Coherent light that contains two wavelengths, 660 nm (red) and 470 nm (blue), passes through two narrow slits that are separated by 0.310 mm. Their interference pattern is observed on a screen 4.40 m from the slits. What is the disatnce on the screen between the first order bright fringe for each wavelength?

Answer:

The probability that it will take a week for it three wet weather on 3 separate days is 0.06166 and its standard deviation is 0.9447

Explanation:

We are given that A city of Punjab has 15 percent chance of wet weather on any given day.

So, Probability of wet weather = 0.15

Probability of not being a wet weather = 1-0.15 =0.85

We are supposed to find probability that it will take a week for it three wet weather on 3 separate days

Total number of days in a week = 7

We will use binomial over here

n = 7

p =probability of failure = 0.15

q = probability of success=0.85

r=3

Formula :[tex]P(r=3)=^nC_r p^r q ^{n-r}[/tex]

[tex]P(r=3)=^{7}C_{3} (0.15)^3 (0.85)^{7-3}\\P(r=3)=\frac{7!}{3!(7-3)!} (0.15)^3 (0.85)^{7-3}\\P(r=3)=0.06166[/tex]

Standard deviation =[tex]\sqrt{n \times p \times q}[/tex]

Standard deviation =[tex]\sqrt{7 \times 0.15 \times 0.85}[/tex]

Standard deviation =0.9447

Hence The probability that it will take a week for it three wet weather on 3 separate days is 0.06166 and its standard deviation is 0.9447

Answer:

Explanation:

Let the race be of a fixed distance x

[tex]Average Speed = \frac{Total Distance}{Total Time}[/tex]

Troy's Average speed = 3 miles/hr = x / 0.2 hr

x = 0.6 miles

Abed's Average speed = 0.6 / 0.125 = 4.8 miles/hr

Answer:

The new volume will be 0.918 x 10^5 L

Explanation:

initial volume  [tex]V_{1}[/tex] = 1.21 x 10^5 L

Initial temperature [tex]T_{1}[/tex] = 265 K

Final volume [tex]V_{2}[/tex] = ?

Final temperature [tex]T_{2}[/tex] = 201 K

Th gas is an ideal gas.

For ideal gases, the equation [tex]V_{1}[/tex]/[tex]T_{1}[/tex] = [tex]V_{2}[/tex]/[tex]T_{2}[/tex] = constant

substituting value, we have

(1.21 x 10^5)/265 = [tex]V_{2}[/tex]/201

[tex]V_{2}[/tex] =  24321000/265 = 91777.4 L

= 0.918 x 10^5 L

Answer:

there are over 100 billion stars in our galaxy.

Answer:

30cm

Explanation:

assume that the eyes are substantially above the water so that sin(theta) is approximately theta.

( small angle approximation).

The point at which a ray leaving the fish hits the surface of the water is x to the side of the centreline and the depth of the water is d

x/d = sin( angle of incidence)

if the apparent depth of the water is h then

x/h = sin( angle of refraction)

and applying snells law

1 sin ( theta air) = 1.33 sin( theta water)

1 * x/h = 1.33 * x/d

d/h = 1.33

or h/d = 1/1.33

h/39 = 1.33

h = 39 /1.33 so that is the apparent depth of the stream assuming:-

1. Your eyes are almost directly overhead

and

2. your eyes are a significant distance above the surface of the water.

x/d = 1.33 x/h

h/d =39/1.3

= 30cm

Answer:

The magnitude of the total linear acceleration is 0.27 m/s²

b. 0.27 m/s²

Explanation:

The total linear acceleration is the vector sum of the tangential acceleration and radial acceleration.

The radial acceleration is given by;

[tex]a_t = ar[/tex]

where;

a is the angular acceleration and

r is the radius of the circular path

[tex]a_t = ar\\\\a_t = 1.6 *0.13\\\\a_t = 0.208 \ m/s^2[/tex]

Determine time of the rotation;

[tex]\theta = \frac{1}{2} at^2\\\\0.4 = \frac{1}{2} (1.6)t^2\\\\t^2 = 0.5\\\\t = \sqrt{0.5} \\\\t = 0.707 \ s\\\\[/tex]

Determine angular velocity

ω = at

ω = 1.6 x 0.707

ω = 1.131 rad/s

Now, determine the radial acceleration

[tex]a_r = \omega ^2r\\\\a_r = 1.131^2 (0.13)\\\\a_r = 0.166 \ m/s^2[/tex]

The magnitude of total linear acceleration is given by;

[tex]a = \sqrt{a_t^2 + a_r^2} \\\\a = \sqrt{0.208^2 + 0.166^2} \\\\a = 0.266 \ m/s^2\\\\a = 0.27 \ m/s^2[/tex]

Therefore, the magnitude of the total linear acceleration is 0.27 m/s²

b. 0.27 m/s²

Answer: i think it is d. none of them.

Explanation: The speed of light in a vacuum is 186,282 miles per second and so when you look and the answer choices and the question it doesnt make any since.

Answer:

[tex]\theta_1 = 0.400^o[/tex]

[tex]\theta_2 =0.378^o[/tex]

Explanation:

From the question we are told that

    The  number of slits per cm is  k =  [tex]161\ slits\ per\ cm = 161 \ slits\ per\ 0.01 m[/tex]

    The order of the maxima is  n =  1

    The wavelength are  [tex]\lambda_1 = 434 nm = 434 *10^{-9} \ m \ \ \ , \lambda_2 = 410nm = 410 *10^{-9} \ m[/tex]

The  spacing between the slit is mathematically represented as

           [tex]d = \frac{ 0.01}{k}[/tex]

=>       [tex]d = \frac{ 0.01}{161}[/tex]

=>         [tex]d = 6.211 *10^{-5} \ m[/tex]

Generally the condition for constructive interference is  

        [tex]n\lambda = d \ sin \theta[/tex]

At  [tex]\lambda_1[/tex]

      [tex]\theta _1 = sin^{-1} [ \frac{1 * 434 *10^{-9}}{6.211 *10^{-5}} ][/tex]

      [tex]\theta_1 = 0.400^o[/tex]

At  [tex]\lambda_2[/tex]

       [tex]\theta _2 = sin^{-1} [ \frac{1 * 410 *10^{-9}}{6.211 *10^{-5}} ][/tex]

       [tex]\theta_2 =0.378^o[/tex]

Answer:

The percentage is  [tex]k = 12.5 \%[/tex]

Explanation:

From the question we are told that

    The  axis is is  at  [tex]\theta = 45 ^o[/tex]

Generally the of intensity light emerging from the first polarizer is mathematically represented as

                [tex]I_{1} = \frac{I_o}{ 2}[/tex]

Where  [tex]I_o[/tex] is the intensity of unpolarized light

       Now the light emerging from the second polarizer is mathematically represented as

         [tex]I_2 = I_ 1 * cos ^2(\theta )[/tex]

         [tex]I_2 = \frac{I_o}{2} * cos ^2(45 )[/tex]

        [tex]I_2 = \frac{I_o}{2} * \frac{1}{2} = \frac{I_o}{4}[/tex]

  Now the light emerging from the third  polarizer is mathematically represented as      

       [tex]I_3 = I_ 2 * cos ^2(\theta )[/tex]

       [tex]I_3 = \frac{I_o}{4} * cos ^2(45 )[/tex]

      [tex]I_3 = \frac{I_o}{8}[/tex]

Now the percentage of the intensity of light that emerged with respect to the intensity of  the unpolarized light is

      [tex]k = \frac{\frac{I_o}{8} }{I_o } * 100[/tex]

     [tex]k = 12.5 \%[/tex]

The percentage of light that gets through the three successive Polaroid filters is; 12.5%

We are given;

Angle of transmission axis; θ = 45°

Formula for intensity of light from first polarizer is;

I₁ = ¹/₂I₀

Formula for intensity of light from second polarizer is;

I₂ = I₁cos²θ

Formula for intensity of light from third polarizer is;

I₃ = I₂cos²(90 - θ)

Combining the 3 equations;

Put ¹/₂I₀ for I₁ in second formula to get;

I₂ = ¹/₂I₀cos²θ

Put ¹/₂I₀cos²θ for I₂ in third formula to get;

I₃ = ¹/₂I₀cos²θ*cos²(90 - θ)

Plugging in 45° for θ gives;

I₃ = ¹/₂I₀cos²45*cos²(90 - 45)

⇒ I₃ = ¹/₂I₀cos²45*cos²45

⇒ I₃ = ¹/₂I₀cos⁴45

Now, cos 45 in surd form is 1/√2. Thus;

I₃ = ¹/₂I₀(1/√2)⁴

I₃ = ¹/₂I₀(¹/₄)

I₃ = ¹/₈I₀

I₃/I₀ = ¹/₈

I₃/I₀ = 0.125

In percentage form, we have;

I₃/I₀ = 12.5%

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Answer:

Explanation:

Laser angle with water surface is given by: Tan α = 1/2.0= 0.5/

α = 26.56°

Laser angle with Normal = 90 - 26.56 = 63.44 °

Assuming a red laser, refractive index in water is 1.331.

Angle of refraction in water is given by:

Ref Ind = Sin i / Sin r

1.331 = Sin 63.44 / Sin r

Sin r = 0.8945 / 1.331 = 0.6721

Angle r = 42.22°

For the path in water:

Tan 42.22 = x / 3.2

x = 2.9m where x is the lateral displacement of the laser ince it hits the water

So the goggles are 2.0 + 2.9 = 4.9 m from edge of pool

Answer:

photon density = 1.0 × [tex]10^{16}[/tex] photon/m³

Explanation:

given data

frequency f = 100 mhz = 100 × [tex]10^{6}[/tex] Hz

we consider here intensity I = 0.2 W/m²

solution

we take here plank constant is h i.e = 6.626 × [tex]10^{-34}[/tex] s

and take energy density is E

so here

E × C = I  

E = [tex]\frac{I}{C}[/tex]   ................1

here C = 3 × [tex]10^{8}[/tex] m/s

so photon density is

photon density = [tex]\frac{I}{C} \times \frac{1}{f \times h}[/tex]     ...............2

photon density = [tex]\frac{0.2}{3 \times 10^8} \times \frac{1}{100 \times 10^6 \times 6.626 \times 10^{-34} }[/tex]

photon density = 1.0 × [tex]10^{16}[/tex] photon/m³

Answer:

B. constant pressure, isothermal, adiabatic

Explanation:

A quantity of an ideal gas is compressed to half its initial volume.

The process may be adiabatic, isothermal or occurring at constant pressure.

Adiabatic-constant heat

Constant pressure or isobaric

Isothermal or constant temperature

An external agent is a system that does work on a system or a machine.

This external agent applies force , or changes the state of the body it is acting on.

In order of the work required of an external agent, least to greatest

The following processes will be arranged.

constant pressure, isothermal, adiabatic

Answer:

C

They allow light to pass only if their directions of polarizations are exactly 90° apart.

Answer:

-0.24diopters

Explanation:

The lens is intended that makes an object at infinity appear to be 4.2 m away, so do=infinity, dI = - 4.2m (minus sign because image is on same side of lens as object)

So 1/do +1/di = 1/f

1/infinity + 1/-4.2 = 1/f

1/f = 1/-4.2 = -0.24diopters

The bullet's vertical velocity at time [tex]t[/tex] is

[tex]v=1400\dfrac{\rm m}{\rm s}-gt[/tex]

where [tex]g=9.80\frac{\rm m}{\mathrm s^2}[/tex] is the acceleration due to gravity.

At its highest point, the bullet's vertical velocity is 0, which happens

[tex]0=1400\dfrac{\rm m}{\rm s}-gt\implies t=\dfrac{1400\frac{\rm m}{\rm s}}g\approx\boxed{142.857\,\mathrm s}[/tex]

(or about 140 s, if you're keeping track of significant figures) after being fired.

Answer:

Explanation:

[tex]Force = 25N\\Area = 0.05m^2\\\\Pressure = \frac{Force}{Area}\\ \\Pressure = \frac{25}{0.05}\\\\ Pressure = 500 Pascals[/tex]

Answer:

ΔE = GMm/24R

Explanation:

centripetal acceleration a = V^2 / R = 2T/mr

T= kinetic energy

m= mass of satellite, r= radius of earth

= gravitational acceleration = GM / r^2

Now, solving for the kinetic energy:

T = GMm / 2r = -1/2 U,

where U is the potential energy

So the total energy is:

E = T+U = -GMm / 2r

Now we want to find the energy difference as r goes from one orbital radius to another:

ΔE = GMm/2 (1/R_1 - 1/R_2)

So in this case, R_1 is 3R (planet's radius + orbital altitude) and R_2 is 4R

ΔE = GMm/2R (1/3 - 1/4)

ΔE = GMm/24R

Answer:

Kindly check explanation

Explanation:

Length of race = 5km

Maximum speed = 45 yards

Converting from yards to kilometer :

1km = 1093.613 yards

x = 45 yards

(1093.613 * x) = 45

x = 45 / 1093.613

x = 0.0411480 km

Where x = maximum length for which he can maintain his maximum speed expressed in kilometers.

Therefore, with the available information, it can be concluded that Lamar cannot maintain his maximum speed for the entire 5km race and will only be able maintain his maximum speed for 0.0411 kilometers.

Lamar cannot maintain his maximum speed for the entire 5km race and will only be able maintain his maximum speed for 0.0411 kilometers.

Length of race = 5km

Maximum speed = 45 yards

Converting from yards to kilometer :

1km = 1093.613 yards

x = 45 yards

[tex](1093.613 \times x) = 45[/tex]

[tex]x = 45 \div 1093.613[/tex]

x = 0.0411480 km

here x represent maximum length for which he can maintain his maximum speed expressed in kilometers.

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Complete question is;

A force stretches a wire by 0.60 mm. A second wire of the same material has the same cross section and twice the length.

a) How far will it be stretched by the same force?

b) A third wire of the same material has the same length and twice the diameter as the first. How far will it be stretched by the same force?

Answer:

0.15 mm

Explanation:

According to Hooke's Law,

E = Stress(σ)/Strain(ε)

Where E is youngs modulus

Formula for stress is;

Stress(σ) = Force(F)/Area(A)

Formula for strain is;

Strain(ε) = Change in length/original length = (Lf - Li)/Li

We are also told that a second wire of the same material has the same cross section and twice the length.

Thus;

Rearranging Hooke's Law to get the constants on one side, we have;

F/(AE) = ε

Thus from the conditions given;

ε1 = 0.6/Li

ε2 = (Change in length)/(2*Li)

And ε1 = ε2

Thus;

0.6/Li = Change in length/(2*Li)

Li will cancel out and we now have;

Change in length = 2 × 0.6 = 1.2 mm

Finally, we are told A third wire of the same material has the same length and twice the diameter as the first.

Area of a circle;A1 = πd²/4

Now, we are told d is doubled.

Thus, new area of the new circle is;

A2 = π(2d)²/4 = πd²

Rearranging Hooke's Law,we have;

F/A = εE

Since F and E are now constants, we have;

F/E = constant = Aε

Thus;

A1(ε1) = A2(ε2)

A1 = πd²/4

e1 = 0.60/Li

A2 = πd²

e2 = Change in length/Li

Thus;

((πd²/4) × 0.6)/Li = (πd² × Change in length)/ Li

Rearranging, Li and πd² will cancel out to give;

0.6/4 = Change in length

Change in length = 0.15 mm

Answer:

0.99Hz

Explanation:

Using F= -mx ( spring force)

At equilibrium the gravitational force will be balanced by the spring force so mg= kx

K= mg/ 0.25 N/m

But

Frequency f= 1/2pi √g/0.25

Frequency is 0.99Hz

The block is pulled down slightly and released so, Frequency of oscillation is 3.15 Hz

What information do we have?

Length starched = 2.5 cm

F = Kx

We know that

F = mg

So,

mg = Kx

K/m = g/x

[tex]f=\frac{1}{2\pi}\sqrt{\frac{g}{x} }\\f=\frac{1}{2\pi}\sqrt{\frac{9.8}{0.025} }[/tex]

Frequency of oscillation = 3.15 Hz

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Answer:

The  angular acceleration is  [tex]\alpha = 3.235 \ rad/s ^2[/tex]

Explanation:

From the question we are told that

    The moment of inertia is  [tex]I = 0.034\ kg \cdot m^2[/tex]

     The  net torque is  [tex]\tau = 0.11\ N \cdot m[/tex]

Generally the net torque is mathematically represented as

           [tex]\tau = I * \alpha[/tex]

Where [tex]\alpha[/tex] is the angular acceleration so  

        [tex]\alpha = \frac{\tau }{I}[/tex]

substituting values

         [tex]\alpha = \frac{0.1 1}{ 0.034}[/tex]

        [tex]\alpha = 3.235 \ rad/s ^2[/tex]

Answer:

0.61 m

Explanation:

The smallest observable length by the radar must be at least equal to or greater than the wavelength of the radar.

using the relationship

c = fλ

where

c is the speed of light in vacuum = 3 x 10^8 m/s

f is the frequency of the wave = 495 MHz = 4.95 x 10^8 Hz

λ is the wavelength = ?

λ = c/f = (3 x 10^8)/(4.95 x 10^8) = 0.61 m

answer to your question is 0.6m

Answer:

10.8rev

Explanation:

Using

Wf²-wf = 2 alpha x theta

0²- 56.36x56.36/ 2(-20.13) x theta

Theta = 68.09 rad

But 68.09/2π

>= 10.8 revolutions

Explanation:

Answer:

a)   I = I₀/2, b)  I = I₀/2 cos² θ

Explanation:

To answer these questions, let's analyze a little the way of working of a polarized

* When a non-polarized light hits a polarizer, the electric field that is not in the direction of the polarizer is absorbed, so the transmitted light is

          i = I₀ / 2

and is polarized in the direction of the polarizer

* when a polarized light reaches the analyzer it must comply with Malus's law

          I = I₁ cos² θ

where the angle is between the polarized light and the analyzer.

With this, let's answer the questions

a) When a polarizer is placed in the non-polarized light path, half of it is absorbed and only the light that has polarization in the direction of the polarizer is transmitted with an intensity of

                  I = I₀/2

b) when a polarizer and an analyzer are fitted, the intensity of the light transmitted by the analyzer is

                I = I₀/2 cos² θ

where the final value depends on the angle between the polarizer and the analyzer.

Let's look at two extreme cases

θ = 0          I = Io / 2

θ = 90º      I = 0

Answer:

The magnification is  [tex]m = -2.15[/tex]

Explanation:

From the question we are told that

   The  radius is  [tex]r = 14.0 \ m[/tex]

    The  focal length eyepiece is  [tex]f_e = 3.25 \ m[/tex]

Generally the objective focal length is mathematically represented as

        [tex]f_o = \frac{r}{2}[/tex]

=>     [tex]f_o = \frac{14}{2}[/tex]

=>     [tex]f_o = 7 \ m[/tex]

The  magnification is mathematically represented as

      [tex]m = - \frac{f_o }{f_e }[/tex]

=>    [tex]m = - \frac{7 }{ 3.25 }[/tex]

=>   [tex]m = -2.15[/tex]

Answer:

A The father should sit closer to the pivot.

C The longer wrench makes the job easier because less force is needed when there is more distance from the pivot.

A As far from the head of the hammer as possible because this will maximize torque.

D at the opposite side of the seesaw towards the middle

:) gl

Explanation:

If a father and his son want to play on a seesaw then to balance the torque of the seesaw the father should sit near the pivot as he had more weight as compared to his son, while the son should sit a little farther from the pivot point as compared to his father.

Mechanical advantage is defined as a measure of the ratio of output force to input force in a system, It is used to analyze the forces in simple machines like levers and pulleys.

Mechanical advantage = output force(load) /input force (effort)

As given in the problem statement If a father and his son wish to play on a seesaw,

The father should sit close to the pivot because he weighs more than his son, and the son should sit a little farther away from the pivot point than his father. This will help balance the torque of the seesaw.

Thus, the father should sit near the pivot on the one side and the son should sit a little farther from the pivot of a seesaw on the other side.

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Answer:

a

    [tex]n = 1.119 *10^{18} \ photons[/tex]

b

  [tex]P = 1.6 \ W[/tex]

Explanation:

From the question we are told that

    The wavelength is  [tex]\lambda = 2780 nm = 2780 *10^{-9} \ m[/tex]

     The  energy  is  [tex]E = 80 mJ = 80 *10^{-3} \ J[/tex]

This energy is mathematically represented as

     [tex]E = \frac{n * h * c }{\lambda }[/tex]

Where  c is the speed of light with a value  [tex]c = 3.0 *10^{8} \ m/s[/tex]

             h is the Planck's  constant with the value  [tex]h = 6.626 *10^{-34} \ J \cdot s[/tex]

             n is the number of pulses

So

      [tex]n = \frac{E * \lambda }{h * c }[/tex]

substituting values

       [tex]n = \frac{80 *10^{-3} * 2780 *10^{-9}}{6.626 *10^{-34} * 3.0 *10^{8} }[/tex]

       [tex]n = 1.119 *10^{18} \ photons[/tex]

Given that the pulses where emitted 20 times in one second then the period of the pulse is

       [tex]T = \frac{1}{20}[/tex]

      [tex]T = 0.05 \ s[/tex]

Hence the average power of photons in one 80-mJ pulse during 1 s is mathematically represented as

       [tex]P = \frac{E}{T}[/tex]

substituting values

       [tex]P = \frac{ 80 *10^{-3}}{0.05}[/tex]

        [tex]P = 1.6 \ W[/tex]

Answer:

a) 360.7 J/s

b) 16.23 °C

c) 34.48 g

Explanation:

The mass of the person = 80 kg

The person is a perfect emitter, ε = 1

surface area of the person = 2.5 m^2

a) If he emits radiation at 37 °C, [tex]T_{out}[/tex] = 37 + 273 = 310 K

and receives radiation at 13 °C, [tex]T_{in}[/tex] = 13 + 273 = 286 K

Rate of energy loss E = Aεσ([tex]T^{4} _{out}[/tex] - [tex]T^{4} _{in}[/tex] )

where σ = 5.67 x 10^-8 J/(s m^2 K^4)

substituting values, we have

E = 2.5 x 1 x 5.67 x 10^-8 x ([tex]310^{4}[/tex] - [tex]286^{4}[/tex]) = 360.7 J/s

b) If they have specific heat about equal to that of water = 1 Cal/kg-°C

but 1 Cal = 1 kcal = 10^3 cal

specific heat of person is therefore = 10^3 cal/kg-°C

heat loss = 360.7 J/s = 360.7 x 3600 = 1298520 J/hr

heat lost in 1 hour = 1 x 1298520 = 1298520 J

This heat lost = mcΔT

where ΔT is the temperature fall

m is the mass

c is the specific heat equivalent to that of water

the specific heat is then = 10^3 cal/kg-°C

equating, we have

1298520 = 80 x 10^3 x ΔT

1298520 = 80000ΔT

ΔT = 1298520/80000 = 16.23 °C

c) 1298520 J = 1298520/4184 = 310.35 Cal

density of fat = 9 Cal/g

gram of fat = 310.35/9 = 34.48 g

Answer:

The velocity is 40 ft/sec.

Explanation:

Given that,

Force = 3200 lb

Angle = 30°

Speed = 64 ft/s

The resistive force with magnitude proportional to the square of the speed,

[tex]F_{r}=kv^2[/tex]

Where, k = 1 lb s²/ft²

We need to calculate the velocity

Using balance equation

[tex]F\sin\theta-F_{r}=m\dfrac{d^2v}{dt^2}[/tex]

Put the value into the formula

[tex]3200\sin 30-kv^2=m\dfrac{d^2v}{dt^2}[/tex]

Put the value of k

[tex]3200\times\dfrac{1}{2}-v^2=m\dfrac{d^2v}{dt^2}[/tex]

[tex]1600-v^2=m\dfrac{d^2v}{dt^2}[/tex]

At terminal velocity [tex]\dfrac{d^2v}{dt^2}=0[/tex]

So, [tex]1600-v^2=0[/tex]

[tex]v=\sqrt{1600}[/tex]

[tex]v=40\ ft/sec[/tex]

Hence, The velocity is 40 ft/sec.

Answer:

E = 1336.71875 J

Explanation:

We are given;. Capacitance of Capacitor 1; C1 = 10.7 µF

Capacitor 2; C2 = 23.0 µF

Capacitor 3; C3 = 29.3 µF

Supply voltage;V = 125 V

Formula for capacitance in series is;

Capacitors in series circuit: C(eq) = 1/C(1) +1/C(2) +1/C(3) .......

Thus, equivalent capacitance is;

C(eq) = (1/10.7) + (1/23) + (1/29.3) = 0.1711 µF = 0.1711 × 10^(6) F

Now, the formula for maximum energy stored is;

E = ½ × C(eq) × V²

E = ½ × 0.1711 × 10^(-6) × 125²

E = 1336.71875 J