A + 9.12 nC point charge and a - 2.78 nC point charge are 4.99 cm apart. What is the electric field strength at the midpoint between the two charges?

It would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

1. The decay rate of a radioactive isotope is proportional to the number of radioactive atoms present in the sample at any given time.

2. The decay rate can be expressed as a function of time using the formula: R(t) = R₀ * \(e^{(-\lambda t\)), where R(t) is the decay rate at time t, R₀ is the initial decay rate, λ is the decay constant, and e is the base of the natural logarithm.

3. The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms in a sample to decay. In this case, the half-life is given as 210 days.

4. Using the half-life, we can find the decay constant (λ) using the formula: λ = ln(2) / T₁/₂, where ln(2) is the natural logarithm of 2 and T₁/₂ is the half-life.

5. Substituting the given half-life into the formula, we have: λ = ln(2) / 210.

6. Now, we need to find the time it takes for the decay rate to fall to 0.58 of its initial rate. Let's call this time "t".

7. Using the formula for the decay rate, we can write: 0.58 * R₀ = R₀ * e^(-λt).

8. Simplifying the equation, we get: 0.58 = \(e^{(-\lambda t\)).

9. Taking the natural logarithm of both sides, we have: ln(0.58) = -λt.

10. Substituting the value of λ from step 5, we get: ln(0.58) = -(ln(2) / 210) * t.

11. Solving for t, we have: t = (ln(0.58) * 210) / ln(2).

12. Evaluating the expression, we find: t ≈ 546.

13. Therefore, it would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

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-200 N

Explanation

Step 1

we can see that on the object are acting vertical forces, if we assume the y-positive axis as positive ( upwards) then we have

therefore, the answer is -200

Answer:

Lost Mechanical Power = 7.7565 KW

Head Loss = 26.35 m

Explanation:

First, we will find the useful mechanical power used to transport water to the higher reservoir:

\(P_{useful} = \rho ghV\)

where,

P_useful = Useful mechanical Power = ?

ρ = density of water = 1000 kg/m³

g = acceleration due to gravity = 9.81 m/s²

h = height = 45 m

V = Volume flow rate = 0.03 m³/s

Therefore,

\(P_{useful} = (1000\ kg/m^3)(9.81\ m/s^2)(45\ m)(0.03\ m^3/s)\\P_{useful} = 13243.5\ W = 13.2435\ KW\)

Now, the lost mechanical power will be:

\(Lost\ Mechanical\ Power = Total\ Mechanical\ Power - Useful\ power\\Lost\ Mechanical\ Power = 21\ KW - 13.2435\ KW\\\)

Lost Mechanical Power = 7.7565 KW

Now, for the head loss:

\(Lost\ Mechanical\ Power = \rho g(Head\ Loss)V\\Head\ Loss = \frac{Lost\ Mechanical\ Power}{\rho gV} \\\\Head\ Loss = \frac{7756.5\ W}{(1000\ kg/m^3)(9.81\ m/s^2)(0.03\ m^3/s)} \\\)

Head Loss = 26.35 m

8.3 m/s is the terminal velocity of the squirrel can be calculated using the equation for terminal velocity and 10.8 m/s is the velocity of a 50.0 kg person hitting the ground.

What is velocity?
Velocity is a measure of the speed of an object's motion in a particular direction. It is a vector quantity, meaning it has both magnitude and direction. Velocity is usually measured in meters per second (m/s).

The terminal velocity of the squirrel can be calculated using the equation for terminal velocity of an object in a fluid, which is given by Vt = (2×m×g)/(ρ×Cd×A). Here, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the fluid, Cd is the drag coefficient, and A is the reference area of the object. The drag coefficient for a horizontal skydiver is 0.8, and the density of air is 1.225 kg/m^3. Therefore, the terminal velocity of the squirrel can be calculated as Vt = (2×500×9.8)/(1.225×0.8×895) = 8.3 m/s.

The velocity of a 50.0 kg person hitting the ground can be calculated using the equation for the velocity at the end of a fall, which is given by Vf = sqrt(2×g×h). Here, g is the acceleration due to gravity and h is the height of the fall. Therefore, the velocity of the person hitting the ground can be calculated as Vf = sqrt(2×9.8×5.6) = 10.8 m/s.

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\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

Gravitational Potential of an object with mass m, and height of h metre is :

\(\qquad \sf  \dashrightarrow \:mgh\)

Now, if the mass of object is 2100 kg, height of 18 m is placed in there, then it's gravitational potential energy is ~

\(\qquad \sf  \dashrightarrow \:2100 \times 10 \times 18\)

\(\qquad \sf  \dashrightarrow \:378000 \: \: joules\)

\(\qquad \sf  \dashrightarrow \:3.78 \times 10 {}^{5} \: \: joules\)

The crane weighs 441 N. The horizontal component of the normal force at an angle of 35° is 361 N.

Force is physical quantity generating a displacement or deformation for a body. Force is having a magnitude and direction thus, it is a vector quantity.

The normal force acting on a body is mg, that is the product of its mass and acceleration due to gravity. Force can have a vertical and horizontal component.

vertical component of normal force  = N sin ∅

horizontal component = N cos  ∅.

Given the angle in the inclined plane is 35°  in horizontal direction.

Thus normal force = 441 N × cos 35°  = 361 N.

Therefore, the magnitude of normal force acting on the crane is 361 N.

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Answer:

What Is Moral Subjectivism? Moral subjectivism is based on an individual person's perspective of what is right or wrong. An individual can decide for themselves that they approve or disapprove of a certain behavior, and that is what determines if the behavior is right or wrong.

Answer:

20*365=7300

Explanation:

1 Year=365day

20years = x days

Answer:

B

Explanation:

Monucles work in different shapes

Answer:

2.1x10^6m/s

Explanation:

One electron has a charge of –1.602e-19 C

mass of electron is 9.1e-31 kg

mass of proton is 1.6726e−27 kg

mass ratio is 1.6726e−27 / 9.1e-31 = 1838

The force is constant, F

distance is constant, d

a = F/m

a increases by a factor 1838, as m decreases by that factor

a = a₀1838

v₀² = 2a₀d

v² = 2a₀d1838

v²/v₀² = 2a₀d1838 / 2a₀d = 1838

v² = 1838v₀² = 1838(45000)²

v = 45000√1838 = 2.1e6 m/s

Answer:a vertical expanse of water stretching between the surface and the floor of a body of water

Explanation:

9\(\^{i}\)+8\(\^{j}\)/\(\sqrt{136}\)

F=(9.00i-8.00j)N

we are now to find the unit vector

according to formula

unit vector = \(\frac{vector of F}{Magnitude of F}\)

Now :

vector form of F = 9\(\^{i}\)+8\(\^{j}\)

magnitude of F =\(\sqrt{9^2+8^2}\)

magnitude of F=\(\sqrt{136}\)

now put that in formual

unit vector = 9\(\^{i}\)+8\(\^{j}\)/\(\sqrt{136}\)

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Answer:

The boiling point of nitrogen on the absolute temperature scale is 77.15 K

Explanation:

Temperature in Kelvin(Absolute temperature) = Temperature in Celcius + 273.15.

Answer: Radiation

Explanation:

Radiation refers to the transfer of heat from one source to another material. The transfer of heat energy from the sun to the earth is called radiation. The grilling of the hamburgers is an example of the radiation as in grilling no direct heat is involved instead the radiations or flames beneath the grilling barbeque burn or grill the hamburgers. Fumes or flames of a charcoal transfer radiations to the grilling hamburgers.

Answer:

Here you go, hope this helps! :)

Explanation:

Opportunity cost is the value of the next best thing you give up whenever you make a decision. It is "the loss of potential gain from other alternatives when one alternative is chosen". ... For example, opportunity cost is how much leisure time we give up to work.

The electric field at point B, located at the midpoint between the upper left and right corners of the square, can be approximated as 3.244 x \(10^6\) N/C in the upward direction.

To find the electric field at point B, we can consider the contributions from the two charges placed at the lower corners of the square. Since the charges are the same and the distance to point B is the same for both charges, the magnitudes of the electric fields produced by each charge will be equal.

First, let's calculate the magnitude of the electric field produced by one of the charges at point B using Coulomb's Law:

Electric field due to a point charge (E) = (k * q) / \(r^2\)

Where:

- k is the electrostatic constant, approximately equal to 8.99 x 10^9 \(10^9\)N \(m^2/C^2\)

- q is the charge of the object, 7.25 μC (7.25 x \(10^-^6\) C)

- r is the distance from the charge to point B, which is half the length of the square's side, 0.201 m / 2 = 0.1005 m

Plugging in the values, we have:

E = (8.99 x \(10^9 N m^2/C^2\) * 7.25 x \(10^-^6\) C) / (0.1005 \(m)^2\)

E ≈ 1.622 x \(10^6\) N/C

Since the electric fields from the two charges at the lower corners have equal magnitudes and point in the same direction (upward), the total electric field at point B is twice the magnitude of the individual electric field:

Electric field at point B = 2 * E ≈ 2 * 1.622 x \(10^6\) N/C

Electric field at point B ≈ 3.244 x \(10^6\) N/C

Therefore, the electric field at point B, midway between the upper left and right corners of the square, is approximately 3.244 x \(10^6\)N/C upward.

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As the distance between the parallel plates increases, the voltage between  them increases leading to an increase in charge. Hence option  C is correct.

Capacitance of an object is its ability to store electrical charge. The devices able to store massive charge for longer times are called capacitors. The unit of capacitance is faraday.

The relation between charge Q, potential difference v and the capacitance c of a parallel plate capacitance is:

Q = CV.

Here V = Ed.

where d is the distance between the plates of capacitor and E be the magnitude of electric field. Hence, as the voltage increases, capacitance decreases and charge increases. Therefore option c is correct.

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The statements that apply are;

We know that the pressure can be taken as the force with which the molecules of the substance are able to hit the walls of the container in this case, we need to obtain the  pressure of the ethanol vapor when the volume has been reduced.

Using

P1 = initial pressure

P2 = final pressure

V 1 = initial volume

V2 = final volume

By the use of the Boyle's law we have;

P1V1 = P2V2

P2 = P1V1 /V2

P2 = 67.0 * 529/344

P2 = 103 mmHg

Thus, as the volume is reduced there would be an increase in the pressure and some of the ethanol would condense and we would have liquid ethanol in the system.

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Answer:

Explanation:

\(a_{x}=0\) \(v_{xo}= v_{o}cos(delta)t\) \(a_{y}=-g\) \(v_{yo}=sin\)θ

X-direction                                     | Y-direction

\(x=x_o+v_{xo}t\) ⇒ \(x=v_{xo}cos(delta)t\) |

Your weight at the top of the ladder would be one-quarter of its normal value. The correct option is C.

The gravitational pull of the Earth, denoted by g, is the net acceleration imparted to objects by the combined effect of gravitation and centrifugal force. It is a vector quantity whose direction corresponds to a plumb bob and whose strength or magnitude is determined by the norm.

The formula for gravity is,

g = GM / R²

g = 1 / R²

gt = 1 / (2R)²

gt / g = R² / 4R²

gt = 1 / 4g

Therefore, at the top of the ladder, your weight would be one-quarter of its normal value.

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Answer:

Option B, Geiger counter

Explanation:

Option D

The law of conservation of charge states that the amount of charge in a system is constant

This means that as time changes, the amount of charge in a system does not change

By careful consideration of the options stated:

Each of options A to C either shows that charge is lost or gained

Only option D typifies the law of conservation of conservation of charges because charges are not lost or gained by the ballon so described.

Answer:

The correct answer is "\(4.49\times 10^{10} \ joules\)".

Explanation:

According to the question,

The work will be:

⇒ \(Work=-\frac{kQq}{R}\)

              \(=-\frac{1}{4 \pi \varepsilon \times (18-30)\times 3\times 0.2}\)

              \(=-\frac{1}{4 \pi \varepsilon \times (-12)\times 3\times 0.2}\)

              \(=\frac{0.3978}{\varepsilon }\)

              \(=4.49\times 10^{10} \ joules\)

Thus the above is the correct answer.    

We have that the workdone  is mathematically given as

W=4.49*10e10 J

From the question we are told

Generally the equation for the workdone   is mathematically given as

W=-kQq/R

Therefore

0.3978/ε0 =-1/(4πε0*(18-30)*3*0.2

Hence

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Answer:

18 m/s

Explanation:

Range of a projectile on level ground is:

R = v₀² sin(2θ) / g

14.3 m = v₀² sin(2×13°) / 9.8 m/s²

v₀ = 17.9 m/s

Rounded to two significant figures, the launch speed was 18 m/s.

If the bullet is launched at an angle of 50 degrees above ground level, the target will be struck. The angle remains the same. The launch angle obtained is 50 degrees.

Given:

The initial shot was fired at an angle of 50 degrees above ground.

The projectile's starting velocity (v) and magnitude of velocity will remain constant if it is shot at the same pace.

Let the angle of the projectile is x,

The horizontal component of velocity can be calculated as follows:

\(v(x) = v * cos(x)\)

We can write:

since the horizontal part of velocity remains constant:

\(v(x1) = v(x2)\)

\(cos(50) = cos(x)\)

\(50 = x\)

Therefore, if the projectile is launched at the same speed at a 50° angle above ground level, it will strike the target.

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The correct response is given when the angle is asked a question.

Acceleration is the rate of change of velocity as a function of time. For example a car traveling at 50 km/hr starts to accelerate, 10 seconds after, its speed changes to 100 km/hr then the acceleration of the car during the time can be calculated as below: initial speed = 50 km/hr.

The wavelength of this radio signal is equal to 3.18 meters.

Given the following data:

Wavelength can be defined as the distance between two (2) successive crests (troughs) of a wave.

Mathematically, the wavelength of a wave is given by this formula:

\(\lambda = \frac{V}{F}\)

Where:

Substituting the given parameters into the formula, we have;

\(\lambda = \frac{3 \times 10^8}{9.45 \times10^7}\)

Wavelength = 3.18 meters.

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The wavelength of the radio signal travel at speed of light is 3.17m.

Given the data in the question;

Wavelength the spatial period of a periodic wave. That is to say, when the shapes of waves are Wavelength , the distance over which they are repeated is called wavelength. Wavelength  is expressed as;

\(\lambda = \frac{v}{f}\)

Where \(\lambda\) is wavelength, f is the frequency of the wave and c is the velocity or speed of light ( \(c = 3*10^8m/s\) )

We substitute our values into the expression above.

\(\lambda = \frac{c}{ f}\\ \\\lambda = \frac{3*10^8m/s}{9.45*10^7s^{-1}} \\\\\lambda = \frac{3*10^8ms/s}{9.45*10^7}\\\\\lambda = 3.17m\)

Therefore, the wavelength of the radio signal travel at speed of light is 3.17m.

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Answer:

In the absence of thrust, the lunar lander moves downward toward the surface of the moon. At this point, the only force acting on the lunar lander is gravity, which is directed toward the center of the moon. Because the net force is in the downward direction, the lunar lander moves downward.

Explanation: plato

Answer: In the absence of thrust, the lunar lander moves downward toward the surface of the moon. At this point, the only force acting on the lunar lander is gravity, which is directed toward the center of the moon. Because the net force is in the downward direction, the lunar lander moves downward.

Explanation: edmentum sample answer

The power to stop the car with kinetic energy of a car is  \(8*10^{6} J\) as it travels along a horizontal road is  \(8*10^{5} watt\), option B

Kinetic energy can be seen as one that is been recorded when an object is able to move from a place , in a broad term we can say this is the energy that can be attributed to that of someone leaving a place and go to another place hence we can see it as the one in the motion.

The definition of energy as the "power to accomplish work" refers to the capacity to apply a force that moves an object. Even if the word is vague, it is clear what energy actually means: it is the force that causes objects to move. The two types  can be attributed to the one we know which are kinetic and potential energy.

\(Power \frac{Energy}{time}\)

\(Energy = 8*10^{6} J\)

\(time = 10 s\)

\(Power = \frac{8*10^{6} J}{10}\)

\(power = 8*10^{5} watt\)

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proper question;

The kinetic energy of a car is 8 × 106 J as it travels along a horizontal road. How much power is required to stop the car in 10 s? (A) zero joules (B) 8  105 J (C) 8  107 J (D)8  104 J (E) 8  106 J​