On mars, the acceleration due to gravity is 3.77 m/s2. how far would a 47 g rock fall from rest in 6.5 s if the only force acting on it was the gravitational force due to mars?

A cyclist starts from rest and accelerates at 4.0 m/s^2 for 3.0 s. After that, the biker travels for 20 seconds at a steady speed. The cyclist travels 258 meters.

This kind of motion is described as the motion of an item traveling in a straight line while maintaining a constant speed along that path while it traverses equal distances in similar amounts of the time, regardless of the length of the time.

A body's acceleration must be zero if it is moving rectilinearly and is doing so consistently.

When an object is travelling uniformly, its speed remains constant. When an item moves uniformly, its displacement is given by the formula x=vt, where v stands for constant velocity and t for the motion's time interval.

Given by, is the displacement of a motion with constant acceleration.

v is constant velocity

t is time interval of the motion.

Given by, is the displacement of a motion with constant acceleration.

[tex]x=v_{i}t+\frac{1}{2}at^{2}[/tex], where

It has a constant acceleration of a

[tex]v_{i}[/tex] is the motion's time interval, and t is the beginning velocity.

Answer and justification

Given: The cyclist's starting speed is,

[tex]v_{i}[/tex]=0

The cyclist's initial acceleration is 4 m/s2.

The span of time during which motion has a constant acceleration is,

[tex]t_{1}[/tex]=3s

The cyclist's displacement in 3 seconds will be,

[tex]x_{1}= v_{i}t_{1}+\frac{1}{2}at_{1}^{2}=0(3)+\frac{1}{2}(4)(3)^{2}=18m[/tex]

After 3 seconds, the cyclist's final speed will be,

[tex]v_{f}= v_{i}+at_{1}=0+4(3)=12m/s[/tex]

t2=20s is the time interval for a cyclist traveling at a steady speed.

The biker will move x2 in the following 20 seconds at a constant speed,

x2=[tex]v_{f}t^{2}[/tex]=(1/2)(20)=240m

The biker will have covered a total distance of

x=x1+x2=18+240=258m.

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4.6 ml of a 5.0 m solution of sodium borate must be added to a 200 ml solution of 50 mm boric acid in order for the ph to be 9.6. the pka of boric acid is 9.24.

Borax, also known as sodium hydrated borate, is an ionic molecule having the chemical formula Na2H20B4O17, also written as Na2B4O710H2O. It is a crystalline solid that has no color and dissolves in water to form a simple solution.

It is frequently sold in powder or granular form and has a wide range of industrial and domestic applications, including as a pesticide, metal soldering flux, ingredient in glass, enamel, and pottery glazes, tanning agent for skins and hides, artificially ageing agent for wood, pharmaceutic alkalizer, and pesticide.

It serves as a buffer in laboratories that work with chemicals.

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The work done to haul up the rope is Nm.

We need to know about work to solve this problem. Work can be defined as the energy transferred to or from an object via the application of force along a displacement. It can be written as

W = F x s

where W is work, F is force and s is the displacement.

From the question above, we know that

λ = N/m

s = m

Find the force applied

F = λ . s

F = N/m . m

F = N

Find the work done

W = F . s

W = N . m

W = Nm

Hence, the work done to haul up the rope is Nm.

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The distance of ball from the launch point is

0.92 m

Given:

U = 4.5 m/s = initial speed

V = 0.7 m/s = final speed

g = 10 m/s^2 = acceleration due to gravity

To Find:

distance of ball from the launch point

Solution: The law of motion equation

V^2 - U^2 = 2aS

(0.7)^2 - (4.5)^2 = 2*10*S

0.49 - 18.9 = 20S

- 18.41 / 20 = S

S = - 0.92 m

The distance of ball from the launch point is 0.92 m

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By the half-life of radioactive, the remaining mass of radioactive elements is 2.47 pounds.

We need to know about the half-life of the radioactive elements to solve this problem. The radioactive element will decay over time and follow the equation

N = No(1/2)^(t/t'')

where N is the final quantity, No is the initial quantity, λ is the decaying constant, t is time and t'' is the half-life of a radioactive element.

From the question above, we know that

t'' = 9 years

No = 6 pounds

t = 11.5 years

Calculate the remaining mass

N = No(1/2)^(t/t'')

N = 6(1/2)^(11.5/9)

N = 2.47 pounds

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18.45 % percent of the distribution falls between 400 and 500 feet.

Z score is a standard score that tells you how many standard deviations away from the mean an individual value X.

Mean value ,μ= 410 feet

Standard deviation, σ = 45 feet

X = square of an individual

In a set with mean value and standard deviation the z score of a measure X is given by:

 Z = (X - μ)/σ

percent of the distribution that falls between 400 and 500 feet

when

X = 400feet

Z = 400-410 / 45 = -0.22

p-value for Z= 400 is 0.4129

X = 500 feet

Z = 500- 410 / 45 = 2

p-value for Z = 500 is 0.2275

So there is 0.4129 - 0.2275 = 0.1854 = 18.45 %percent of the distribution falls between 400 and 500 feet.

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The number of outcomes in the compliment of the event are 0.54

No of strawberry plants in the field = 259259

No of plants that are ready for picking = 142142

so no of outcomes = 142142/ 259259 = 0.54 outcomes

The area of mathematics that deals with probability is called probability theory.

Probability is a concept that can be interpreted in a variety of ways, but probability theory tackles the idea in a rigorous mathematical way by expressing it through a series of axioms.

Typically, these axioms formalize probability in terms of a probability space, which links a collection of outcomes known as the sample space to a measure taking values between 0 and 1. An event is any defined subset of the sample space.

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The time taken for the APUSH textbook to hit the ground is determined as 0.55 seconds.

The time of motion of an object is the time taken for the object to travel from its initial point to the final point.

The time taken for the APUSH textbook to hit the ground is calculated as follows;

t = √(2h/g)

where;

t = √(2 x 1.5/9.8)

t = 0.55 seconds

Thus, the time taken for the APUSH textbook to hit the ground is determined as 0.55 seconds.

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The only dissimilarity between Coulomb's law and Newton's law of gravitation other than the type of force considered is Newton's law only considers negative force while Coulomb's law considers both forces.

In these contexts, it is considered that repulsive forces are positive and attractive forces are negative. So, Newton's law of gravitation considers gravitational force which only attracts. So, Newton's law of gravitation takes only negative force into account while Coulomb's law considers both electric charges.

According to Newton's law of gravitation,

F = G [tex]m_{1} m_{2}[/tex] / [tex]r^{2}[/tex]

According to Coulomb's law

F = k [tex]q_{1} q_{2}[/tex] / [tex]r^{2}[/tex]

Therefore, the only dissimilarity between Coulomb's law and Newton's law of gravitation other than the type of force considered is Newton's law only considers negative force while Coulomb's law considers both positive and negative forces.

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Wavelength of radiation must be used to eject electrons with a velocity of 2300 km/s is 63.9nm.

Einstein's equation for the photoelectric effect

hv = A + W

Where,

Energy of photon : E = hvx = hxc/λ

The work function for chromium is A

Planck's constant h= 6.626X 10⁻³⁴ Js

speed of light c = 2.998X10⁸ m/s

Velocity of 2300 km/s = 2300 X 10⁶ m/s

The kinetic energy of emitted electron

W = mv²/2 = (9.10939 X 10⁻³¹ kg X (2300X10⁶ m/s)²)/2 = 2.409X10⁻¹⁸

Hence,

    λ = ch/A+W

λ = (6.626X10⁻³⁴JsX2.998X10⁸m/s)/(7X10⁻¹⁹J + 2.409X10⁻¹⁸J)

  = 19.865X10²⁶Jm/3.109X10⁻¹⁸J = 6.39X10⁻⁸= 63.9 nm

Wavelength of radiation must be used to eject electrons with a velocity of 2300 km/s is 63.9nm

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I understand that the question you are looking for is "The work function for chromium metal is 7.0 x 10-19 J (4.37 eV). What wavelength of radiation must be used to eject electrons with a velocity of 2300 km/s?"

Water is the only substance that is naturally present near the surface of the planet in the current atmosphere as a solid, liquid, and a gas.

The gaseous mixture that covers the planet is its atmosphere. The Earth's atmosphere contributes to the viability of life. In addition to giving us air to breathe, it protects us from the majority of the Sun's harmful ultraviolet (UV) radiation, increases the surface temperature of our planet by around 33° C (59° F) due to the greenhouse effect, and mainly eliminates dramatic temperature variations between day and night. There is an atmosphere on each of the other planets in our solar system, but none of them has the same proportion of gasses or layered structure as Earth's atmosphere.

The most prevalent elements are nitrogen and oxygen, which make up about 78% of dry air (N2) and about 21% of it, respectively (O2). Argon, carbon dioxide (CO2), and numerous other gases are also present in the atmosphere, although at considerably smaller concentrations; each makes up less than 1% of the total gas mixture. Water vapor is also present in the atmosphere. Water vapor is present, but its usual concentration is only about 1%. Additionally, there are a lot of tiny liquids and solids "floating" in the atmosphere. The term "aerosols" refers to a group of particles that also includes dust, pollen, spores, salt from sea spray, volcanic ash, smoke, and other substances.

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Two or more vectors are equivalent if they have same magnitude and direction.

Vectors are formed by joining tail with head and forming an arrow in the direction of head.

Lets find each of these vectors.

(i) v1= (position vector of Q)-(position vector of P)

 = (4i+4j)-(2i+4j)= 4i+4j-2i-4j=2i

v1= 2i

if a vector V= xi+yj

then the length of vi =2i

length of v1=2

(ii )v2= (position vector of Q)-(position vector of P)

(i=3j)-(-i+3j)= i+3j+i-3j=2i

v2= 2i

length of v2= 2

(iii)  v3= (2i+4j)-(-i+3j)= 2i+4j+i-3j

v3= 3i+j

length of v3= [tex]\sqrt{10}[/tex]

(iv) v4= (6i+3j)-(4i+j)= 6i+3j-4i-j

Length of v4= [tex]\sqrt{8}[/tex]

Two vectors are equivalent if they have same magnitude and direction.

Clearly vectors V1 and V2 have same magnitude and they have same direction as represented of their sketch.

Hence vectors V1 and V2 are equivalent.

Magnitude is a term used to describe size or distance. We can relate the magnitude of the movement to the size and movement speed of the object. The magnitude of a thing or an amount is its size.

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The net forces on the first car is zero, the middle car is zero, and the last car is also zero.

In mechanics, the net force is the vector sum of all forces acting on a particle or object. The original forces' impact on the particle's motion is replaced by the net force, which is a single force. It causes the particle to accelerate at a rate equal to the sum of all those actual forces, as stated by Newton's second law of motion.

It is possible to figure out the torque connected to the point at which a net force is applied in order to keep the object's jets moving in the direction of the initial force field. Its resulting torque, the net force, has the same impact on the object's rotational motion as all actual forces combined.

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The unknown metal with a mass of 39.27 g is potassium with the symbol K.

The mass of an atom is due to protons and neutrons present in it.

The protons and neutrons are together present in the nucleus of an atom.

The mass of any element is given by its mass number whose formula is

Mass Number = Number of protons + Number of neutrons

In the given case 39 = Number of protons + Number of neutrons

The only element of the periodic table which satisfies the above equation is potassium because it has 19 protons and 20 neutrons.

Thus, the unknown metal with a mass of 39.27 g is potassium with the symbol K.

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Mutation provides the raw material for evolution because it can create new alleles, which are alternative forms of the same gene.

A mutation is a variation or change that occurs spontaneously in the sequence of the genes that make up the deoxyribonucleic acid (DNA).

Mutations can occur at three different levels:

In biology, a gene is a unit composed of a chain of deoxyribonucleic acid (DNA) that contains the necessary information to transfer hereditary traits from one generation to the next.

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The average acceleration of the car as it accelerates from 15 m/s to 25 m/s will be 2.5 m/s².

Average acceleration is the average rate of change of velocity with respect to time. Mathematically -

a = Δv/Δt

Given that a car is traveling at 15 m/s in north direction and in 4 seconds it accelerates to 25 m/s in the north direction only. Therefore, we can write -

initial velocity [u] = 15 m/s

final velocity [v] = 25 m/s

time taken [Δt] = 4 s

The magnitude of the average acceleration can be calculated as follows-

a = Δv/Δt

Δv = v - u = 25 - 15

Δv = 10 m/s

Therefore -

a = 10/4

a = 2.5 m/s².

Therefore, the average acceleration of the car will be 2.5 m/s².

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Given, Force = 390 N

Diameter of piston (1) = 4 cm

Diameter of piston (1) = 10 cm

now,

By using Pascal's Law which that states that " a pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere", i.e. force per unit area is constant at any point in a confined incompressible fluid flow.

Mathematically, [tex]p=\frac{F1}{A1} = \frac{F2}{A2}[/tex]

where P is pressure at any point in a confined incompressible fluid

F1 and F2 = Force at point 1 and 2 respectively

A1 and A2 = Area of point 1 and 2

So,  [tex]F2 = \frac{F1}{A1} * A2[/tex]

[tex](A1 = \frac{\pi D1^{2} }{4} )\\(A2= \frac{\pi D2^{2} }{4} )[/tex]

[tex]F2 = 390 * \frac{\frac{\pi D2^{2} }{4} }{\frac{\pi D1^{2} }{4} }[/tex]

[tex]F2 = \frac{390}{4*4} * 10^{2}[/tex]

F2 = 2437 N

The magnitude of the force f2 is 2437 N

The given question is complete, complete question is...

"If a 390 N force F1 is applied to the piston with the 4 cm diameter, what is the magnitude of the force F2 that can be resisted by the piston with the 10 cm diameter? Neglect the weights of the pistons."

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

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

a = (v – u) / t

Where

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

a = (v – u) / t

–2 = (v – 0.2) / 7

Cross multiply

v – 0.2 = –2 × 7

v – 0.2 = –14

Collect like terms

v = –14 + 0.2

v = –13.8 m/s

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Answer:

I need help ASAP to with this question

Explanation:

Please hurry up with assignment

Charge must pass by a point in a wire is 5 Coulomb

Given:

time = 10 s = t

current = 0.50 A = I

To Find:

charge = q

Solution: Current is defined as amount of charge passing through a region per unit time. It is given by the formula

I = q/t

q = I x t = 0.50 A x 10 s = 5 Coulomb

Hence, charge must pass by a point in a wire is 5 Coulomb

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The average velocity of  you and your family go from Charleston to New Orleans is (Vₐ)= 152.92 km/h

The term velocity explains that the object or particle displacement within the respected time.  Average velocity is total displacement divided by total time.

To calculate the value of average velocity we are using the formula here is,

Vₐ = (s₁+s₂)/(t₁+t₂)= sₐ/tₐ

Here we are known,

t₁= You and your family leave to go from Charleston to New Orleans = 7:00 am.

t₂=You and your family reached to go from Charleston to New Orleans = 4.00 pm.

tₐ=Time interval between the leaving and reaching time=9 hour.

sₐ= The trip’s distance to go from Charleston to New Orleans= 850 miles

Now we put the values in the above equation we get,

Vₐ =sₐ/tₐ

Or, Vₐ =850 miles/9 hour

Or, Vₐ =94.4 miles/hour.

Or, Vₐ = 152.92 km/hour.

According to the calculation we can write that,

The average velocity of  you and your family go from Charleston to New Orleans is (Vₐ)= 152.92 km/h

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On vacation you and your family go from Charleston to New Orleans you leave at 7:00 am and arrive at 4:00 pm and the trip’s distance is 850 miles. what is the average velocity of the trip?

Rotation curves for spiral galaxies show (C) most have dark halos since It appears that spiral galaxies are encased in the substantial dark matter "halos".

Abstract The main method for ascertaining the mass distribution in spiral galaxies is to analyse the rotation curves of spiral galaxies. They offer vital knowledge for comprehending spiral galaxies' dynamics, evolution, and creation. This substance, which has mass but emits no light, is referred to as "dark matter." The dispersion of dark matter appears to extend much beyond the host galaxy's borders, according to the rotation curves of satellite galaxies.

Rotation curves are used by astronomers to calculate the masses of specific spiral galaxies. There is more mass between the stars and the galactic centre the quicker the stars orbit the galaxy's centre.

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The characteristics of the outer planets are;

- larger size than the inner planets

- evidence of volcanic activity

- thinner atmosphere than inner planets

- reflect light from sun

The solar system is composed of the sun and the planets. The planets move round the sun in concentric circles. The sun is the focus of the solar system. This is the heliocentric model of the ecosystem.

Now there are several planets in the solar system which are;  Mercury · Venus · Earth · Mars · Jupiter · Saturn · Uranus · Neptune. The planets Mercury · Venus · Earth · Mars  are the inner planets while the planets  Jupiter · Saturn · Uranus · Neptune. are the outer planets.

The characteristics of the outer planets are;

- larger size than the inner planets

- evidence of volcanic activity

- thinner atmosphere than inner planets

- reflect light from sun

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Water serves as a lubricant and a shock absorber as part of body fluids.

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Answer:

1568 km/hr

Explanation:

First convert from ft/s to km/s

Do this by using a conversion rate.

3280 ft/km

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

Then convert from km/s to km/hr

Conversion rate 3600 s/hr

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

The new moon, if it were visible, when eastern horizon starts at 6 am.

The first bilingual (Chinese and English) community radio show to be broadcast to a local audience in the United Kingdom is called Eastern Horizon. In recent years, it was primarily carried live on Saturdays between midnight and one in the morning on BBC Radio Manchester in Manchester.

The center of the horizon on the front of the planisphere points in the direction of North (0º azimuth). The eastern horizon is on the horizon's right side (90º azimuth), and the western horizon is on the horizon's left (270º azimuth).

The new moon, if it were visible, when eastern horizon starts at 6 am.

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Answer:

Because volume is determined as the product of length and width as well as height of an object.So change in any dimension can change the other two dimensions as well which brings about a greater change in volume by carrying out the product of the dimensions .

Explanation:

Length x width x height = Volume of a regular shaped object

Voltage polarity can be determined by the direction of current flow through the circuit

All voltages and currents possess both magnitude and polarity. One current flows through the entirety of a series circuit with its polarity flowing from the negative battery terminal to the positive battery terminal. Polarities are also seen in voltage dips across loads. Utilizing the electron current's direction as a starting point is the simplest method for determining these polarities. The voltage is then negative where the electron current enters the load (Figure 31). No matter how many or what kind of loads are present in the circuit, this remains true. The potential drop is opposite of the source across the load.  In opposition to the source voltage, the voltage dips lower it for the other loads.

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The weight percentage of sodium carbonate in the mixture is = 67.71%  

The weight percentage of sodium bicarbonate in the mixture is = 32.57%

The total mass throughout grams of all the atoms needed to form a molecule per mole is what makes up the molar mass, also known as the molecular weight. Grams per mole is the unit measuring molar mass.

The interaction between sodium carbonate and hydrochloric acid has the following equation:

Na₂CO₃ + HCl  --> NaCl  + CO₂ + H₂O

The reaction's balanced equation is,

Na₂CO₃ + 2HCl  --> 2NaCl  + CO₂ + H₂O -------(2).

When sodium hydrogen carbonate as well as hydrochloric acid react, the following equation results.

NaCO₃ + HCl  --> NaCl  + CO₂ + H₂O ----------------(3)

The Molar mass :

Na₂CO₃ = 106g/mol

NaCO₃ = 84g/mol

NaCl  = 58.5g/mol

The mass of the mixture is Na₂CO₃/NaCO₃ = 9.540g

The molar masses of the constituent elements that make up the compounds are added to determine the molar weight of the substances. In both chemical equations (2) and (3), the unitary technique is employed to calculate the mass of the mixture based on the number of moles (3).

The mass of the sodium carbonate and sodium bicarbonate is calculated with the help of the mass of NaCl formed by the mixture of  Na₂CO₃/NaCO₃ with HCl.

The mixture has the following percentage of sodium carbonate:

        % of Na₂CO₃ =  [tex]\frac{x \times 106}{9.540} \times 100\\[/tex]

                             [tex]=\frac{0.061 \times 106}{9.540} \times 100[/tex]

                             = (6.46/9.540)*100

                             = 67.71%        

The weight percentage of sodium carbonate in the mixture is = 67.71%      

The mixture has the following percentage of NaHCO3:

        % of NaHCO₃ =  [tex]\frac{y \times 84}{9.540} \times 100[/tex]

                             = [tex]=\frac{0.037 \times 84}{9.540} \times 100[/tex]

                              = (3.108/9.540)*100

                             = 32.57%

The weight percentage of sodium bicarbonate in the mixture is = 32.57%

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I understand that the question you are looking for is:

A mixture of sodium carbonate and sodium hydrogen carbonate is treated with aqueous hydrochloric acid. the unbalanced equations for the resulting's reactions are:

Na2CO3 (s) + HCl (aq) --> NaCl (aq) + CO2(g) + H2O (l)

NaHCO3(s) + HCl (aq) --> NaCl (aq) + CO2(g) + H2O (l)

You treat 9.540g of Na2CO3/NaHCO3 mixture with an excess of aqueous HCl and isolate 9.355g of NaCl. What is the weight percent of each substance in the mixture?