the atomic number of a nucleus increases during which nuclear reactions

Answer:

Explanation:

dipole moment = qs = q x s

= charge x charge separation

charge = q

separation between charge = s

half separation l = s / 2

dipole has two charges + q and - q separated by distance s .

Potential at distance x along x axis due to + q

[tex]v_1=\frac{1}{4\pi \epsilon } \times\frac{q}{x-l}[/tex]

Potential at distance x along x axis due to - q

[tex]v_2=\frac{1}{4\pi \epsilon } \times\frac{-q}{x+l}[/tex]

Total potential

v = v₁ + v₂

[tex]v=\frac{1}{4\pi \epsilon } \times( \frac{q}{x-l}-\frac{q}{x+l})[/tex]

[tex]v=\frac{1}{4\pi \epsilon } \times\frac{2ql}{x^2-l^2}[/tex]

[tex]v=\frac{1}{4\pi \epsilon } \times\frac{qs}{x^2-(\frac{s}{2}) ^2}[/tex]

Potential at distance y along y axis due to + q

[tex]v_1=\frac{1}{4\pi \epsilon } \times\frac{qs}{(y^2+\frac{s^2}{4})^\frac{1}{2} }[/tex]

Potential at distance y along y axis due to - q

[tex]v_1=\frac{1}{4\pi \epsilon } \times\frac{-qs}{(y^2+\frac{s^2}{4})^\frac{1}{2} }[/tex]

Total potential

v = v₁ + v₂

[tex]v= 0[/tex]

Answer:

  K = 1.6 10⁻¹⁵ J

Explanation:

In an electron microscope, electrons are used to form images, these electrons are accelerated in electric fields so that they have a kinetic energy that allows obtaining a good amplification with the microscope.

electrical potential energy is converted to kinetic energy

                U = K

                e V = ½ m v²

                v = √2eV /m

the wavelength of these electrons we obtain from the de Broglie equation

                λ = h / p

p = mv

               λ = h / mv

               λ = h / mra 2eV / m

               λ = h / ra 2eVm

where we can see that as the potential energy increases, it electrifies the shorter the wavelength of the electrons and consequently the greater the magnification of the microscope

in general these microscopes use from 10000X onwards therefore for this saponification

                K = e V

               K = 1.6 10⁻¹⁹ 10000

               K = 1.6 10⁻¹⁵ J

Answer:

 P = 2923.89 W  

Explanation:

Power is

     P = F v

for which we must calculate the force, let's use Newton's second law, let's set a coordinate system with a flat parallel axis and the other axis (y) perpendicular to the plane

X Axis  

         F - Wₓ = 0

         F = Wₓ

Y Axis

         N -  [tex]W_{y}[/tex] = 0

let's use trigonometry for the components of the weight

         sin 6 = Wₓ / W

         cos 6 = W_{y} / W

         Wₓ = W sin 6

         W_{y} = W cos 6

          F = mg cos 6

          F = 75 9.8 cos 6

          F = 730.97 N

let's calculate the power

        P = F v

        P = 730.97 4.0

        P = 2923.89 W

Answer: I0*0.853

Explanation:

Ok, the Malus's law says that:

If you have light polarized along a given line with an intensity I0, and it passes through a polaroid which axis of polarization forms an angle θ with respect to the polarization of the light, then the intensity of the resulting beam is:

I(θ) = I0*cos^2(θ)

For example, if the axis of the polaroid is exactly the same as the axis of polarization of the light beam that will impact it, then we have θ = 0°, and the equation above says that the intensity of the beam will not change.

In this particular case, we have that the intensity of the light is I0, and the angle is θ = 22.5°

Then:

I(22.5°) = I0*cos^2(22.5°) = I0*0.853

Answer:

no, the truck is not overloaded

Explanation:

The computation is shown below;

Let us assume the mass of the loan in the second truck be M

So, the equation is as follows

{(Mass + M) × second truck × 1000 ÷ 3,600} = {(Mass + M + mass + first truck) × Pair moves away  × 1,000 ÷ 3,600}

{(5500 + M) × 64 × 1,000 ÷ 3,600 = {(5,500 + M + 5,500 + 3,900) × 44 × 1,000 ÷ 3,600}

(5500 + M) × 64 = (14,900 + M) × 44

352,000 + 64 M = 655,600 + 44 M

After solving this

M = 15,180 kg

Therefore the second truck is not overloaded

Answer:

Option 2 (observing, measuring, testing, and explaining their ideas) is the correct choice.

Explanation:

The other three choices have no relation to a particular task. So the option given here is just the right one.

Answer:

The acceleration in the block is 2.1 m/s²

Explanation:

Given that,

Mass = 50 kg

Angle = 54°

Force = 40 N

Coefficient of friction = 0.33

We need to calculate the acceleration in the block

Using balance equation

[tex]F_{net}=F_{f}-F\cos\theta[/tex]

[tex]ma=\mu mg\sin\theta-F\cos\theta[/tex]

[tex]a=\dfrac{\mu mg\sin\theta-F\cos\theta}{m}[/tex]

Put the value into the formula

[tex]a=\dfrac{0.33\times50\times9.8\sin54-40\cos54}{50}[/tex]

[tex]a=2.1\ m/s^2[/tex]

Hence, The acceleration in the block is 2.1 m/s²

Answer:

20.96 m/s^2 (or 21)

Explanation:

Using the formula (final velocity - initial velocity)/time = acceleration, we can plug in values and manipulate the problem to give us the answer.

At first, we know a car is going 8 m/s, that is its initial velocity.

Then, we know the acceleration, which is 1.8 m/s/s

We also know the time, 7.2 second.

Plugging all of these values in shows us that we need to solve for final velocity. We can do so by manipulating the formula.

(final velocity - initial velocity) = time * acceleration

final velocity = time*acceleration + initial velocity

After plugging the found values in, we get 20.96 m/s/s, or 21 m/s

Answer:

The force of the radiation on the surface is 3.33 x 10⁻¹⁰ N

Explanation:

Given;

intensity of light, I = 1kw/m² = 1000 W/m²

area of the surface, A = 1 cm² = 1 x 10⁻⁴ m²

Since the light is completely absorbed, the force of the radiation is given by;

F = P/c

where;

c is the speed of light = 3 x 10⁸ m/s

But P = IA

F = IA /c

F = (1000 X 1 X 10⁻⁴) / 3 x 10⁸

F = 3.33 x 10⁻¹⁰ N

Therefore, the force of the radiation on the surface is 3.33 x 10⁻¹⁰ N

The force of radiation will be "3.33 × 10⁻¹⁰ N"

According to the question,

Intensity of force, I = 1 kW/m² or,

                               = 1000 W/m²

Area of surface, A = 1 cm² or,

                              = 1 × 10⁻⁴ m²  

Speed of light, c = 3 × 10³ m/s

As we know the relation,

→ F = [tex]\frac{P}{c}[/tex]

or,

  P = IA

or,

  F = [tex]\frac{IA}{c}[/tex]

By substituting the values, we get

     = [tex]\frac{1000\times 1\times 10^{-4}}{3\times 10^3}[/tex]

     = 3.33 × 10⁻¹⁰ N

Thus the response above is correct.

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Answer

The capacitor should be connected in parallel as parallel connection gives the arithmetic sum of capacitance which will give a corresponding sum of energy while capacitors in series gives the sum of the reciprocal if the individual capacitance

Answer:

0.2812

Explanation:

Given that

mass of skater 1, m1 = 45 kg

mass of skater 2, m2 = 60 kg

speed of skater 1, v1 = 0.375 m/s

To attempt this question, we would be using the Law of conservation of momentum That says the momentum is constant, before and after the movement.

Thus, momentum p = mv

Law of conservation of momentum infers that,

m1v1 = m2v2

Now we proceed to substitute our values into the formula.

45 * 0.375 = 60 * v2

v2 = 16.875 / 60

v2 = 0.2812 m/s

Therefore the speed of the second skater has to be 0.2812 m/s

Answer;

a 2.00-kg body will vibrate at 0.707Hz

Answer:-7.9

Explanation:

Answer:

HELLO your question has some missing parts below are the missing parts

note: The specific heat ratio and gas constant for air are given as k=1.4 and R=0.287 kJ/kg-K respectively.

--Given Values--

Inlet Temperature: T1 (K) = 325

Inlet pressure: P1 (kPa) = 560

Inlet Velocity: V1 (m/s) = 97

Throat Area: A (cm^2) = 5.3

Pressure upstream of (before) shock: Px (kPa) = 207.2

Mach number at exit: M = 0.1

Answer: A)  match number at inlet  = 0.2683

              B)  stagnation temperature at inlet =  329.68 k

              C)  stagnation pressure = 588.73 kPa

              D) ) Throat temperature = 274.73 k

Explanation:

Determining states at several locations in the system

A) match number at inlet

= V1 / C1 = 97/ 261.427 = 0.2683

C1 = sound velocity at inlet = [tex]\sqrt{K*R*T}[/tex] = [tex]\sqrt{1.4 *0.287*10^3}[/tex]  = 361.427 m/s

v1 = inlet velocity = 97

B) stagnation temperature at inlet

     = T1 + [tex]\frac{V1 ^2}{2Cp}[/tex]  = 325 + [tex]\frac{97^2}{2 * 1.005*10^{-3} }[/tex]

stagnation temperature = 329.68 k

C) stagnation pressure

= [tex]p1 ( 1 + 0.2Ma^2 )^{3.5}[/tex]

Ma = match number at inlet = 0.2683

p1 = inlet pressure = 560

hence stagnation pressure = 588.73 kPa

D) Throat temperature

= [tex]\frac{Th}{T} = \frac{2}{k+1}[/tex]

Th = throat temperature

T = stagnation temp at inlet = 329.68 k

k = 1.4

make Th subject of the relation

Th = 329.68 * (2 / 2.4 ) = 274.73 k

Answer:

a) 5.5×10^17 Hz

b) visible light

Explanation:

Since the wavelength of the electromagnetic radiation must be about the size of the about itself, this implies that;

λ= 5.5 × 10^-10 m

Since;

c= λ f and c= 3×10^8 ms-1

f= c/λ

f= 3×10^8/5.5 × 10^-10

f= 5.5×10^17 Hz

The electromagnetic wave is visible light

Answer:

5.2791264*10¹³

Explanation:

Convert the 9 years to seconds and then multiple it by 186000

The star is 4.62 x 10¹⁶ miles away from Earth.

The speed of light is 186,000 miles per second. It takes light from a particular star approximately 9 years to reach Earth. There are 365 days in 1 year, so it takes 9 x 365 = 3285 days for light from the star to reach Earth.

The distance between the star and Earth is 3285 x 186,000 = 608,810,000 miles. In scientific notation, this is 4.62 x 10¹⁶ miles.

Here is the calculation:

distance = speed * time

distance = 186,000 miles/second * 3285 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute

distance = 608,810,000 miles

distance = 4.62 x 10¹⁶ miles

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Answer:

It does not violate the first law because the total energy taken is what is used 100J = 25J + 75J

But violates 2nd lawbecause the engine has a higher energy after doing work than the initial for e.g A cold object in contact with a hot one never gets colder, transferring heat to the hot object and making it hotter confirming the second law

Answer:

Star A has a higher surface temperature than star B.

Explanation:

The effective temperature of a star can be determined by means of its spectrum and Wien's displacement law:

[tex]T = \frac{2.898x10^{-3} m. K}{\lambda max}[/tex] (1)

Where T is the effective temperature of the star and [tex]\lambda_{max}[/tex] is the maximum peak of emission.  

A body that is hot enough emits light as a consequence of its temperature. For example, if an iron bar is put in contact with fire, it will start to change colors as the temperature increase, until it gets to a blue color, that scenario is known as Wien's displacement law. Which establishes that the peak of emission for the spectrum will be displaced to shorter wavelengths as the temperature increase and higher wavelengths as the temperature decreases.

Therefore, star A has a higher surface temperature than star B, as it is shown in equation 1 since T and [tex]\lambda max[/tex] are inversely proportional.

Answer:

[tex]\frac{di}{dt} = 7.31 \ A/s[/tex]

Explanation:

From the question we are told that  

     The  number of turns is  [tex]N = 450 \ turns[/tex]

      The  radius is  [tex]r = 1.17 \ cm = 0.0117 \ m[/tex]

       The  position from the center consider is  x =  3.45 cm  =  0.0345 m

       The  induced emf is  [tex]e = 8.20 *10^{-6} \ V/m[/tex]

Generally according to Gauss law

        [tex]\int\limits { e } \, dl = \mu_o * N * \frac{di}{dt } * A[/tex]

=>    [tex]e * 2\pi x = \mu_o * N * \frac{d i }{dt } * A[/tex]

Where A is the  cross-sectional area of the solenoid which is mathematically represented as

                [tex]A = \pi r ^2[/tex]

=>      [tex]e * 2\pi x = \mu_o * N * \frac{d i }{dt } * \pi r^2[/tex]

=>       [tex]\frac{di}{dt} = \frac{2e * x }{\mu_o * N * r^2}[/tex]ggl;

Here  [tex]\mu_o[/tex] is the permeability of free space with value

          [tex]\mu_o = 4\pi * 10^{-7} \ N/A^2[/tex]

=>     [tex]\frac{di}{dt} = \frac{2 * 8.20*10^{-6} * 0.0345 }{ 4\pi * 10^{-7} * 450 * (0.0117)^2}[/tex]

=>      [tex]\frac{di}{dt} = 7.31 \ A/s[/tex]

The value of di/dt from the given values of the solenoid electric field is;

di/dt = 7.415 A/s

We are given;

Number of turns; N = 450 per m

Radius; r = 1.17 cm = 0.0117 m

Electric Field; E = 8.2 × 10⁻⁶ V/m

Position of electric field; r' = 3.45 cm = 0.0345 m

According to Gauss's law of electric field;

∫| E*dl | = |-d∅/dt |

Now, ∅ = BA = μ₀niA

where;

n is number of turns

i is current

A is Area

μ₀ = 4π × 10⁻⁷ H/m

Thus;

E(2πr') = (d/dt)(μ₀niA)  (negative sign is gone from the right hand side because we are dealing with magnitude)

Since we are looking for di/dt, then we have;

E(2πr') = (di/dt)(μ₀nA)

Making di/dt the subject of the formula gives;

di/dt = E(2πr')/(μ₀nA)

Plugging in the relevant values gives us;

di/dt = (8.2 × 10⁻⁶ × 2 × π × 0.0345)/(4π × 10⁻⁷ × 450 × π × 0.0117²)

di/dt = 7.415 A/s

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Answer:

4.245s

Explanation:

Given that,

Hypothetical value of speed of light in a vacuum is 18 m/s

Speed of the car, 14 m/s

Time given is 6.76 s, and we're asked to find the observed time, T

The relationship between the two times can be given as

T = t / √[1 - (v²/c²)]

The missing variable were looking for is t, and we can find it if we rearrange the formula and make t the subject

t = T / √[1 - (v²/c²)]

And now, we substitute the values and insert into the equation

t = 6.76 * √[1 - (14²/18²)]

t = 6.76 * √[1 - (196/324)]

t = 6.76 * √(1 - 0.605)

t = 6.76 * √0.395

t = 6.76 * 0.628

t = 4.245 s

Therefore, the time the driver measures for the trip is 4.245s

Answer:

v = - 14.08 m / s

Explanation:

The definition of center of mass is

        [tex]x_{cm}[/tex] = 1 /M  ∑sun [tex]x_{i} m_{i}[/tex]

where M is the total mass of the system and [tex]x_{i}[/tex] and [tex]m_{i}[/tex] are the position and mass of each component.

The velocity of the center of mass can be found by deriving this expression with respect to time

         [tex]v_{cm}[/tex] = 1 / M ∑ m_{i} [tex]v_{i}[/tex] vi

let's find the total mass

          M = m₁ + m₂ + m₃ + m₄

          M = 1.45 + 2.81 +3.89 + 5.03

          m = 13.18 kg

let us substitute in the velocity of the center of mass [tex]v_{cm}[/tex] = 0

          0 = 13.18 (m₁ v₁ + m₂ v₂ + m₃v₃ + m₄v₄)

          v₄ = - (m₁ v₁ + m₂ v₂ + m₃v₃) / m₄

let's substitute the given values

v₄ = -[1.45 (6.09 +0.299 t) +2.81 (7.83 + 0.357t) +3.89 (8.09 + 0.405 t)] / 5.03

They ask us for the calculations for a time t = 2.83 s

          v₄ = - [8.8305 + 1.227 + 22.00 + 2.839 + 31.47 +4.4585] / 5.03

          v = - 14.08 m / s

The velocity of the particle 4 at time, t = 2.83 s, is -14.1 m/s.

The given parameters;

[tex]m_1 = 1.45 \ kg, \ \ v_1(t) = (6.09 \ m/s) + (0.299 \ m/s^2)\times t\\\\m_2 = 2.81 \ kg, \ \ v_2(t) = (7.83 \ m/s) + (0.357 \ m/s^2)\times t \\\\m_3 = 3.89 \ kg, \ \ v_3(t) = (8.09 \ m/s) + (0.405 \ m/s^2)\times t\\\\m_4 = 5.03 \ kg[/tex]

The velocity of the center mass of the particles is calculated as;

[tex]M_{cm}V_{cm} = m_1v_1 + m_2 v_2 + m_3v_3 + m_4v_4\\\\V_{cm} = \frac{m_1v_1 + m_2 v_2 + m_3v_3 + m_4v_4}{M_{cm}} \\\\0 = \frac{m_1v_1 + m_2 v_2 + m_3v_3 + m_4v_4}{M_{cm}}\\\\m_1v_1 + m_2 v_2 + m_3v_3 + m_4v_4 = 0\\\\m_4v_4 = -(m_1v_1 + m_2 v_2 + m_3v_3)\\\\v_4 = \frac{-(m_1v_1 + m_2 v_2 + m_3v_3)}{m_4}[/tex]

The velocity of particle 1 at time, t = 2.83 s;

[tex]v_1 = 6.09 \ + \ 0.299\times 2.83\\\\v_1 = 6.94 \ m/s[/tex]

The velocity of particle 2 at time, t = 2.83 s;

[tex]v_2 = 7.83\ + \ 0.357\times 2.83\\\\v_2 = 8.84 \ m/s[/tex]

The velocity of particle 3 at time, t = 2.83 s;

[tex]v_3 = 8.09\ + \ 0.405 \times 2.83\\\\v_3 = 9.24 \ m/s[/tex]

The velocity of the particle 4 at time, t = 2.83 s;

[tex]v_4 = \frac{-(m_1v_1 + m_2v_2 + m_3v_3)}{m_4} \\\\v_4 = \frac{-(1.45\times 6.94\ + \ 2.81\times 8.84\ + \ 3.89 \times 9.24)}{5.03} \\\\v_4 = -14 .1 \ m/s[/tex]

Thus, the velocity of the particle 4 at time, t = 2.83 s, is -14.1 m/s.

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Answer:

B.

Explanation:

The water collects in the ocean; it is then evaporated by the sun. After evaporation the water turns into water vapor, it then condenses to form clouds.

The ocean water prior to the part of the water cycle should be option B.

The ocean water should be collected back in the ocean prior to the part of the water cycle.

Because this should be done when it is evaporated by the sun.  When the evaporation is done so the water should be transformed into water vapor.

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Answer:

The direction of the magnetic field on point P, equidistant from both wires, and having equal magnitude of current flowing through them will be pointed perpendicularly away from the direction of the wires.

Explanation:

Using the right hand grip, the direction of the magnet field on the wire M is counterclockwise, and the direction of the magnetic field on wire N is clockwise. Using this ideas, we can see that the magnetic flux of both field due to the currents of the same magnitude through both wires, acting on a particle P equidistant from both wires will act in a direction perpendicularly away from both wires.

Answer:

300 W

Explanation:

power of each bulb P = 75 W

voltage in the circuit = 120 V

we know that electrical power P = IV    ....1

and V = IR

we can also say that I = V/R

substituting for I in  equation 1, we have

P = [tex]V^{2}/R[/tex]    ....2

The total total power in the circuit = 75 x 2 = 150 W

from equation 2, we have

150 = [tex]120^{2} /R[/tex]

R = [tex]120^{2}/150[/tex] = 96 Ω    this is the resistance of the whole circuit.

This resistance is due to the two light bulbs, for each light bulb since they are arranged in series

R = 96/2 = 48 Ω

From P =  [tex]V^{2}/R[/tex]  

for each light bulb, power is

P = [tex]120^{2} /48[/tex] = 300 W

Answer:

In a tuning fork, two basic qualities of sound are considered, they are

1) The pitch of the waveform: This pitch depends on the frequency of the wave generated by hitting the tuning fork.

2) The loudness of the waveform: This loudness depends on the intensity of the wave generated by hitting the tuning fork.

Hitting the tuning fork harder will make it vibrate faster, increasing the number of vibrations per second. The number of vibration per second is proportional to the frequency, so hitting the tuning fork harder increase the frequency. From the explanation on the frequency above, we can say that by increasing the frequency the pitch of the tuning fork also increases.

Also, hitting the tuning fork harder also increases the intensity of the wave generated, since the fork now vibrates faster. This increases the loudness of the tuning fork.

Answer:

2/5 m/s

Explanation:

There are two vectors  v and w . Let θ be angle b/w the two vector.

[tex]cos\theta =\frac{\overleftarrow{v}\cdot \overleftarrow{w}}{\left | v \right |\left | w \right |}\\=\frac{6-4}{\sqrt(2^2+1^2)\sqrt(3^2+4^2)} =\frac{2}{5\sqrt(5)}[/tex]

velocity of the ball in direction of the the wind

[tex]\left | vcos\theta \right |\\\left | v \right |cos\theta\\\sqrt(2^2+1^2)\frac{2}{5\sqrt(5)} = \frac{2}{5}[/tex]

The size of the velocity of the ball in the direction of the wind is 2/5 ms.

Since there are two vectors v and w

Also, here we assume θ be angle b/w the two vector.

So

Cos θ = 6-4 / √(2^2 + 1^2) √(3^2 + 4^2)

= 2/5√5

Now the velocity of the ball should be

= √(2^2 + 1^2) 2 ÷ 5√(5)

= 2 /5

hence, The size of the velocity of the ball in the direction of the wind is 2/5 ms.

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Answer:

At 3 meter distance, the per-second count is 222.22 and at a 10 meter distance, the per-second count is 20.

Explanation:

The number of particles (N)  counts are inversely proportional to the distance between the source and the detector.  

By using the below formula we can find the number of counts.

[tex]N2 = \frac{(D1)^2}{(D2)^2} \times N1 \\N1 = 2000 \\D 1 = 1 \ meter \\D2 = 3 \\[/tex]

The number of count per second, when the distance is 3 meters.

[tex]= \frac{1}{3^2} \times 2000 \\= 222.22[/tex]

Number of count per second when the distance is 10 meters.

[tex]= \frac{1}{10^2} \times 2000 \\= 20[/tex]

Answer:   2

Explanation:

1/2=1/1 +1/x

x=-2

magnification= 2/1

magnification=2

Answer:

F = 4212 N

Explanation:

Given that,

Mass of a car, m = 1300 kg

Speed of car on the road is 9 m/s

Radius of curve, r = 25 m

We need to find the magnitude of the unbalanced force that steers the car out of its natural straight-  line path. The force is called centripetal force. It can be given by :

[tex]F=\dfrac{mv^2}{r}\\\\F=\dfrac{1300\times 9^2}{25}\\\\F=4212\ N[/tex]

So, the force has a magnitude of 4212 N

Answer:

Explanation:

Concave mirrors is otherwise known as converging mirrors: These are mirrors that are caved inwards (reflecting surface is on the outside curved part). It is called a converging mirror due to the fact that light converges to a point when it strikes and reflects from the surface of the mirror. This type of mirror is used to focus light; parallel rays that are directed towards it will be concentrated to a point.

For a concave mirror to reflect light with properties that are the same as a spotlight (directed light rays parallel to each other), one has to consider its property to gather light to a point after reflecting. Meaning that, we can achieve the spotlight by locatng the point where the rays will be parallel, this point is called the focal point.

Therefore, the light bulb should be placed at the focal point of the mirror.

Answer:

77.96dB

Explanation:

Recall that decibels are a unit of measuring intensity of sound, and depend on the logarithm of the intensity

the intensity, measured in decibels is given by:

I(db)=10log(I/I0)

I is the intensity in MKS units; I0 is the threshold intensity for human hearing (10^-12 W/m^2)

Thus, if the two sounds together have a dB of 81, we know:

81=10log(I/I0)

using the data above, we can find the intensity of the two sounds to be

0.000125 W/m^2

therefore, one firecracker has an intensity half of that, or 0.0000625W/m^2

now use this value to find the dB of one firecracker:

I(dB0=10log(0.0000625/10^-12)=77.96dB