u

Solution: Velocity is the prime indicator of the position as well as the rapidity of the object.

v = u + at

u = v - at = 9.41 - 6.14*0.3 = 7.568 m/s

Hence, initial velocity of particle is 7.568 m/s

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If you want to add 5 calories of heat to 1 gram of water, how will the temperature change?

Answers

Answer:

It will increase to 5ᵒC.

Explanation:

Calculating The Milky Way galaxy contains
between 200 and 400 billion stars. Estimate the
number of stars in a cluster of 30 galaxies similar
in size to the Milky Way. Your answer should
consist of a low estimate and a high estimate,
both expressed in scientific notation.

——I NEED HELP ASAP!! PLEASE

Answers

The number of stars range between 6 * 10^9 stars and 1.2 * 10^10 stars.

What is the number of stars?

We know that a galaxy is composed of many stars. The stars in the galaxy as we saw from the question, using the milky way as a template may have between 200 and 400 billion stars.

The number of stars could be obtained as the product of the number of galaxies and the number of stars in the lower and the upper limits.

Number of stars in the lower estimate = 200 * 10^6 * 30 = 6 * 10^9 stars

Number of stars in the higher estimate = 400  * 10^6 * 30 = 1.2 * 10^10 stars

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In animals, carbohydrates are stored in ______ granules adjacent to the smooth er membrane in liver cells. these release energy upon demand.

Answers

As the liver cells of animals, carbohydrates are kept in glycogen granules close to the inner membrane. On demand, these release energy.

Where can you find glycogen ?

In addition to human muscle and liver cells, other cells such as those in the brain, heart, smooth muscle, kidney, red and white blood cells, and even adipose tissue also store modest amounts of glycogen.

Glucose is stored in the form of glycogen. It is a sizable, multi-branched polymer of glucose that is converted back into glucose in response to glucagon and accumulates in response to insulin. The fact is that because fat is such an energy-dense molecule and contains so many calories per gram, ounce, or pound, it is far simpler to lose weight when your body burns carbohydrates instead of fat. While a gram of glycogen only contains four calories, a gram of fat has nine calories.

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The earth is an open system for energy. What should be added to the pyramids to make them correct due to that statement?

Answers

The earth is an open system for energy. Sunlight should be added to the pyramids to make them correct.

A system that is in touch with its surroundings or the external environment through the exchange of energy, matter, and materials is called an open system.

In an open system, the energy and matter flow in and out of the boundaries of the system. Earth is a perfect example of the open system as it is in contact with its surroundings.

The exchange between materials such as energy and information takes place in such a system.

The stove top is an example of an open system because in this system the exchange of both heat and moisture occurs with the surrounding. On the other hand, in a closed system, only energy is exchanged.

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What is the average rate from 2.0 to 6.0 seconds in mol / l s? use 4 decimal places

Answers

The average rate from 2.0 to 6.0 seconds in mol/L is 0.004025 mol/L.

What is decomposition reaction ?

Decomposition reactions are those in which a reactant undergoes reaction to form two or more products.

2AX2(g) -------> 2AX(g) + X2(g)

t1 = 2.0 s and t2 = 6.0 s

x1 = 0.0249 and x2 = 0.0088

Average rate of reaction:

Ra = ∆[x]/DeltaT = X2 - X1/t2 - t1

Ra = 0.0088 - 0.0249/6 - 2 = 0.004025 mol

Thus, the average rate is 0.004025 mol/L.

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At what point on a line through the ends of the meter stick is the electric field equal to zero?

Answers

The point on a line through the ends of the meter stick is the electric field equal to zero is 4.7 m from the 0 cm mark.

What is electric field?

An electric field is the physical field that surrounds the electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to physical field for a system of charged particles. Electric fields originate from the electric charges and time-varying electric currents. Electric fields and the magnetic fields are both manifestations of the electromagnetic field, one of the four fundamental interactions (also called forces) of nature.

Electric fields are important in many areas of the physics, and are exploited in electrical technology. In atomic physics and chemistry, for the instance, the electric field is the attractive force holding the atomic nucleus and electrons together in atoms. It is also force responsible for chemical bonding between atoms that result in molecules.

The electric field is defined as a vector field that associates to each point in the space the (electrostatic or Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point. The derived SI unit for electric field is the volt per meter (V/m), which is equal to the newton per coulomb (N/C)

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The correct question will be:

"A +5.00-μC point charge is placed at 0.0 cm mark of meter stick and a -4.00-μC point charge is placed at 50.0 cm mark. At what point on a line through the ends of meter stick is electric field equal to zero?"

Electromagnetic (em) radiation penetrates the atmosphere of earth at what portions of the electromagnetic spectrum?

Answers

Longwave radiation is the name given to the infrared component of the spectrum of radiation that Earth emits; its usual wavelengths range from 4 to 30 micrometers (0.0002 to 0.001 inch).

The electromagnetic spectrum is made up of radio waves, microwaves, infrared light, visible light, ultraviolet light, X-rays, and gamma rays, among other types of electromagnetic radiation. The earth's atmosphere blocks out the majority of electromagnetic radiation from space, preventing most of it from reaching the planet's surface.

Visible light is electromagnetic radiation with wavelengths between 400 and 700 nm. A portion of the electromagnetic spectrum that humans can see with our eyes is the visible light or spectrum. The outside of Earth. Effectively, visible light can pass through Earth's atmosphere.

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How many grams of calcium metal is required to react with 7.75 g water to produce calcium hydroxide and hydrogen gas?

Answers

87.69 grams of calcium metal is required to react with 7.75 g water to produce calcium hydroxide and hydrogen gas.

Ca (OH)2+2H2 = CaH2 + 2H2O

Convert grams of hydrogen to moles of hydrogen.

H2 has a molar mass of 2.016 g/mol.

1 mol H2 x 8.400g H2

2.016g H2 equals 4.1667 mol H2

Calculate the moles of CaH2 using the molar ratio.

The molar ratio is 1 mol CaH2: 2 mol H2, according to the equation that is balanced.

2.0833 mol CaH2 = 4.1667 mol H2 1 mol CaH2 2 mol H2

grams of CaH2 to CaH2

CaH2 has a molar mass of 42.09 g/mol.

1.mol CaH2=87.69 g CaH2 2.0833mol CaH2=42.09 g CaH2

87.69 g CaH2 are required for the reaction.

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You would like to know whether silicon will float in mercury and you know that can determine this based on their densities. unfortunately, you have the density of mercury in units of:_________

Answers

The density of mercury in units 2.33 x 10³ kg / m³.

What is density of mercury?

At room temperature, mercury, a very heavy, dense silver-white metal, is a liquid. (To learn more about mercury, click here.) A small amount of mercury like this feels surprisingly heavy because mercury has a density of 13.5 g/mL, which is approximately 13.5 times denser than water (1.0 g/mL).

According to the given information:

To convert gram divided centimeter³ to kg / m³

gram / centimeter³

= 10⁻³ kg / centimeter³

= 10⁻³  / (10⁻²)³ kg / m³

= 10⁻³ / 10⁻⁶ kg / m³

= 10⁻³⁺⁶ kg / m³

= 10³ kg / m³

To convert the amount from gm/cm3 to kg/m3, we must multiply it by 10^3

2.33 gram / cm³

= 2.33 x 10³ kg / m³ .

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I understand that the question you are looking for is:

You would like to know whether silicon will float in mercury and you know that can determine this based on their densities. Unfortunately, you have the density of mercury in units of kilogram-meter^3 and the density of silicon in other units: 2.33 gram-centimeter^3. You decide to convert the density of silicon into units of kilogram-meter^3 to perform the comparison.

By which combination of conversion factors will you multiply 2.33 gram-centimeter^3 to perform the unit conversion?

Due to radiation and absorption, what is the maximum flame temperature in a fire?

Answers

The maximum flame temperature in a fire is 1500-1600K due to radiation and absorption.

What do you mean by radiation and absorption?

In physics, matter (usually electrons bound in atoms) absorbs electromagnetic radiation in order to convert the energy of a photon into the internal energy of the absorber (for example, thermal energy). Attenuation, or the steady decrease in light wave intensity as it travels through a medium, is a prominent effect. In some circumstances (optics), the medium's transparency changes by a factor that varies as a function of wave intensity, leading to saturable absorption (or nonlinear absorption), even though the absorption of waves typically does not depend on their intensity (linear absorption).

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1. How many milligrams are in 25 grams?

Answers

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.

Crystal lake, inc., has a total debt ratio of 0.36. what is its debt-equity ratio?

Answers

When the total debt ratio is 0.36, the debt-equity ratio is 0.5625.

What does debt-to-equity ratio mean?

The debt-to-equity ratio is a financial metric that shows how much debt and shareholder equity were utilized to finance the assets of a company. The ratio, often known as risk, gearing, or leverage, is closely related to leveraging. The debt-equity ratio serves as a gauge for how equally creditors and owners or shareholders contributed to the capital used by the company. The debt-equity ratio is the simple ratio of all long-term debt and equity capital in the company. The debt-to-equity ratio is calculated by dividing a company's total liabilities by the sum of its shareholders' equity. For the majority of businesses and industries, a desirable debt-to-equity ratio is around 2.0. A high debt-to-equity ratio shows that a business is using more market capital to finance its operations, whereas a low debt-to-equity ratio shows that the business is making better use of its assets and using less market capital. The debt-to-equity ratio is often higher in the capital industries.

Total Debt ratio = Debt/Asset

Hence, Debt=0.36*Total Assets

Assets = Debt*Equity

Hence Equity=(1-0.36)*Total Assets=0.64*Total Assets

So, Debt-Equity Ratio=Debt/Equity

=0.36Total assets/0.64Total assets

=0.5625

⇒Debt-Equity Ratio=0.5625

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If the spectrometer had been set to a different wavelength to measure absorbances (one where the copper would have absorbed more or less light), how would that have changed the results?

Answers

If the spectrometer had been set to a different wavelength to measure absorbances (If the spectrometer had been set to a different wavelength to measure absorbances) then the calculated unknown concentration should same.

Absorbance is directly proportional to  the concentration of the substance.

higher concentration gives higher absorbance because the light absorbed is affected by the interacted no. of molecules.

Spectrometer - An instrument used to measure wavelength of spectra over a wide range.

types of spectrometer

emission absorption

If the spectrometer had been set to a different wavelength to measure absorbances (If the spectrometer had been set to a different wavelength to measure absorbances) then the calculated unknown concentration should same.

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A particle is moving along a projectile path at an initial height of 96 feet with an initial speed of 16 feet per second. this can be represented by the function h(t) = −16t2 16t 96. what is the maximum height of the particle? 100 feet 96 feet 60 feet 56 feet

Answers

The maximum height of the particle is 100feet

Calculation

Applying linear motion equations,

v^2 = u^2 - 2as

v = final velocity

u = initial velocity

g = acceleration due to gravity

s = height travelled

At max height,

velocity = 0 i.e. V=0,  initial velocity u = 16ft/sec

g = 32ft/[tex]sec^{2}[/tex]

so we have

0 = [tex]u^{2}[/tex] -2gs

S = [tex]u^{2}[/tex]/2g

= 16*16/2*32

= 4 feet

So maximum height = initial height + height travelled

= 96 + 4 = 100 feet

What is the maximum height and range formula?

The range is u2sin2g and the needed value of the maximum height is u2sin2g. Not to be confused with flying time is the maximum height attained.

What is the highest point?

Maximum Height refers to a structure or sign’s highest point as measured from the average natural ground level at the base of the supporting structure.

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Answer:

100 feet

Explanation:

Watch the animation and identify the correct conditions for forming a hydrogen bond.

Answers

When a hydrogen atom forms a covalent link with an N, O, or F atom, hydrogen bonding takes place.

Only a few substances that contain hydrogen can form a hydrogen bond.

The hydrogen bonds in the CH4 molecule are visible.

When a F atom and a hydrogen atom are covalently bound, the hydrogen atom gains a slight positive charge.

Covalent bonds and hydrogen bonds are interchangeable terms.

What is hydrogen bond?

The interaction known as hydrogen bonding, which involves a hydrogen atom sandwiched between two other atoms with a high affinity for electrons, is stronger than van der Waals forces but weaker than ionic or covalent bonds. Atoms in separate molecules or distinct regions of the same molecule can form hydrogen bonds with one another. A hydrogen atom (FH, NH, or OH) is covalently bound to one of the pair's (the donor) typically fluorine, nitrogen, or oxygen atoms, with which it shares electrons unevenly. As a result of this high electron affinity, the hydrogen gains a little positive charge. The other atom in the pair, which is usually F, N, or O, has an unshared electron pair, giving it a little negative charge.

The donor atom efficiently transfers its hydrogen to the receiver atom by electrostatic attraction, creating a connection. Water (H2O) is liquid over a much wider temperature range than would be anticipated for a molecule of its size due to its extensive hydrogen bonding. Because it quickly forms hydrogen bonds with the solute, water is an excellent solvent for ionic compounds as well as many other types of solutes. A linear protein molecule's ability to fold into its functional configuration depends on the hydrogen bonds formed between the amino acids. The double-helix structure of DNA is essential for the transmission of genetic information. It is created by hydrogen bonds between nitrogenous bases in nucleotides on the two strands of DNA (guanine partners with cytosine, adenine couples with thymine).

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What is the atomic number for an element whose mass number is 115, which contains 66 neutrons per atom?

Answers

The atomic number for an element whose mass number is 115, which contains 66 neutrons per atom is: 49

The formula and procedure we will use to solve this problem is:

number of protons = mass number - number of neutronsatomic number = number of protons

Information about the problem:

mass number = 115number of neutrons = 66atomic number =?

Applying the number of protons formula  we get:

number of protons = mass number - number of neutrons

number of protons = 115 - 66

number of protons = 49

Applying the atomic number formula  we get:

atomic number =number of protons

atomic number = 49

What is an atom?

The atom is the smallest part of the composition of matter, it is indivisible and is composed of a nucleus that has protons and neutrons, and around the nucleus there are the electrons.

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The pendulum is a thin ring with a radius of R 10 cm and a mass of m 500 g, suspended on a weightless thin rod with a length of l 0.4 m. Determine the moment of inertia of the pendulum relative to the axis around which the oscillations occur

Answers

The moment of inertia of the pendulum is determined as 0.0025 kgm².

What is moment of inertia?

The moment of inertia of an object is defined as a measurement the rotation of the object around a fixed axis.

The pendulum can be modelled as a circular disk and the moment of inertia is calculated as follows;

I = ¹/₂Mr²

where;

M is mass of the pendulumr is the radius of the pendulumI is the moment of inertia of the pendulum

Substitute the given parameters and solve for the moment of inertia of the pendulum.

I = 0.5 X 0.5 kg x (0.1)²

I = 0.0025 kgm²

Thus, the moment of inertia of the pendulum is determined as 0.0025 kgm².

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Calculate the energy of a photon emitted when an electron in a hydrogen atom undergoes a transition from =6 to =1.

Answers

When an electron in a hydrogen atom transitions from the state of n=6 to n=1, a photon with an energy of 13.2 eV is released.

What components make up a photon?A photon is a microscopic particle that is part of electromagnetic radiation waves. Maxwell demonstrated that photons are merely electric fields flowing through space.A single photon can trigger a response from sensors in the retina.What is the difference between an electron and a photon?Photons and electrons. One of the fundamental quantum-mechanical particles is an electron, although photons also exist and have entirely distinct properties. While the electron is a subatomic particle found in every atom, the photon is a sort of elementary particle that serves as an energy carrier.

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7. 122 10 292 252 Fig. 6.31 a The effective resistance of the circuit shown in the figure above is ? NE​

Answers

R1+R2+R3 =1+1+1=3 is used to represent the circuit's overall resistance.

The 3 resistors on the upper side of the circuit are linked in series in this instance, and the total resistance R1 is expressed as 1+1+1=3.

The combined resistance R2 is expressed as 2+2+2=6 due to the series connection of the three 2-ohm resistors on the lower part of the circuit. The intermediate resistances R1, R2, and 2 are linked in parallel. This parallel connection's total resistance, R3, is therefore represented as 2/1+ 2/1+ 6/1 = 1/1=1 ohm.

In other words, the closed loop's resistance is decreased to 1 ohm.

Now, R1+R2+R3 =1+1+1=3 is used to represent the circuit's overall resistance (R).

As a result, the resistance in the circuit from point A to point B is 3.

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Sketch the vector v in space and write its component form. v lies in the xz-plane, has magnitude 5, and makes an angle of 45 degree with the positive z-axis.

Answers

The component form is [tex]5/2 [\sqrt{2} /2,0,\sqrt{2}/2], 5/2 [-\sqrt{2} /2,0,\sqrt{2}/2][/tex].

If vv lies in the xz-plane then yy coordinate is 0.

We can have two scenarios: when vv lies in front of yz-plane and when vv lies behind yz-plane.

If vv lies in front of yz plane, then v=5×[tex][\sqrt{2} /2,0,\sqrt{2}/2][/tex]

If vv lies behind yz-plane then v=[tex][-\sqrt{2} /2,0,\sqrt{2}/2][/tex]

What is a vector parametric equation?

A linear combination of vectors with potentially unknowable coefficients makes up a vector equation. It is the same as asking if a given vector is a linear combination of some other provided vectors to determine whether or not a vector equation has a solution.

The vector equation's components, x = x0 + at, y = y0 + bt, and z = z0 + ct, are the line's parametric equations. The direction numbers of the line are the three elements a, b, and c.

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If the lead can be extracted with 92.5fficiency, what mass of ore is required to make a lead sphere with a 7.00 cm radius? the density of lead is 11.4 g/cm3.

Answers

The mass of the ore required to make the lead sphere 7 cm is 17.7 kg.

The radius of the lead sphere = 7 cm

The density of the lead = 11.4 g/cm³

The efficiency of lead extraction = 92.5 %

Let the mass of the lead = m.

Let the mass of the ore = M.

So the mass of the lead is,

[tex]m =(Density) \times[ \frac{4}{3} \pi(Radius) ^{3} ][/tex]

[tex]m = 11.4 \times \frac{4}{3} \times \frac{22}{7} \times( 7 )^{3} [/tex]

[tex] = 16385.6 \: g[/tex]

[tex] = 16.38 \: kg[/tex]

The efficiency constant is,

[tex]η = \frac{mass \: of \: lead}{mass \: of \: ore} [/tex]

[tex]η = \frac{m}{M}[/tex]

[tex]92.5\% = \frac{16.38}{M}[/tex]

[tex]M = \frac{16.38}{ \frac{92.5}{100} } [/tex]

[tex]M = \frac{16.38}{0.925} [/tex]

[tex] = 17.7 \: kg[/tex]

Therefore, the mass of the ore required to make the lead sphere of 7 cm is 17.7 kg.

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