The half life of Po-218 is three minutes. How much of a 2.0 gram sample remains after 15 minutes? Suppose you wanted to buy some of this isotope, and it required half an hour for it to reach you. How much should you order if you needed to use 0.10 gram of this material?

Answer: s(5) = -200,  v(5) = -90

              s(10) = -900, v(10) = -190

Explanation:

Position: s(t)

Velocity:  s'(t) = v(t)                ⇒      \(s(t)=\int {v(t)} \, dt\)

Acceleration     v'(t) = a(t)      ⇒      \(v(t)=\int {a(t)} \, dt\)

We are given that acceleration a(t) = -20   and velocity v(t) = 10

\(v(t)=\int {a(t)} \, dt\\\\v(t)=\int{-20}\, dt\\\\v(t)=-20t + C \\\\v(t)=10\quad \longrightarrow \quad C=10\\\\v(t)=-20t+10\)

\(s(t)=\int {v(t)} \, dt\\\\s(t)=\int {(-20t+10)} \, dt\\\\s(t)=-10t^2+10t\\\\\)

(a) Input t = 5 into the s(t) and v(t) equations

   s(5) = -10(5)² + 10(5)           v(5) = -20(5) + 10

          =  -250  +  50                     = -100   +  10

          =       -200                          =        -90

(b) Input t = 10 into the s(t) and v(t) equations

     s(10) = -10(10)² + 10(10)           v(10) = -20(10) + 10

            =  -1000  +  100                     = -200   +  10

            =       -900                          =        -190

The Hertzsprung-Russell diagram plots stars according to:   the colour of stars (or spectral type) against their absolute magnitude (the observational HR diagram, also known as a colour-magnitude diagram) or the temperature of stars against their luminosity (the theoretical HR diagram).

The Hertzsprung-Russell diagram, also known as the HR diagram, HRD, or H-R diagram, is a scatter plot of stars that illustrates the correlation between the stars' absolute magnitudes or luminosities and their stellar classifications or effective temperatures.

The diagram, which was independently produced in 1911 by Ejnar Hertzsprung and in 1913 by Henry Norris Russell, marked a significant advancement in our understanding of star evolution.

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Newton's Second Law of Motion states "The rate of change of momentum of a body is directly proportional to the applied unbalanced force in the direction of force".

The statement "They have a positive charge and are present in the nucleus of an atom along with the neutrons" correctly describes protons.

Protons are small particles that make up the nucleus of an atom. They carry a positive charge and have a mass of approximately 1 atomic mass unit. The number of protons within an atom's nucleus defines its atomic number and thus its identity as an element.

For instance, carbon atoms have 6 protons, and oxygen atoms have 8 protons. Protons are vital building blocks of all atoms and play a significant role in the chemical behavior and reactions of elements.

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Answer:

Explanation:

I think that you to run more than 12 miles

The kinetic energy ratio of second object to the first object is 4 : 1

We need to know about kinetic energy to solve this problem. Kinetic energy depends on the mass of the object and the speed of the object. It can be defined as

KE = 1/2 . m .v²

where KE is kinetic energy, m is the mass of the object and v is the velocity.

From the question above, we know that:

m1 = 500 kg

m2 = 2000 kg

v1 = v2 = v

The kinetic energy of the first object is

KE1 = 1/2 . m1 .v²

KE1 = 1/2 . 500 . v²

KE1 = 250v²

The kinetic energy of the second object is

KE2 = 1/2 . m1 .v²

KE2 = 1/2 . 2000 . v²

KE2 = 1000v²

Hence, the ratio of KE2 to KE1 is

KE2 / KE1 = 1000v² / 250v²

KE2 / KE1 = 4 : 1

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An electric current produces a (c) magnetic field.

When an electric current flows through a conductor, it generates a magnetic field around the conductor. This relationship between electric current and magnetic fields is described by Ampere's law and is the basis for electromagnetism.

current is the rate at which the charge pases through an electric conductor in a circuit.

formula: I = Q/t

 where I is current, Q is charge and t is the time period.

An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface.[1]: 2 [2]: 622  The moving particles are called charge carriers, which may be one of several types of particles, depending on the conductor.

In electric circuits the charge carriers are often electrons moving through a wire. In semiconductors they can be electrons or holes. In an electrolyte the charge carriers are ions, while in plasma, an ionized gas, they are ions and electrons.

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26.0 mL of water were initially present in the graduated cylinder. The water level in the cylinder was 39.0 mL after inserting an object.

Volume is the three-dimensional space inhabited by matter or encompassed by a surface, and it is expressed in cubic units. The SI unit of capacity is the cubic meter (m3), which is a derived unit.

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Answer:

they are gas giants. they are much much more bigger then terrestrial

False. Velocity is a vector and is measured in m/s (in SI, anyway).

Answer:

The correct option is (a)

Explanation:

Impulse is given by the product of force and time. It is denoted by J. So,

\(J=F\times t\)

or

\(F=\dfrac{J}{t}\)

It can be seen that the relation between the force and the impact time is inverse. Hence, the impact force and impact time possess inverse relation.  

Answer:

I am pretty sure that it is one

Answer:

Explanation: is 1

The calculated average rate of motion for the Pacific Plate, given the measured Kilauea-Midway distance and the ages of the volcanoes, is [insert calculated value] kilometers per million years, rounded to the nearest 0.1 km/my.

By utilizing the measured distance between Kilauea and Midway, along with the ages of the volcanoes, it is possible to determine the average rate of motion for the Pacific Plate. The calculation involves dividing the distance traveled by the plate by the time elapsed, and expressing the result in kilometers per million years (km/my).

The measured distance between Kilauea and Midway provides an indication of the plate's displacement over a certain time period. By considering the age difference between the two volcanoes, it becomes possible to estimate the time it took for the Pacific Plate to move that distance. Dividing the distance by the time yields the average rate of motion for the plate.

This average rate of motion provides valuable insights into the tectonic activity and dynamics of the Pacific Plate. It allows scientists to study the plate's movement over geologic timescales and gain a better understanding of plate tectonics and Earth's overall geology.

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Polaris, which is the tip of the handle of the Little Dipper or the tail of the little bear in the constellation Ursa Minor, is indicated by the two stars at the end of the Dipper's "cup."

Polaris, the North or Pole Star, is by far the most important and well-known star in Ursa Minor. The star at the very end of the bear's lengthy tail is this. Polaris is significant because it is practically immediately over the North Pole. This means you can use it as a compass to locate your way north.

The Indian name for the constellation Ursa Minor is Laghu Saptharishi where 'Laghu' means 'Small'. The name is sequential with the name Saptharishi for the constellation Ursa Major.The Ursa Minor Dwarf is a dwarf spheroidal galaxy discovered during the Palomar Sky Survey in 1955 by A.G. Wilson of the Lowell Observatory in the United States. It is a Milky Way satellite galaxy that may be found in the constellation Ursa Minor.

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Milliliters (ml) or cubic millimetres are the most suitable units for calculating a raindrop's volume (mm3).

Raindrops are quite tiny and usually have volumes between 0.1 and 0.5 millilitres. Small, precise volume measures like millilitres or cubic millimetres are ideal for measuring these volumes.

A raindrop's volume can change depending on its size and form, as well as external conditions like air pressure and temperature.

For measuring the volume of a single raindrop, units of volume such as litres or cubic metres are too vast and would not offer sufficient precision. Thus, the units that are best suited for measuring the volume of a raindrop are millilitres or cubic millimetres.

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Given:

The time period for which Nora rides the bicycle, t=5 min

The speed of the bicycle, s=10 m/s

To find:

The description of the ride.

Explanation:

The speed is a scalar quantity and has only magnitude. The velocity and acceleration are vector quantities and have magnitude and direction.

When the bicycle is traveling on a curved path at a constant speed, there will be an acceleration acting on it which keeps it on its path. This acceleration is called the centripetal acceleration.

The centripetal acceleration changes only the direction of the velocity and not the magnitude. Thus the speed will be constant. But the velocity will be changing at a constant acceleration.

According to the question, the critical angle for total internal reflection within the water is 48.9 degrees.

Reflection is a process of thinking deeply and critically about a particular topic or experience. It is a way to gain deeper understanding and create connections between the past and the present. Reflection is often used to help people make sense of their own experiences and to gain insight into the impact of their actions. Reflection can also be used as a way to make sense of the world around us, to gain insight into different perspectives, and to develop empathy for people from different backgrounds.

In this case, the incident medium is water and the refracting medium is glass. Therefore, we can solve for the angle of incidence (θi) using the following equation: sin θi = (1.50/1.33) × sin θr

where θr is the angle of refraction in the glass. Since θr is 90 degrees when total internal reflection occurs, the critical angle for total internal reflection in water is:

θi = sin-1((1.50/1.33) × sin 90) = 48.9 degrees

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Dimensionally F=Gm/r² is real .

Newton’s Law of Gravitation is an important formula in physics. It states that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.

The formula for gravitational force is F = Gm₁m₂/r², where F is the force, m₁ and m₂ are the masses of the two objects, r is the distance between the two objects, and G is the gravitational constant. The dimensional analysis of the given equation is given below: Gravitational constant G: Its units are N m² kg⁻². Distance or radius r: Its units are meters (m)

Mass m: Its units are kilograms (kg)Force F: Its units are newtons (N)

Dimensional formula of force F = [MLT⁻²]

Putting the units of the given terms into the equation F=Gm/r², we get the following:

\($$F=\frac{Nm^2/kg^2*kg}{m^2}$$\)

\($$F=\frac{Nm^2}{kg^2}$$\)

Therefore, dimensionally F=Gm/r² is real.

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To find the couple moment acting on the block, we can use the formula:

Couple Moment = Force * Perpendicular Distance

Perpendicular Distance (l1) = l1 * sin(θ) = 9 m * sin(25°) ≈ 3.75 m

Similarly, the perpendicular distance associated with l2 is given by:

Perpendicular Distance (l2) = l2 * sin(θ) = 7 m * sin(25°) ≈ 2.92 m

First, we need to determine the perpendicular distance between the line of action of the force and the axis of rotation. In this case, we have two distances: l1 and l2.

Using trigonometry, we can find the perpendicular distance associated with l1 by calculating l1 * sin(θ):

Perpendicular Distance (l1) = l1 * sin(θ) = 9 m * sin(25°) ≈ 3.75 m

Similarly, the perpendicular distance associated with l2 is given by:

Perpendicular Distance (l2) = l2 * sin(θ) = 7 m * sin(25°) ≈ 2.92 m

Now we can calculate the couple moment for each distance:

Couple Moment (l1) = Force * Perpendicular Distance (l1) = 95 N * 3.75 m ≈ 356.25 Nm

Couple Moment (l2) = Force * Perpendicular Distance (l2) = 95 N * 2.92 m ≈ 277.4 Nm

The total couple moment acting on the block is the sum of these two individual moments:

Total Couple Moment = Couple Moment (l1) + Couple Moment (l2)

≈ 356.25 Nm + 277.4 Nm

≈ 633.65 Nm

Therefore, the couple moment acting on the block is approximately 633.65 Nm.

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Answer:

The efficiency of the Bluetooth speaker is 62.13 %.

Explanation:

Given;

input electrical energy of the Bluetooth speaker, = 573 J

output sound energy of the Bluetooth speaker, = 356 J

The efficiency of the Bluetooth speaker in transforming electrical energy into sound energy is given by;

\(Efficiency = \frac{0utput\ Energy}{1nput \ Energy} *100\% \\\\Efficiency = \frac{356}{573}*100 \% \\\\Efficiency = 62.13 \ \%\)

Therefore, the efficiency of the Bluetooth speaker is 62.13 %.

Answer:

cluttered

Explanation:

The correct word to describe the garage would be cluttered.

A place is said to be cluttered when it is filled with an untidy collection of material things. In this case, the garage is filled with materials such as bike wrenches, tires, frames, etc.

Inviting can also mean tempting, attractive, etc, and has no relevance to the condition of the garage as described in the excerpt.

Dangerous can also mean harmful, and not the right word to describe the garage.

Sparse can also mean scanty, scattered, and would be the opposite of the condition of the garage.

Correct answer: cluttered

Answer:

c.  cluttered

Explanation:

Answer:

C

Explanation:

a series circuit would be an odd choice to power a battery or light a lamp when a direct would be much more efficient, and it's not converting types of energy, so C is the best possible answer

The speed of the melon as it flies off the performer's head is 0.3 m/s

The law of conservation of momentum states that for a system of colliding bodies, the total momentum before the collision is equal to the total momentum after the collision, provided there is no net external force acting on the bodies.

To find the speed of the melon, we use the formula from the law of conservation of momentum.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, The speed of the melon as it flies off the performer's head is 0.3 m/s.

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Answer:

The correct option is C) III. That is, the trout will suffer from disease.

Explanation:

Note: This question is not complete as the options are not included. The complete question with the options is therefore provided before answering the question as follows:

A lake is home to a large number of trout. Identify what is most likely to happen if a chemical is dumped into the lake.

I. The trout will not be affected by the pollution.

II. The number of trout will increase.

III. The trout will suffer from disease.

A) I

B) I and II

C) III

D) II and III

The explanation of the answer is now provided as follows:

Natural selection is the process that took place in the lake. Only those trouts that were fit to survive, or those that have alleles that allow them adapt to new conditions, live and multiply in the presence of an external environmental effect like pollution. In such a circumstance, the fittest organisms would have survived, and the population's allelic frequency would have grown through time. Due to pollution, creatures harboring the other alleles died, causing the total frequency of alleles to alter.

Therefore, the correct option is C) III. That is, the trout will suffer from disease.

Answer:

Below

Explanation:

384 400 km / 300 000 km/s = 1.28 seconds

Answer:

The work done on the hose by the time the hose reaches its relaxed length is 776.16 Joules

Explanation:

The given spring constant of the of the spring, k = 88.0 N/m

The length by which the hose is stretched, x = 4.20 m

For the hose that obeys Hooke's law, and the principle of conservation of energy, the work done by the force from the hose is equal to the potential energy given to the hose

The elastic potential energy, P.E., of a compressed spring is given as follows;

P.E. = 1/2·k·x²

∴ The potential energy given to hose, P.E. = 1/2 × 88.0 N/m × (4.20 m)²

1/2 × 88.0 N/m × (4.20 m)² = 776.16 J

The work done on the hose = The potential energy given to hose, P.E. = 776.16 J

Answer:

\(\huge\boxed{10\:watts}\)

Explanation:

Power = Current × Voltage

P = I × V

P = 2 × 5

P = 10 watts

Answer:

6.0 m/s vertical and 9.0 m/s horizontal

Explanation:

For the vertical component, we use the formula:

Then we solve for y:

And for the horizontal component, we use the formula:

Then we solve for x:

So the answer is " 6.0 m/s vertical and 9.0 m/s horizontal".

The components of an electrical circuit represented by the model are as follows:

The figure models resistance in a circuit because just as resistance in a circuit opposes the flow of current, the load resists the movement of the man.

An electrical circuit is a complete path that is provided for the flow of electric current.

Tue components of an electric circuit includes:

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