In ernest rutherford's gold foil experiment, why did alpha particles sometimes (1 in 8,000) fly violently in a random direction?

(a) The speed as the stone hits the ground is 29.4 m/s (b) The distance at which the stone fell is 44.1 m.

Speed can be defined as the ratio of distance to time.

(a) To calculate the speed at which the stone hit the ground, we use the formula below.

Formula:

Where:

Substitute the values above into equation 1

(b) To calculate the distance the stone fell, we use the formula below.

Where:

Solving for S by substituting into equation 2

Hence, (a) The speed as the stone hits the ground is 29.4 m/s (b) The distance at which the stone fell is 44.1 m.

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Answer:

Kg to g we multiply by 1000

Explanation:

6.57×1000=6570g

Answer:

W = 1/2 k x^2           work done in extending a distance x

x = (2 W / k)^1/2 =  (2 * 50 N / 50 kn / m)^1/2

x = (.1 kn / 50 kn/m)^1/2 = .045 m

The length of the shortest curve would be √2.

The paraboloid x2 + y2 = z2 + 1 is a doubly ruled surface, which means, it can be swept out by a moving the line in space in two different ways.

So, then we have to verify the fact that the line defined by the two given points lies entirely on the surface of the paraboloid.

The vector valued function that describes the straight line connecting the points (1, 0, 0) and (1, 1, 1) is

r (t) = < 1, t, t >, t ∈ R

and it can be stated by inspection that this satisfies the equation of the paraboloid.

Thus, it is found that the length of the line segment connecting the points is √2

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The average amount of small-town teens with cell phones for the age groups 14, 15, and 16 would be 348 as the average is given by the total sum divided by the number of items.

Finding the product of two or more numbers in mathematics is done by multiplying the numbers.

As given in the problem we have to find out  the average amount of teens with cells for the age groups 14, 15, and 16,

The average number of teens with cells = (273 + 341 + 430) / 3

The average number of teens with cells = 1044/ 3

                                                                   =348

Thus, the average number of teens with cell phones for the age groups 14, 15, and 16 would be 348.

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The kinetic and potential energy of a harmonic oscillator in motion

d) are perfectly anti-correlated.

A restoring force in a harmonic oscillator works in the direction of an equilibrium point.

Simple harmonic motion, which we refer to as repetitive motion, is produced by the force.

The system's mechanical energy, which includes both potential and kinetic energy, is ideally constant.

In actuality, the energy is preserved by allowing one quantity to grow as the other shrinks, and vice versa.

An anti-correlation is a term that describes a negative correlation.

Kinetic energy and potential energy are two types of energy that are frequently found in mechanical systems and are referred to as mechanical energy in physics.

The idea of mechanical energy conservation is based on an even more general principle known as the law of conservation of energy; the only distinction is that in mechanical energy conservation, all of the system's energy is either in the form of kinetic energy, potential energy, or both.

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The output work done by the lever is 18.9 J.

Output work is the product of laod and the distance moved by load.

The S.I unit of output work is Joules (J).

To calculate the output work done by the lever, we use the formula below,

Formula:

Where:

Make W' the subject of the equation

From the question,

Given:

Substitute these values into equation 2

Hence, the output work done by the lever is 18.9 J.

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The properties of physical changes of matter include the following:

Physical change is a form of change that occurs in matter in which no new substances are formed.

Matter undergoes two types of changes:

Physical change is a change that affects or changes only the physical properties of a substance.

The physical properties of matter include the following:

During physical changes of matter, the following are observed:

Examples of physical changes include:

In conclusion, physical changes are changes which affect only the physical properties of a substance and in which no new substance is formed.

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The change in internal energy is -48 joule.

We need to know about internal energy to solve this problem. For a closed system, with matter transfer excluded, the changes in internal energy are due to heat transfer and due to thermodynamic work done by the system on its surroundings. It can be determined as

ΔU = Q - W

where ΔU is the change in internal energy, Q is heat and W is work done.

From the question above, we know that

W = 74 joule

Q = 26 joule

By substituting the given parameter, we can calculate the change in internal energy

ΔU = Q - W

ΔU = 26 - 74

ΔU = -48 joule

The internal energy change is negative because the work done on the system is greater than the heat released.

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The result of two or more vectors is the outcome.  it's the outcome of multiplying two or more vectors.  The resultant result of adding the displacement vectors A, B, and C are vector R. An appropriately drawn, scaled, vector addition diagram is often used to compute vector R, as illustrated within the diagram.

What do three resultant vectors add up to?

Afbeeldingsresultat for these vectors' offspring

The outcome of multiplying vectors A + B + C is the same as that of multiplying vectors B + A + C or even C + B + A.  The resultant result will be the same as long as all three vectors are present with the appropriate magnitude and direction. The resultant of two or more vectors is the outcome.

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If Jonathan walks 3 meters to the west, 2 meters south, 5 meters to the east, and 4 meters to the north, his displacement would be 2.8 meters.

The final position of Jonathan is 2 m exact North-East to the starting point. This forms a square. We need the diagonal of the square which is the displacement of Jonathan.

Diagonal of a square = a √ 2

a = Side of the square

a = 2 m

d = 2 √ 2

d = 2.8 m

Displacement is the distance between initial and final position whereas distance travelled is the total distance travelled throughout the given amount of time.

Therefore, Jonathan's displacement was 2.8 meters.

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We can select the cases in the order of selection matters 254,251,200

Permutation is the act of putting all the members of a set into a sequence or order in mathematics. In other words, if the set is already sorted, the act of reordering its pieces is known as permuting. Permutations may be found in practically every branch of mathematics, at varying degrees of prominence. They frequently appear when alternative orderings on finite sets are examined. The permutation formula is as follows.

nPr = ((n!) )/((n-r)!)

nPr = ((50!) )/((50-5)!)

nPr = ((50!) )/((45)!)

nPr = ((50*49*48*47*46*45)!)/((45)!)

nPr = 11441304000/45

nPr = 254,251,200

Therefore, there are 254,251,200 ways to select these cases if order of selection matters.

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The volume of gasoline with a density of 0.680 g/cm3 and a mass of  4,400 g is: 6,470.58 cm3

The density formula and the procedure we will use is:

d = m/v

Where:

Information about the problem:

Applying the density formula and clearing the volume we get:

d = m/v

v = m/ d

v = 4,400 g/0.680 g/cm3

v = 6,470.58 cm3

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

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It would decrease cardiac output, peripheral resistance, and blood volume.

Cardiac output (CO), the volume of blood the heart pumps each minute, is the mechanism through which blood circulates throughout the body, particularly supplying the brain and other crucial organs with blood flow. When exercising, for example, the body's need for oxygen fluctuates, and changing both heart rate (HR) and stroke volume affects cardiac output (SV).

As a result, a complicated mechanism combining the autonomic nervous system, endocrine, and paracrine signaling pathways is responsible for controlling cardiac output. Every tissue in the body depends on the heart to pump blood to it in order to survive, hence any cardiovascular failure could have a large negative impact on morbidity and mortality.

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The correct answer would be the first option. That means completely vaporizing 1 kg of saturated liquid water at 1 atm pressure would require more energy.

The enthalpy of vaporization, also known as the heat of vaporization or heat of evaporation, is the quantity of energy that must be added to a liquid substance in order to transform a quantity of that substance into a gas.

The enthalpy of vaporization decreases as the pressure increases, so it takes more energy to completely vaporize 1 kg of saturated liquid water at 1 atm than at 8 atm.

The enthalpy of vaporization depends on the pressure at which that transformation occurs.

40.65 kJ/mol

The heat of vaporization value for water is 40.65 kJ/mol.

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The  nominal interest rate is being charged is 19.56 %

Interest bearing financial instruments state the rate of interest they pay. this is often the nominal interest rate. The effective rate of interest , on the opposite hand, accounts for the rate of interest compounding effect, thus, it's the actual interest rate an instrument pays during a given period (often a year).

18% is the nominal annual interest rate.

The monthly interest rate is 1.5%. Hence, the nominal interest rate in a year (12 months) is 18% = 12 x 1.5%.

19.56% is the (annual) effective interest rate (EIR).

EIR = ( 1+( r / n))ⁿ − 1, such as r is the annual interest rate and n is the number of periods.

Here, n = 12 and ( r/ n ) = .015  or 1.5%. Therefore,

EIR =( 1 + .015 ) 12 − 1 = .1956  or 19.56%.

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To connect the wires in a 110 block and trim off the excess at the same time, use a punch down tool with a notched blade and point the cut side of the tool towards the wire end.

A 110 block is used to terminate wiring in a cabling system. It is a type of punch down block. This block has a plastic base and have 50 slots for individual wires, meaning it can terminate 25 pairs.

A punch down tool is used insert wire into insulation displacement connectors present in punch down blocks such as 110 block and also in other electrical panels and modules.

Therefore, to connect the wires in a 110 block and trim off the excess at the same time, use a punch down tool with a notched blade and point the cut side of the tool towards the wire end.

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To reach a height of 12.0 feet with an angle of 45° the animal must leave the ground with a velocity of: 39.295 ft/s

The formulas for projectile motion that we will use to solve this exercise is:

h max = [vi² * (sinθ)²] / (2*g)

Where:

Information about the problem:

Applying the maximum height formula an clearing the initial velocity we have:

h max = (vi² * (senθ)²) / (2*g)

vi= √ [(h max * 2 * g) / (senθ)²]

vi= √ [12 ft * 2 * 32.17 ft/s² ) / (sen 45º)²]

vi= √ [772.08 ft²/s² / 0.5]

vi= √1544.16 ft²/s²

vi = 39.295 ft/s

The projectile motion is the motion whose trajectory describes a parabola having a horizontal and a vertical component of motion.

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230km far does it travel during 14.2 minutes.

A car travels straight down a highway with cruise control set to = 100 km/h

how far does it travel during 14.2 minutes

so, now we use

Distance = velocity [tex]\times[/tex] time

1 min = 1/60 hour

14.2 min = 14.2 / 60 hour

= 0.23 hour

now,

Distance = 1000[tex]\times[/tex]0.23 km

= 230km

so.  230km  it travel in 14.2 minutes

Distance is the length of the path between two points. and it's standard unit is meter while displacement is shortest distance between final position and initial position and it also has meter as a standard unit.

written as m.

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The desired outcomes for standard variation are;

a. [tex]P(X < 860) = P(z < -2.80) = 0.0026 = 0.26%[/tex]

b.[tex]P(1055x1100) = P(z2.00-z1.10) = 0.9772-0.8643 = 0.1129 = 11.29%[/tex]

c.[tex]86.17%[/tex]% if [tex]P(860 X 1055) = P(z 1.10) - P(z -2.80) = 0.8643 - 0.0026[/tex]

You will need the probabilities P(X 860), P(X 1055) and P(X 1100) from the cumulative normal probability distribution for the variable X in order to calculate these values (the weight of a can of pears, in this case).

The straightforward approach is to use the connection to reduce the required values of X to the reduced parameter z instead of laboriously deriving this information from the equation for this distribution and the given values for its mean and standard deviation.

z = (X - μ)/σ

which results in X = 860 z = -2.80, X = 1055 z = +1.10, and X = 1100 z = +2.00 in this instance.

You then check a public table for the cumulative standard normal distribution for the fractional probability for the necessary z values.

- To the tabular value P, add 0.5 for positive z. (z)

- To account for negative z, deduct from 0.5 the P(z) value that corresponds to positive z.

[tex]P(z) = 0.4974 for z = 2.80,[/tex] which means that,[tex]P(z -2.80) = 0.5 - 0.4974 = 0.0026.[/tex]

[tex]P(z) = 0.3643[/tex] and [tex]P(z 1.10) = 0.3643 + 0.5 = 0.8643[/tex]                                      for [tex]z = 1.10[/tex] respectively

[tex]P(z) = 0.4772[/tex] and [tex]P(z 2.00) = 0.4772 + 0.5 = 0.9772[/tex]                                     for [tex]z = 2.00.[/tex]

Finally, we can get the desired outcomes.

a. [tex]P(X < 860) = P(z < -2.80) = 0.0026 = 0.26%[/tex]

b.[tex]P(1055x1100) = P(z2.00-z1.10) = 0.9772-0.8643 = 0.1129 = 11.29%[/tex]

c.[tex]86.17%[/tex]% if [tex]P(860 X 1055) = P(z 1.10) - P(z -2.80) = 0.8643 - 0.0026[/tex]

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To launch a 100 kg human at the given speed, the spring constant needed is 400 N/m.

This is the ratio of applied force on a spring to the extension produced  by the spring.

The spring constant of the spring is calculated by applying the principle of conservation of energy.

The elastic potential energy of the spring will be converted into kinetic energy of the human so that the human will be launched at the desired speed.

U = K.E

¹/₂kx² = ¹/₂mv²

k = mv²/x²

where;

Substitute the given parameters and solve for the spring constant.

k = (100x 4²) / (2²)

k = 400 N/m

Thus, a spring constant of  400 N/m is need to maintain the law of conservation of energy, from elastic potential energy of the spring to kinetic energy of the human,

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The calculated final velocity is Vf = 4.77 m/s

When gravity first exerts force on an object, its initial velocity defines how quickly the object moves. The final velocity, on the other hand, is a vector number that gauges a moving body's speed and direction after it has reached its maximum acceleration. By applying the third equation of motion during the downward motion, we can quickly determine the final velocity or the velocity at which the ball reaches the ground. Following is the third equation of motion:

Where g = the acceleration of gravity = 9.8 m/s², h = the height = 1.16 m, and Vf = the final velocity of the ball =?

Vi = Ball's Initial Velocity = 0 m/s (Since the ball was at rest initially)

As a result, when we use these values in the equation, we obtain:

(2) Vf2 = (9.8 m/s²) (1.16 m) - (0 m/s)

Vf = 4.77 m/s

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Answer: No, they cannot

Explanation:

Because every individual has different emotions, different beliefs.

No. this is not true for a spherical capacitor.

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Answer:Доброе утро, отв

Explanation:

Доброе утро, отвДоброе утро, ответт

The differentiated equation for the triangle in the middle as per the Pythagorean rule appears to be as db = dl = -h/b dh = -h/bx

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in familiar algebraic notation, a2 + b2, are equal to the squares on the legs.

Book I, Proposition 47, that is also known as I 47 or Euclid I 47, was mentioned and demonstrated for the first time by Euclid. Among all the Pythagorean proposition proofs, this one is arguably the most well-known.

By applying Pythagoras Theorem,

h^2/4 + b^2/4 = a^2

⇒ h^2 + b^2 = 4a^2

Then differentiating the equation, we have

2hdh + 2bdb = 0 (da = 0)

So db = dl = -h/b dh = -h/b x

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The work done on a 50 Kg student by the elevator in 2 seconds if the elevator is accelerating upwards from rest at a rate of 2 ms⁻² would be

The total amount of energy transferred when a force is applied to move an object through some distance.

The work done is the multiplication of applied force with displacement.

Work Done = Force × Displacement

As given in the problem we have to find the work done  on a 50 Kg student by the elevator in 2 seconds if the elevator is  accelerating upwards from rest at a rate of 2 ms⁻²,

Lets us first calculate the displacement of the elevator in 2 seconds if it is accelerating upwards from rest at a rate of 2 ms⁻².

s = ut + 0.5at²

  = 0 + 0.5×2×2²

  = 4 meters

The work done on the elevator = mgh

                                                    =50×9.81×4

                                                    =1962 joules

Thus, the work done on the elevator would be 1962 joules.

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It is needed to connect seven solar panels in series to get 3.5 volts.

We need to know about the power supply circuit to solve this problem. When the power supply are connected in series, the total voltage is added up. It can be written as

V = V1 + V2 + .... + Vn

From the question above, we know that

V = 3.5 volt

Veach = 0.5 volt

Hence, we can calculate how many solar cells connected in series

V = V1 + V2 + .... + Vn

3.5 = 0.5(n)

n = 3.5 / 0.5

n = 7

Thus, we need to connect seven solar panels in series to get 3.5 volt.

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  The value of the resultant force and its direction is Fr = 8.03 kN; Ф = 1.22°

  Forces are the definition of Newton's second law, which is stated under the relation:

∑ Force = mass × acceleration.

 In other words, force is the origin of motion since it generates acceleration in a system.

   We will use the parallelogram method to determine the magnitude of the resultant force, as follows:

Fr = √F2² + F1² - 2(F2×F1)Cos105°

Fr = √6² + 4² - 2(6×4)Cos105°

Fr = 8.03 kN

  We apply the law of sines

Sen∅/6 = Sen105°/8.026

∅ = 46.22°

   The Ф direction of Fr measured clockwise from the positive u-axis is

Ф = 46.22° - 45°

Ф = 1.22°

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Answer : Natural

Explanation : Natural resources are the resources that are found in the environment and are developed without the intervention of humans