We are asked to determine the continuous growth rate. To do that we will use the following function:
[tex]P(t)=P_0e^{kt}[/tex]Where "P0" is the initial population, "k" is the growth rate, and "t" is time. Replacing the initial population of 5 we get:
[tex]P(t)=5e^{kt}[/tex]Now we are told that the population is 13 when the time is 3 hours. Replacing we get:
[tex]13=5e^{3k}[/tex]Now we solve for "k". First, by dividing both sides by 5:
[tex]\frac{13}{5}=e^{3k}[/tex]Now we take natural logarithm to both sides:
[tex]\ln (\frac{13}{5})=\ln (e^{3k})[/tex]Now we use the following property of logarithms:
[tex]\ln x^y=y\ln x[/tex]Applying the property:
[tex]\ln (\frac{13}{5})=3k\ln e[/tex]We have that the value of ln(e) is 1, therefore:
[tex]\ln (\frac{13}{5})=3k[/tex]Now we divide both sides by 3:
[tex]\frac{1}{3}\ln (\frac{13}{5})=k[/tex]Solving the operation we get:
[tex]0.319=k[/tex]Therefore, the growth rate is 0.319.
What are the two most important factors in determining if a force is doing physics work?
The important factors in determining if a force is doing physics work include
1) The amount or magnitude of the force being applied
2) The displacement caused by the applied force
Hence,
Work = force x displacement
A bullet of mass 18.8 grams is fired with a speed of 399 meters per second toward a wood block of mass 277 grams initially at rest on a very smooth surface. What is the change in momentum of the bullet if it ricochets in the opposite direction with a speed of 386 meters per second? The answer must be in 3 significant digits.
Given data
*The given mass of the bullet is m = 18.8 g = 0.0188 kg
*The bullet is moving at a speed is u = 399 m/s
*The given final speed of the bullet is v = -386 m/s
*The mass of the wooden block is M = 277 g = 0.277 kg
The formula for the change in momentum is given as
[tex]\begin{gathered} \Delta p=mv_{}-mu \\ =m(v_{}-u_{}) \end{gathered}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} \Delta p=0.0188(-386-399) \\ =-14.758\text{ kg.m/s} \end{gathered}[/tex]Hence, the change in momentum is -14.758 kg.m/s
Amanda's Coffee Shop makes a blend that is a mixture of two types of coffee. A coffee costs Amanda $5.60 per pound, and type B coffee costs $4.55 per pound. This month, Amanda made 141 pounds of the blend, for a total cost of $728.70. How many pounds of type B coffee did she use?
We are given that Amanda made 141 pounds of coffee. If "x" is the pounds of type A coffee and "y" is the amount of type b coffee then we can write this mathematically as:
[tex]x+y=141,(1)[/tex]We are also given that the cost of type A is $5.6 per pound and that the cost of type B is $4.55 per pound and that the total cost is $728.70, this can be written mathematically as:
[tex]5.6x+4.55y=728.7,(2)[/tex]Now, we solve for "x", first by subtracting "y" from both sides:
[tex]y=141-x[/tex]Now, we substitute the value of "y" in equation (2):
[tex]5.6x+4.55(141-x)=728.7[/tex]Now, we apply the distributive property in the parenthesis:
[tex]5.6x+641.55-4.55x=728.7[/tex]Now, we add like terms:
[tex]1.05x+641.55=728.7[/tex]Now, we subtract 641.55 from both sides:
[tex]\begin{gathered} 1.05x=728.7-641.55 \\ 1.05x=87.15 \end{gathered}[/tex]Now, we divide both sides by 1.05:
[tex]x=\frac{87.15}{1.05}[/tex]solving the operations:
[tex]x=83[/tex]Now, we substitute the value of "x" in equation (1):
[tex]\begin{gathered} y=141-83 \\ y=58 \end{gathered}[/tex]Therefore, the amount of coffee type A is 83 pounds and type B is 58 pounds.
A ball is moving at 5.0 m/s and has a mass of 3.0 kg. It strikes a second ball with a mass of 4.0 kg that is sitting
motionless. What is the velocity of the second ball if the first ball stops immediately after the collision?
3.75 m/s is the velocity of the second ball if the first ball stops immediately after the collision
initial momentum=final momentum
m1v1=m2v2
3×5=4×v2
15=4v2
v2=15/4
v2=3.75 m/s
"The rate at which an item changes its position" is described by a vector number called velocity. Imagine someone walking swiftly, one step forward, one step back, and starting each step from the same location. Velocity is a vector quantity. Therefore, velocity is cognizant of direction. The direction must be taken into account when determining an object's velocity. A velocity of 55 miles per hour is not adequate information. It is necessary to account for the direction in order to accurately describe the object's velocity. Simply put, the direction of the velocity vector represents the motion of the object.
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!!
Answer: Maybe B or D
Explanation:
One force that has always on you is the gravitational force on you by earth what is the newtons third law paired to this forth think opposites
c. The normal force on you by earth
The Newton's third law states that, for every action there is equal and opposite reactionhe
What is a limitation to using nuclear fusion for energy?
Answer:
Explanation:
The radiation of components in a fusion reactor is not much enough for the materials to be reused or recycled within centuries
Two equally charged, 4.982 g spheres are placed with 3.173 cm between their centers. When released, each begins to accelerate at 258.312 m/s2. What is the magnitude of the charge, in micro-Coulombs, on each sphere?
Given:
The mass of the spheres is m = 4.982 g
The distance between the center of spheres is d = 3.173 cm
The acceleration is a = 258.312 m/s^2.
To find the magnitude of charge in micro Coulomb on each sphere.
Explanation:
According to Newton's second law, the force will be
[tex]F\text{ =ma}[/tex]According to Coulomb's law, the force will be
[tex]F=\frac{kq^2}{r^2}[/tex]Here, k is the Coulomb's constant whose value is
[tex]k=9\times10^9\text{ N m}^2\text{ /C}^2[/tex]On equating the forces, the charge will be
[tex]\begin{gathered} ma=\frac{kq^2}{r^2} \\ q=\sqrt{\frac{mar^2}{k}} \end{gathered}[/tex]On substituting the values, the magnitude of charge will be
[tex]\begin{gathered} q=\sqrt{\frac{(4.982\times10^{-3})\times258.312\times(3.173\times10^{-2})^2}{9\times10^9}} \\ =3.79\text{ }\times10^{-7}\text{ C} \\ =0.379\text{ }\times10^{-6}\text{ C} \\ =0.379\text{ }\mu C \end{gathered}[/tex]The magnitude of the charge of each sphere is 0.379 microCoulomb
How much force must I lift with to lift a 30kg object off the ground?
The force required to lift the object is 294 N.
Given data:
The mass of object is m=30 kg.
The force applied to lift an object will be equal to the weight of the object.
The weight of the object can be calculated as,
[tex]\begin{gathered} W=mg \\ W=(30)(9.8) \\ W=294\text{ N} \end{gathered}[/tex]The weight of the object is 294 N; therefore, the force required to lift the object is 294 N.
In which of the following processes does the Sun play little to no role inproviding energy?A. Plate tectonicsB. Ocean currentsC. SeasonsD. Trophic levels
Plate tectonics are influenced by the earth's mantle and its variations, therefore, the role of the sun is less in comparison with the other processes described.
When the length of a pendulum is doubled, its frequency will be cut in half. Is this true or false?
The period T of a pendulum with length L is given by the formula:
[tex]T=2\pi\cdot\sqrt[]{\frac{L}{g}}[/tex]Where g is the acceleration of gravity:
[tex]g=9.81\frac{m}{s^2}[/tex]If the length of the pendulum is doubled, the period will be:
[tex]\begin{gathered} T^{\prime}=2\pi\cdot\sqrt[]{\frac{2L}{g}} \\ =\sqrt[]{2}\times2\pi\cdot\sqrt[]{\frac{L}{g}} \\ =\sqrt[]{2}\times T \end{gathered}[/tex]On the other hand, the frequency is the reciprocal of the period. Then:
[tex]\begin{gathered} f=\frac{1}{T} \\ f^{\prime}=\frac{1}{T^{\prime}}=\frac{1}{\sqrt[]{2}\times T}=\frac{1}{\sqrt[]{2}}\times\frac{1}{T}=\frac{1}{\sqrt[]{2}}\times f \end{gathered}[/tex]Then, if the length of the pendulum is doubled, the frequency is cut by a factor of 1/√2:
[tex]f^{\prime}=\frac{1}{\sqrt[]{2}}\times f[/tex]This is not the same as if the frequency was cut by a factor of 1/2.
Therefore, the statement is:
[tex]\text{False}[/tex]Why is the sand on a dry beach not a fluid but when a wave comes in and out the sand does become a fluid and your feet sink when standing on it?
When the sand is mixed with the water, it will form a quicksand. It behaves like a solution, and when the water is removed from the sand, it will act as a solute.
When our feet sink into the sand, our movements will cause you to dig yourself deeper into it.
Two equally charged, 3.699 g spheres are placed with 3.592 cm between their centers. When released, each begins to accelerate at 297.727 m/s2. What is the magnitude of the charge on each sphere? Express your answer in microCoulombs.
Given:
The mass of the first sphere is: m1 = 3.699 g.
The mass of the second sphere is: m2 = 3.699 g
The distance between their centers is: d = 3.592 cm
The acceleration of each sphere is: a = 297.727 m/s^2
To find:
Since the spheres are identical in their masses, the force on each sphere is:
[tex]F=ma[/tex]Substitute the values in the above equation and simplify it, we get:
[tex]\begin{gathered} F=3.699\text{ g}\times297.727\text{ m/s}^2 \\ \\ F=3.699\text{ g }\times\frac{1\text{ kg}}{1000\text{ g}}\times297.727\text{ m/s}^2 \\ \\ F=3.699\times10^{-3}\text{ kg}\times297.727\text{ m/s}^2 \\ \\ F=1.1012\text{ N} \end{gathered}[/tex]This is the force experienced by each sphere and is has a magnitude equal to the magnitude of the electrostatic force.
The electrostatic force of attraction or repulsion between two charges is given by:
[tex]F=\frac{1}{4\pi\epsilon_0}\frac{q^2}{r^2}[/tex]Substitute the values in the above equation and simplify it, we get:
[tex]\begin{gathered} 1.1012\text{ N}=\frac{9\times10^9\text{ N}\cdot m^2\text{/C}^2\times q^2}{(3.592\text{ cm})^2} \\ \\ 1.1012\text{ N}=\frac{9\times10^9\text{ N}\cdot m^2\text{ / C}^2\times q^2}{(3.592\text{ cm}\times\frac{1\text{ m}}{100\text{ cm}})^2} \\ \\ 1.1012\text{ N}=\frac{9\times10^9\text{ N}\cdot m^2\text{ /C}^2\times q^2}{(3.592\times10^{-2})^2\text{ m}^2} \\ \\ 1.1012\text{ N}=\frac{9\times10^9\text{ N.m}^2\text{/C}^2\times q^2}{1.2902\times10^{-3}\text{ m}^2\text{ }} \\ \\ 1.1012\text{ N}=6.9757\times10^{12}\text{ N/C}^2\times q^2 \\ \\ \end{gathered}[/tex]Rearranging the above equation and simplify it, we get:
[tex]\begin{gathered} q^2=\frac{1.1012\text{ N}}{6.9757\times10^{12}\text{ N/C}^2} \\ \\ q=\sqrt{1.5786\times10^{-13}\text{ C}^2} \\ \\ q=0.3973\times10^{-6}\text{ C} \\ \\ q=0.3973\text{ }\mu\text{C} \end{gathered}[/tex]Final answer:
The magnitude of the charge on each sphere is 0.3973 microcolumns.
I need help filling out the acceleration for gravity due to the numbers in this chart
In order to calculate the acceleration of gravity, we can use the free fall formula:
[tex]d=\frac{gt^2}{2}\to g=\frac{2d}{t^2}[/tex]Where d is the distance travelled and t is the time.
So for each distance in the chart, we have:
[tex]\begin{gathered} d=0.2\colon \\ g=\frac{0.4}{0.184^2}=11.81 \\ \\ d=0.4\colon \\ g=\frac{0.8}{0.258^2}=12.02 \\ \\ d=0.6\colon \\ g=\frac{1.2}{0.4^2}=7.5 \\ \\ d=0.8\colon \\ g=\frac{1.6}{0.236^2}=28.73 \\ \\ d=1\colon \\ g=\frac{2}{0.33^2}=18.37 \end{gathered}[/tex](All gravity units in m/s²)
Now, calculating the average, we have:
[tex]g=\frac{11.81+12.02+7.5+28.73+18.37}{5}=15.69[/tex]Finally, calculating the percent error, we have:
[tex]\text{Percent error}=\frac{|9.81-15.69|}{9.81}=0.5994=59.94\text{\%}[/tex]Point charges create equipotential lines that are circular around the charge (in the plane of the paper). What is the potential energy, in nJ, of a 1 nC charge located 2.82 m from a 2 nC charge ?
The potential energy U of a system formed by two point charges separated a distance r is:
[tex]U=k\frac{q_1q_2}{r}[/tex]Where k is Coulomb's Constant:
[tex]k=8.98755\times10^9N\frac{m^2}{C^2}[/tex]Repace q1=1nC, q2=2nC and r=2.82m to find the potential energy of the system:
[tex]\begin{gathered} U=k\frac{q_1q_2}{r} \\ \\ =(8.98755\times10^9N\frac{m^2}{C^2})\times\frac{(1\times10^{-9}C)(2\times10^{-9}C)}{2.82m} \\ \\ =6.3741489...\times10^{-9}Nm \\ \\ \approx6.37nJ \end{gathered}[/tex]Therefore, the potential energy of the system is approximately 6.37 nanoJoules.
A force gives energy to an object and that energy can:set the object in motion.stop its motion.change the speed and direction of its motion.All of the choices are correct.
To find:
Which of the given statements is the correct answer?
Explanation:
The work done is the measure of the transfer of energy through the application of force.
The force thus applied can either change the state of motion of the object or the speed and direction of the motion.
That is, when a force is applied to an object, the force can bring the object in motion to rest or set the object in rest, into motion. Or it can also change the speed or direction of motion of the object.
Final answer:
The correct answer is option D, All of the choices are correct.
usWhich of the following X-Y tables agrees withthe information in this problem?A missile is moving 1810 m/s at a 20.0° angle. It needsto hit a target 29,500 m away in a 65.0° direction in9.20 s. What acceleration must its engine produce?хYB)хYC)хYA)ViVE1700619V;17006191700619<<??V?a??aa?AX12500 | 26700Ax 12500 26700Ax 12500 26700t9.209.20t9.209.20t8.653.15
The given value of the distance at which the target is present is
[tex]d=29500\text{ m}[/tex]The distance along the x-axis is,
[tex]\begin{gathered} d_x=d\cos (65^{\circ}) \\ d_x=29500\times\cos (65^{\circ}) \\ d_x=12467 \\ d_x\approx12500\text{ m} \end{gathered}[/tex]As in the given tables, the value of the distance and time 9.2 s is correct in first two only. So, the third one is not the correct option.
From the given question, the value of the acceleration is to be found.
The question mark arrows are on the acceleration is only on the b table.
Hence, Table B agrees with the information in the given situation.
What is the acceleration of a car that starts at rest and achieves a final velocity of 33.5 m/s in a time of 12 seconds?
Variables we are given and that we know:
vi: initial velocity; vi = 0 m/s
vf: final velocity; vf = 33.5 m/s
t: time; t = 12 s
We need to find a: acceleration
We can use the formula:
vf = vi + a*t
Let's substitute the values we know:
33.5 = 0 + a*12
33.5 = 12a
Let's solve for a:
a = 33.5/12
a = 2.7917 m/s^2
D. O499.917 JE. O 1358.602 J4. An object of mass 5 kg is sliding downa friction less inclined plane of length3 m that makes an angle of10 deg. Calculate its speed just before it hits the ground. (1 point)A. 03.195 m/sB. O 1.958 m/sC. O5.58 m/sD. O2.525 m/sE. 04.225 m/s5. A roller coaster extends to the groundfrom a height of 39 m (point A) and then risesAn obiect of mass 12 kg
Given
Mass of the object, m=5 kg
Length of the inclined plane, s=3m
Angle of inclination,
[tex]\theta=10^o[/tex]To find
Calculate its speed just before it hits the ground.
Explanation
Here the acceleration is
[tex]\begin{gathered} a=gsin\theta \\ \Rightarrow a=9.8sin10^o \end{gathered}[/tex]The initial velocity is zero.
So the final velocity is
[tex]\begin{gathered} v=\sqrt{2as} \\ \Rightarrow v=\sqrt{2\times9.8sin10^o\times3} \\ \Rightarrow v=3.19\text{ m/s} \end{gathered}[/tex]Conclusion
The velocity before it hit the ground, A.3.19 m/s
In the table below place the different forms of electromagnetic radiation and visible light in order of lowest energy to highest energy
Answer:
Step-by-step explanation:
The electromagnetic spectrum is the range of all types of EM radiation. I will write the electromagnetic spectrum from lowest energy/longest wavelength to highest energy/shortest wavelength:
*Visible light refers to the visible region of the electromagnetic spectrum, that is the range of wavelengths that trigger brightness and color perception in humans. It lies between Ultraviolet and Infrared radiation
How much work is done to transfer 0.15 C of charge through a potential difference of 9.0 V?
Answer:
6.075J
Explanation:
The formula is 0.5X0.15X9X9. Hal of CxVxV. This results in 6.075J
A box sits on a table. The box weighs 80 N. If I attach a rope to the box and lift in the upward direction with a 25 N force, what is the normal force acting on the box
If I tie a rope to an 80N box that is resting on a table and push it upward with a 25N force, the normal force operating on the box will be (80N-25N) = 55N force.
What is force?A force is just an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. A pushing or a pulling motion is a straightforward way to describe force. A force is a vector quantity since it has either magnitude and direction. A force or energy that has been applied, exerted, or brought about to move or transform the natural forces. In science, the term "force" has a particular definition. At this level, calling a force a pushing or a pull is entirely appropriate. An object doesn't "have a force in it" or "contain a force." A force is applied to one thing by another. The idea of a force encompasses both living and non-living things.
How do you calculate force and why force unit is Newton?The SI unit measuring force is the newton, denoted by the letter N. The definition of a force formula is given by Newton's second law of motion: An object's forces are equal towards its mass times its acceleration. F = m ⨉ a. You must use SI units of force (newtons), mass (kg), and acceleration in order to apply this formula (meters per second squared).
The force that causes a mass of one kilogram to accelerate by one metre per second per second is known as 1 kgm/s₂. In terms of its contribution to classical mechanics, especially Newton's second law of motion, it is named after Isaac Newton.
F = m × a
F = Force
m = mass of an object
a = acceleration
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. Car D is heading East at 25 m/s and Car T is heading West at 10 m/s. What is the relative velocity between car D and car T? How would the passenger in Car D describe Car T’s motion?
Cars D and T are travelling at a relative speed of 35 m/s.
Car D's velocity is u = + 25 m/s because it is travelling east at a speed of 25 m/s. (because it is travelling in the direction of positive x-)
Additionally, Car T is moving at v = -10 m/s and travelling west at a speed of 10 m/s. (because it is travelling opposite in the direction of positive x-)
Thus, relative velocity = velocity of D - velocity of T
relative velocity = 25 - (-10)
relative velocity = 35m/s
So, the relative velocity between Car D and Car T is 35 m/s.
Car D is travelling in the direction of the position axis' positive arrow, whereas Car T is moving in the direction of the axis' negative arrow, therefore the two automobiles are moving in the opposite direction.
As a result, car D is driving more quickly than car T, and both vehicles are travelling in the opposite direction.
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Create a table comparing and contrasting constructive and destructive interference .
Constructive interference:-
1. The constructive interference takes place, when the amplitude of the two or more waves combines to form the resultant wave with more amplitude.
2. The phase difference between the waves during the constructive interference is,
[tex]\varnothing=\frac{n\pi}{2}[/tex]where n is the even number.
3. In the constructive interefernce, the bright fringes are observed.
Destructive interference:-
1. The destructive interference takes place when the ampltude of two or more wave combines to form the resultant wave with less amplitude.
2. The phase difference between the waves during the destructive interference is,
[tex]\varnothing=\frac{n\pi}{2}[/tex]where n is the odd number.
3. In the destructive interference, the dark fringes are formed.
In the lab, a student is reading the amount of water in this graduated cylinder.
What is the amount of water in this cylinder?
A) 20.5 mL
B) 25mL
C) 250 mL
D) 24mL
2 similar metal spheres, A and B, have charges of +2.0×10^-6 coulomb and +1.0×10^-6 coupons, respectively, as shown in the diagram below. The magnitude of the electrostatic force on fear a do to sphere B is 2.4 in period what is the magnitude of the electrostatic force on sphere B due to spear A?
Given data:
The magnitude of the electrostatic force on sphere A due to sphere B is Fab = 2.4 N
The magnitude of the electrostatic force on sphere A due to sphere B is equal to the magnitude of the electrostatic force on sphere B due to sphere A.
Therefore, the magnitude of the electrostatic force on sphere B due to sphere A is given as:
[tex]F_{ba}=2.4\text{ N}[/tex]Thus, the magnitude of the electrostatic force on sphere B due to sphere A is 2.4 N.
An astronaut has a mass of 59 kilograms. What will her gravitational force be on the Moon? The
gravitational attraction on the Moon is 1.62 (1 point)
O 578.2 N
O 60.62 N
O 95.58 N
O 36.42 N
Taking into account the Newton's Second Law, the correct answer is the third option: the gravitational force of the astronaut on the Moon is 95.58 N.
Newton's second lawAcceleration in a body occurs when a force acts on a body. There are two factors that influence the acceleration of an object: the net force acting on it and the mass of the body.
Newton's second law defines the relationship between force and acceleration mathematically. This law says that the acceleration of an object is directly proportional to the sum of all the forces acting on it and inversely proportional to the mass of the object.
Mathematically, Newton's second law is expressed as:
F= m×a
where:
F = Force [N]m = Mass [kg]a = Acceleration [m/s²]Gravitational force be on the MoonIn this case, you know:
F= ?m= 59 kga= gravitational attraction on the Moon= 1.62 m/s²Replacing in Newton's second law:
F= 59 kg× 1.62 m/s²
Solving:
F= 95.58 N
Finally, gravitational force on the Moon is 95.58 N.
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A rocket weighing 220,000 N is taking off from Earth with a total thrust of 500,000 N at an angle of 20 degrees, as shown in the image below. What is the approximate vertical component of the net force that is moving the rocket away from Earth?A. 400,000 NB. 350,000 NC. 250,000 ND. 300,000 N
ANSWER
[tex]C.250,000N[/tex]EXPLANATION
Parameters given:
Weight of rocket, W = 220,000 N
Thrust, F = 500,000N
Angle of thrust, θ = 20°
The vertical forces acting on the rocket are the thrust (acting at an angle) and its weight. This means that the sum of vertical forces is:
[tex]F_y=F\cos \theta-W[/tex]Note: W is negative since it acts opposite the motion of the rocket.
Therefore, we have that the net vertical force (vertical component of forces) is:
[tex]\begin{gathered} F_y=500000\cos 20-220000 \\ F_y=469,846.31-220000 \\ F_y=249,846.31N \\ F_y\approx250,000N \end{gathered}[/tex]The answer is option C.
what is the speed (m/s) of a caterpillar traveling 45m along a sidewalk in 50hr?
We will have the following:
[tex]v=\frac{45m}{50h}\cdot\frac{1h}{60s}\Rightarrow v=\frac{3}{200}m/s[/tex][tex]\Rightarrow v=0.015m/s[/tex]So, the speed is 0.015 m/s.
A dog barks with an intensity level of 80 decibels. Two barking dogs produce what intensity level?
We are given that a dog barks with an inetensity level of 80 dB and asked to find out the intensity level produced by two barking dogs.
The combined intensity level of both dogs is the sum of each dog's intensity level.
[tex]\begin{gathered} I_{net}=I_1+I_2 \\ I_{net}=2I_{} \\ I_{net}=2\cdot I_0\cdot10^{\frac{\beta}{10}}_{} \end{gathered}[/tex]Where β is 80 dB and I0 is the reference intensity (1x10^-12 W/m^2)
[tex]\begin{gathered} I_{net}=2\cdot10^{-12}\cdot10^{\frac{80}{10}}_{} \\ I_{net}=2\cdot10^{-12}\cdot10^8_{} \\ I_{net}=2\cdot10^{-12+8} \\ I_{net}=2\cdot10^{-4} \end{gathered}[/tex]The net β is given by
[tex]\begin{gathered} \beta_{\text{net}}=10\log (\frac{I_{net}}{I_0}) \\ \beta_{\text{net}}=10\log (\frac{2\cdot10^{-4}}{10^{-12}}) \\ \beta_{\text{net}}=10\log (2\cdot10^{-4+12}) \\ \beta_{\text{net}}=10\log (20^8) \\ \beta_{\text{net}}=10(8.301) \\ \beta_{\text{net}}=83\; dB \end{gathered}[/tex]Therefore, two barking dogs produce 83 dB intensity level.