Once dark adapted, the pupil of your eye is approximately 7 mm in diameter. The headlights of an oncoming car are 120 cm apart. If the lens of your eye is diffraction limited, at what distance are the two headlights marginally resolved? Assume a wavelength of 565nm and that the index of refraction inside the eye is 1.33. (Your eye is not really good enough to resolve headlights at this distance, due both to aberrations in the lens and to the size of the receptors in your retina, but it comes reasonably close.) (km)

Answer:

To answer your question:

a) The formula to calculate the number of wavelengths within a laser pulse is:

number of wavelengths = pulse duration / wavelength

Plugging in the values given in the question, we get:

number of wavelengths = 38 ps / 1062 nm

Converting picoseconds to seconds and nanometers to meters, we get:

number of wavelengths = 38 x 10^-12 s / 1062 x 10^-9 m

number of wavelengths = 0.0358

Therefore, there are approximately 0.0358 wavelengths within the laser pulse.

b) To fit only one wavelength, the pulse duration would need to be equal to the wavelength. The formula to calculate the pulse duration is:

pulse duration = wavelength

Plugging in the value given in the question, we get:

pulse duration = 1062 nm

Converting nanometers to picoseconds using the speed of light ©, we get:

pulse duration = wavelength / c

pulse duration = 1062 x 10^-9 m / 3 x 10^8 m/s

pulse duration = 3.54 x 10^-12 s

Therefore, the pulse would need to be approximately 3.54 ps long to fit only one wavelength.

I hope this helps

Answer:

calculate each person's relative strength

Explanation:

Answer:

I think it is: "calculate each person's relative strength"

Explanation:

The momentum of the kid weighing 30kg is 210kgm/s.

Momentum in physics refers to the tendency of a body to maintain its inertial motion i.e. the product of its mass and velocity, or the vector sum of the products of its masses and velocities.

According to this question, a 30kg kid on a bike is moving in the positive direction at 7 m/s. The momentum is calculated thus;

Momentum = 30kg × 7m/s = 210kgm/s

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The power gain when the gain falls by 3 dB is approximately 300.7 mW, which is closest to option D: 244.2 mW.

The power gain of an amplifier can be calculated using the formula:

Power Gain (dB) = 10 * log10(Pout / Pin)

where Pout is the output power and Pin is the input power. In this case, the midrange gain of the amplifier is given as 600 mW.

To calculate the power gain when the gain falls by 3 dB, we need to find the new output power. Since the gain is decreasing, the new output power will be lower than the initial power.

First, we convert the midrange gain from milliwatts to watts:

Midrange Gain = 600 mW = 0.6 W

Next, we use the formula:

Pout / Pin = 10^(Power Gain / 10)

Since the gain falls by 3 dB, the new power gain is:

Power Gain = -3 dB

Now we substitute the values into the formula:

Pout / Pin = 10^(-3 / 10)

Pout / Pin = 10^(-0.3)

Pout / Pin = 0.5012

To find the new output power (Pout), we multiply the input power (Pin) by the ratio:

Pout = Pin * 0.5012

Pout = 0.6 W * 0.5012

Pout = 0.3007 W

Finally, we convert the output power back to milliwatts:

Pout = 0.3007 W = 300.7 mW

Therefore, the power gain when the gain falls by 3 dB is approximately 300.7 mW, which is closest to option D: 244.2 mW.

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The value of resistance will be 60 ohms. Resistance is the ratio of the voltage to the electric current passing through the wire.

A resistor is a two-terminal passive electrical component that acts as a circuit element by implementing electrical resistance.

Resistors are used to limit current flow, alter signal levels, divide voltages, bias active devices, and complete transmission lines in electronic circuits.

The given data in the problem is;

V is the voltage =  3. 0 V

I is value of current=  0. 05 A

R is the resistance=?

According to ohm's law, the potential difference between the two ends of the conductor is equal to the product of electric current and the resistance generated.

So from the ohm law;

V= IR

\(\rm R = \frac{V}{I} \\\\ \rm R = \frac{3}{0.05} \\\\ \rm R =60 \ ohm\)

Hence the value of resistance will be 60 ohms.

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Answer:\(\sqrt {\frac{2}{3}}\,A\)

Explanation:

\(v^2=\omega^2(A^2-x^2)\\KE_{\rm max} = \frac 12 m \omega^2A^2\\\frac 13\cdot \frac 12 m \omega^2A^2= \frac 12 m v^2=\omega^2(A^2-x^2)\Rightarrow x=\sqrt{\frac 23}\,A\)

Answer:

D) the preformence of mucles for long periods of time

Answer:

Speed of the satellite V = 6.991 × 10³ m/s

Explanation:

Given:

Force F = 3,000N

Mass of  satellite m = 500 kg

Mass of earth M = 5.97 × 10²⁴

Gravitational force G = 6.67 × 10⁻¹¹

Find:

Speed of the satellite.

Computation:

Radius r = √[GMm / F]

Radius r = √[(6.67 × 10⁻¹¹ )(5.97 × 10²⁴)(500) / (3,000)

Radius r = 8.146 × 10⁶ m

Speed of the satellite V = √rF / m

Speed of the satellite V = √(8.146 × 10⁶)(3,000) / 500

Speed of the satellite V = 6.991 × 10³ m/s

The speed of the petunia rolls is obtained from the calculation as 12.8 Km/hr.

The term speed is the ratio of the distance to the time that is taken by a body. We know that speed is how we would know how fast or slow that a material is moving and the unit that we can use to measure the speed of an object is kilometers per hour.

Distance covered by the object = 16Km

Time taken by the object = 1.25hrs

Speed = Distance/ Time

Speed =  16Km/ 1.25hrs

= 12.8 Km/hr

The speed is 12.8 Km/hr.

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Answer:

Horizontal Component = 129.9 km/h

Vertical Component = 75 km/h

Explanation:

When a vector is resolved on the x-axis and the y-axis, the components so formed are called its rectangular components. The component along y-axis is called the vertical component and the component along x-axis is called horizontal component. These components can be given by following formulae:

Horizontal Component = v Cos θ

Vertical Component = v Sin θ

where,

v = velocity = 150 km/h

θ =  angle = 30°

Therefore,

Horizontal Component = (150 km/h)(Cos 30°)

Horizontal Component = 129.9 km/h

Vertical Component = (150 km/h)(Sin 30°)

Vertical Component = 75 km/h

Answer:O que faz o longa se destacar é seu cenário mergulhado na cultura chinesa e a delicadeza com que o luto e sua superação são tratados.

Explanation:

Por que se você pensar ela estava sempre buscando superar a morte da mãe.

The de Broglie wavelength of the electron is: 4.78×10⁻¹⁰ m. The momentum of the electron is then: 1.31×10⁻²⁴ kg·m/s. Therefore, the kinetic energy of the electron is 1.14×10² eV.

(a) The de Broglie wavelength of a particle is given by the formula:

λ = h/p

where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. We can find the momentum of the electron using the formula:

p = h/λ

where λ is the wavelength of the wave function of the electron. The given wave function of the electron is:

ψ(x) = Aei(2.10×1011x)

We can see that the wave function has the form of a plane wave, and the wave vector is:

k = 2.10×1011 m⁻¹

The momentum of the electron is then:

p = hk = (6.626×10⁻³⁴ J·s)(2.10×10¹¹ m⁻¹) = 1.39×10⁻²⁴ kg·m/s

The de Broglie wavelength of the electron is:

λ = h/p = (6.626×10⁻³⁴ J·s)/(1.39×10⁻²⁴ kg·m/s) = 4.78×10⁻¹⁰ m

(b) The momentum of the electron is given by:

p = mv

where m is the mass of the electron and v is its velocity. We can use the de Broglie wavelength of the electron to find its velocity:

λ = h/p = h/(mv)

v = p/m = h/(mλ) = (6.626×10⁻³⁴ J·s)/[(9.109×10⁻³¹ kg)(4.78×10⁻¹⁰ m)] = 1.44×10⁶ m/s

The momentum of the electron is then:

p = mv = (9.109×10⁻³¹ kg)(1.44×10⁶ m/s) = 1.31×10⁻²⁴ kg·m/s

(c) The kinetic energy of the electron is given by:

K = p²/(2m)

where p is the momentum of the electron and m is its mass. We can use the momentum of the electron that we found in part (b):

K = p²/(2m) = [(1.31×10⁻²⁴ kg·m/s)²]/[2(9.109×10⁻³¹ kg)] = 1.82×10⁻¹⁷ J

We can convert this energy to electron volts (eV) using the conversion factor 1 eV = 1.60×10⁻¹⁹ J:

K = (1.82×10⁻¹⁷ J)/(1.60×10⁻¹⁹ J/eV) = 1.14×10² eV

Therefore, the kinetic energy of the electron is 1.14×10² eV.

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Answer:

C) if they are based on a very small sample

A diverging lens has a focal length that has a magnitude of 33.0 cm. an object is placed 21.0 cm in front of this lens. The magnification will be  -12.833 cm

diverging lens = concave lens

focal length = - 33 cm

u = - 21 cm

magnification = image distance / object distance

using lens formula

1/v - 1/u = 1/f

1/v = 1/f + 1/u

    = 1/-33 -1/21

v   = -12.833 cm

A diverging lens has a focal length that has a magnitude of 33.0 cm. an object is placed 21.0 cm in front of this lens. The magnification will be  -12.833 cm

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The "arm" of the lever is the handle or bar; it is the portion that you push or pull against. The point on which the lever rotates or balances is known as the "fulcrum.

The pivotal point of the beam is known as the fulcrum. A load is applied at the other end of a lever when an effort is exerted to one end of the lever. A mass will be raised as a result.

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Given:

The specific heat of the material is c Cal/(gram°C)

The mass of the material, m=5 g

The initial temperature of the material, T₁=10 °C

The final temperature of the material, T₂=37 °C

To find:

The expression for the amount of heat added to the material.

Explanation:

The specific heat of a material is the heat required to raise the temperature of the unit mass of the material by one degree celcius.

From the equation of specific heat, the amount of the heat added to a material is given by,

On substituting the known values,

Final answer:

Thus the correct answer is option A.

Answer:

27v

Explanation:

10 ohm resistor is the first in series. so it will have the entire current.

voltage across 10ohm resistor = 10*2.7= 27v

The given Lagrangian density isL= 120₁0²3 − 1²m² 3²−194 4!For the real scalar field, the Lagrangian density is given as; L = 1/2 (∂ᵥϕ)² - V(ϕ)where V(ϕ) is the potential energy density associated with the scalar field, ϕ.For this problem,V(ϕ) = (1/2)m²ϕ² + λϕ⁴where λ = 194/4! = 8.08 and m² > 0.

a) If (m²) > 0 and A > O, then the potential energy density will be positive for all values of ϕ. Hence, there is no minimum. It can be shown using calculus that V(ϕ) increases with ϕ. Thus the minimum is at ϕ = 0. So, the minimum value is 0.

b) If (m²) < 0, then the potential energy density has a minimum at some non-zero value of ϕ. This is because the potential energy density is an inverted parabola whose axis is parallel to the ϕ-axis. The minimum value of V(ϕ) can be found by differentiating it with respect to ϕ and equating it to zero, which gives the value of ϕ at which the potential energy density is minimum;∂V(ϕ)/∂ϕ = 0m²ϕ + 4λϕ³ = 0m²ϕ = - 4λϕ³ϕ = 0 or ϕ² = -m²/4λ The second equation has solutions only for (m²) < 0. Hence, for this case, we get two values of ϕ;ϕ = ±√(-m²/4λ)The potential energy density at ϕ = ±√(-m²/4λ) isV(-m²/4λ) = (-m⁴/4λ) + (m⁴/4λ) = 0

Thus, the minimum value of potential energy density is 0. Hence, in this case, the potential energy density is always non-negative. Hence, there is no maximum. Let's plot the potential energy density for (m²) > 0 and (m²) < 0, respectively.

Potential energy density V(ϕ) = (1/2)m²ϕ² + λϕ⁴If (m²) > 0 and A > O, then ϕ = 0.

Hence, V(0) = 0. So, the plot is as follows; \(If\((m^2)\) < 0\) The minimum value of V(ϕ) is at ϕ = ±√(-m²/4λ)As λ = 194/4! = 8.08, we haveϕ = ±√(-m²/4λ) = ±√(-m²/32.3) The plot of V(ϕ) for (m²) < 0 is as follows;Potential energy density plot potential energy density plot.

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The capacitance of the air-filled capacitor is 0.118 πr² meter.

The ideal air-filled parallel-plate capacitor is a simple case of the capacitor. The capacitance of the air-filled capacitor can be determined as

C = ε₀ . A / d

where C is the capacitance of the capacitor, ε₀ is the vacuum permeability (8,85 x 10‾¹² F/m), A is the area of plate (m²) and d is a distance of the plate (m).

From the question above, we know that:

A = 4 x π x r²

C = 300 pF

By substituting the parameter, we get

C = ε₀ . A / d

300 x 10‾¹² = 8,85 x 10‾¹² . 4 x π x r² / d

d = 35.4 x 10‾¹² x π x r² / 300 x 10‾¹²

d = 0.118 πr² meter

where r is radius of plate.

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sis i love the eren season 1-2-3-4 but the eren season 5?....... i just :')

Answer:

Explanation:

Aaron yogurt supremacy

Angular displacement: 10 rad.

linear displacement: 60 cm

In basic terms, angular velocity is the pace at which an item rotates or circles around an axis in time. "ω" is a Greek letter that stands in for angular velocity. Radians per second is the SI unit for angular velocity since it is expressed as an angle per unit of time.

Given that,

Radius of the CD below is 6.0 cm

Angular velocity is 5.0 rad/s.

As we know, angular displacement, (θ) = ω × t

or, θ = 5.0 rad/s × 2.0 sec

or, θ = 10 rad.

Next, linear displacement, (S) = R × θ

or, S = 6 cm. × 10 rad

or, S = 60 cm

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G is the gravitational constant, M is the mass of the gravitating body, and r is the separation between their centers.

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Answer:

All of the above lol!

Explanation:

Brainliest Please!

Answer:

hope i helped even tho i am 100 years late lol not really but STILL  

Explanation:

The Energy Spectral Density (ESD) function of x(t) can be determined by taking the Fourier Transform of the autocorrelation function of the signal. In this case, since the spectrum X(ω) is given as 3e^(-0.1|ω|), we can write the autocorrelation function as R(τ) = (1/2π) ∫ X(ω) e^(jωτ) dω, where τ is the time delay.

To simplify the calculation, we can split the integral into two parts: for positive and negative frequencies. For positive frequencies, we have R(τ) = (1/2π) ∫ (3e^(-0.1ω) e^(jωτ)) dω. By evaluating this integral, we get R(τ) = (15/π) e^(-0.1τ) / (1 + jτ).

For negative frequencies, we have R(τ) = (1/2π) ∫ (3e^(-0.1(-ω)) e^(j(-ω)τ)) d(-ω). By evaluating this integral, we get R(τ) = (15/π) e^(-0.1τ) / (1 - jτ).

The Energy Spectral Density (ESD) function is the Fourier Transform of the autocorrelation function, so we can write ESD(f) = ∫ R(τ) e^(-j2πfτ) dτ. By evaluating this integral, we get ESD(f) = (30/π) / (1 + (2πf)^2)^(1.5).

2. To find the bandwidth B95 of x(t) such that 95% of the total signal energy is contained within B95, we need to determine the frequency range over which the energy is concentrated. We can integrate the ESD function over the frequency range from 0 to f95 such that the integral of ESD(f) from 0 to f95 is equal to 0.95 times the total signal energy.

The total signal energy can be calculated by integrating the ESD function over the entire frequency range from 0 to infinity. By evaluating this integral, we find that the total signal energy is (15/2π).

To find the bandwidth B95, we need to solve the equation ∫ ESD(f) df = 0.95 * (15/2π) for f95. The solution to this equation gives us the bandwidth B95.

3. If x(t) passes through a low-pass filter with a transfer function H(ω) = (1 + jω)^(-1), the ESD function at the output of the filter can be obtained by multiplying the ESD function of the input signal with the squared magnitude of the transfer function.

Let's denote the ESD function at the output as ESD_output(f). Then, ESD_output(f) = |H(f)|^2 * ESD_input(f), where ESD_input(f) is the ESD function of the input signal.

For the given transfer function H(ω) = (1 + jω)^(-1), we have |H(f)|^2 = |(1 + j2πf)^(-1)|^2 = 1 / (1 + (2πf)^2).

Hence, the ESD function at the output of the filter is ESD_output(f) = 1 / (1 + (2πf)^2) * (30/π) / (1 + (2πf)^2)^(1.5).

This is the simplified expression for the ESD function at the output of the low-pass filter.

These steps should help you determine the Energy Spectral Density (ESD) function of x(t), the bandwidth B95, and the ESD function at the output of the low-pass filter. Remember to use the given information and equations provided to solve the problem.

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Answer:

A

Explanation: