Answer:
[tex]l_o=550.055\ cm[/tex]
Explanation:
Given that,
Length of a street bridge, l = 5.5 m
The coefficient of bridge, [tex]\alpha =0.00001 ^0 C[/tex]
We need to find how much will it expand when temperatures is by 10°C.
The change in length per unit original length is given by :
[tex]\dfrac{\Delta l}{l}=\alpha \Delta T\\\\\Delta l = l\alpha \Delta T\\\\=5.5\times 0.00001 \times 10\\\\\Delta l=0.00055\\\\(l_o-l)=0.00055\\\\l_o=0.00055+5.5\\\\=5.50055\ m\\\\l_o=550.055\ cm[/tex]
Hence, the length will expanded 550.055 cm.
The technology in the picture produces which energy conversion?
A. Chemical energy to kinetic energy
B. Thermal energy to kinetic energy
C. Light energy to electrical energy
D. Kinetic energy to electrical energy
Answer:
D
Explanation:
because the whole town needs to be powered through some sort of energy and kinetic energy means the movement of something
The technology in the picture represents the conversion of kinetic energy to electrical energy. So, the correct option is D.
What is meant by kinetic energy ?Kinetic energy of a body is defined as the energy acquired by the body due to the virtue of its motion.
Here,
The given picture represents the dam system at a town.
We know, according to conservation of energy, energy can neither be created nor be destroyed, but can be transferred from one form to another.
In the dam system, the application of conservation of energy is implemented.
Dam consists of a water stream and turbines. The water stream is arranged in such a way that, when the water is running from a height, the water acquires an energy in the form of kinetic energy.
This kinetic energy of the water is converted to electrical energy with the help of the turbines, which are rotating continuously and thus electricity is produced.
Hence,
The technology in the picture represents the conversion of kinetic energy to electrical energy.
To learn more about kinetic energy, click:
https://brainly.com/question/999862
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The two images show side views of ocean waves. How are the two sets of waves different?
Helppppp meeee plssss ASAP
Suppose the atoms of two different nonmetal elements bonded. What type of
substance would most likely form?
A. A metalloid
B. An ionic compound
C. A covalent compound
D. A third element
Answer:
C
Explanation:
covalent. Hope that helps!
Which of the following is true for valence electrons?
Valence electrons are always located in the outer most energy level.
Valence electrons are found only in radioactive isotopes.
Valence electrons are always located in the innermost energy level
Valence electrons are found only in negatively charged ions.
Answer:
Valence electrons are always located in the outer most energy level.
Explanation:
Valence electrons are the ones that are involved in chemical bonds. In order to take part in a chemical bonding, the outermost/valence electron needs to be involved. Thus, the answer is Valence electrons are always located in the outer most energy level.
Suppose three forces are acting on a model rocket launching into the air. The force of gravity is 1.2 N acting downward. The rocket engine has a force of 12.3 N acting at an angle of 65⁰ above the horizontal to the right. The wind pushes the rocket with a force of 2.5 N to the left. Find the magnitude and direction of the resultant force on the rocket.
Please answer!!! Offering 50 points for answer and explanation
Answer:
can you include a picture
Decompose the forces acting on the rocket in horizontal and vertical components.
• net horizontal force:
∑ F = (12.3 N) cos(65°) - 2.5 N ≈ 2.7 N
(notice we're taking "to the right" to be the positive direction)
• net vertical force:
∑ F = (12.3 N) sin(65°) - 1.2 N ≈ 9.9 N
The resultant force then has magnitude
√((2.7 N)² + (9.9 N)²) ≈ 10.3 N
Since the horizontal and vertical components of the resultant are both positive, it points at an angle between 0° and 90° from the positive horizontal, so that
tan(θ) ≈ (9.9 N) / (2.7 N) ≈ 3.69
===> θ ≈ arctan(3.69) ≈ 75°
how many minutes in 1 hour
Answer:
60
Explanation:
Every 60 minutes is an hour
Answer:
60; minute in 1 HR is the answer
Just do the attachment
Answer: your answer is B I know that's what you picked but I believe it is correct! look below...
Explanation: A solution is made when one substance called the solute "dissolves" into another substance called the solvent. Dissolving is when the solute breaks up from a larger crystal of molecules into much smaller groups or individual molecules.
In order to form a solution, the solute must be surrounded, or solvated, by the solvent. Solutes successfully dissolve into solvents when solute-solvent bonds are stronger than either solute-solute bonds or solvent-solvent bonds.
BRAINLIEST?
If a sinusoidal electromagnetic wave with intensity 18 W/m2 has an electric field of amplitude E, then a 36 W/m2 wave of the same wavelength will have an electric field of amplitude?
a. 4E
b. 2 underroot 2E
c. 2E
d. underroot E
Answer:
The correct option is D
Explanation:
From the question we are told that
The intensity of the first electromagnetic wave is [tex]I = 18 \ W/m^2[/tex]
The amplitude of the electric field is [tex]E_{max}_1 =A[/tex]
The intensity of the second electromagnetic wave is [tex]I = 36 \ W/m^2[/tex]
Generally the an electromagnetic wave intensity is mathematically represented as
[tex]I = \frac{1}{2} * \epsilon_o * c * E_{max}^2[/tex]
Looking at this equation we see that
[tex]I \ \ \alpha \ \ E^2_{max}[/tex]
=> [tex]\frac{I_1}{I_2} = [ \frac{ E_{max}_1}{ E_{max}_2} ] ^2[/tex]
=> [tex]E_{max}_2 = \sqrt{\frac{x}{y} } * E_{max}_1[/tex]
=> [tex]E_{max}_2 = \sqrt{\frac{36}{18} } * E[/tex]
=> [tex]E_{max}_2 = \sqrt{2 } E[/tex]
g During the contraction of the heart, 65 cm3 blood is ejected from the left ventricle into the aorta with a velocity of approximately 98 cm/s. The blood volume traverses the aortic arch, exiting with the same speed but opposite direction. Assume the mass density of the blood is 1060 kg/m3 blood, the aortic arch remains stationary, and that the heart rate is 61 bpm. What is the average force exerted by the blood on the wall of the aorta.
Answer:
The force is [tex]F = 0.1441 \ N[/tex]
Explanation:
From the question we are told that
The volume of blood ejected is [tex]V_b = 65cm^3 = 65*10^{-6} \ m^3[/tex]
The velocity of the ejected blood is [tex]v = 98 cm/ s = 0.98 \ m/s[/tex]
The mass density of blood is [tex]\rho = 1060 \ kg/m^3[/tex]
The heart rate is [tex]R = 61 bpm(beats \ per \ miunite) = \frac{61}{60} = 1.0667\ bps[/tex]
Generally the average force exerted is mathematically represented as
[tex]F = 2 * \rho * V_b * R * v[/tex]
=> [tex]F = 2 * 1060 * (65*10^{-6}) *1.0667 * 0.98[/tex]
=> [tex]F = 0.1441 \ N[/tex]
A person pushing a bin with 45 N of force slides the 3 kg plastic bin on a rough surface with friction. The plastic bin is moving with a constant velocity. What is the net force acting on the box?
Answer:
F = 0
Explanation:
Given that,
Force acting to push a bin = 45 N
Mass of the plastic bin, m = 3 kg
The plastic bin is moving with a constant velocity.
We need to find the net force acting on the box. Constant velocity means the change in velocity is equal to 0. It means acceleration will be 0.
As a result, the force acting on the box is equal to 0.
a steel girder weighting 700 lb is hoisted from gund level to the roof of a 70-ft building using a chain that weighs 4lb/running foot. Find the work done
Answer:
66.475kJ
Explanation:
Work done is the product of the force and perpendicular distance in direction of the force.
Work done = Force × distance
Given
Weight = 700lb
Distance = 70ft
1lb force = 4.448N
700lb force = 700(4.448) = 3113.6N
Distance = 70(0.305) = 21.35m
Work done = 3113.6×21.35
Work done ≈ 66,475Joules
Work done = 66.475kJ
A satellite orbits the Earth (mass = 5.98 x 1024 kg) once every = 43200 s. At what radius does the satellite orbit?
Answer:
26621 km
Explanation:
We are given;
Mass: m = 5.98 x 10^(24) kg
Period; T = 43200 s
Formula for The velocity(v) of the satellite is:
v = 2πR/T
Where R is the radius
Formula for centripetal acceleration is;
a_c = v²/R
Thus; a_c = (2πR/T)²/R = 4π²R/T²
Formula for gravitational acceleration is:
a_g = Gm/R²
Where G is gravitational constant = 6.674 × 10^(-11) m³/kg.s²
Now the centripetal acceleration of the satellite is caused by its gravitational acceleration. Thus;
Centripetal acceleration = gravitational acceleration.
Thus;
4π²R/T² = Gm/R²
Making R the subject gives;
R = ∛(GmT²/4π²)
Plugging in the relevant values;
R = ∛((6.674 × 10^(-11) × 5.98 x 10^(24) × 43200²)/(4 × π²))
R = 26.621 × 10^(6) m
Converting to km, we have;
R = 26621 km
Answer:
2.66 *10^7
Explanation:
Sorry I don't know the process if you were interested in that :/
An automobile travels to the right, with the center Aof the wheel moving at a constant speed of 48 mi/h. If the diameter of a wheel is 22in.,determine the velocities of points B, C, D, and E on the rim of the wheelassuming there is no slipping. [Hint: at any given instant the velocity of point C, which is in contact with the ground must be zero]. Please introduce axes and give your answers in vector form.
Answer:
Explanation:
From the question we are told that
Constant speed =48mile/hr
Diameter of a wheel = 22inch therefore [tex]r=\frac{22}{2} =>11[/tex]
Generally Convert from mile/hr to inches/sec
The length in inches is equal to the miles multiplied by 63,360.
an hour is 3600seconds
[tex]\frac{48*63360}{3600}[/tex]
48miles/h = 849.8 inch/sec
[tex]V_a =844.8 inch/sec[/tex]
therefore
[tex]\omega= \frac{v}{r}[/tex]
[tex]\omega= \frac{844,8}{11}[/tex] =>[tex]76.8 sec ^-^1[/tex]
a)Considering the velocity of Vb in inches per seconds
Generally the formula is stated as
[tex]V_b= V_a + V_b_/_a[/tex]
[tex]V_b = 844.8 + \omega r[/tex]
[tex]V_b= 1639.6in/s[/tex]
b)Considering the velocity of Vc in inches per seconds
Since the tire doesn't slip as earlier stated in the question
Therefore [tex]V_c = 844.8 -w(r) =0[/tex]
c)Considering the velocity of Ve in inches per seconds
Generally the formula is stated as
[tex]V_e=V_a + V_e_/_a[/tex]
[tex]V_e = 844.8 \uparrow \theta -844.8 \uparrow = 844.8\sqrt{2}[/tex]
Expressing result with vector
[tex]V_e =844.54 + 20.85j[/tex]
d)Considering the velocity of Vd in inches per seconds
Generally the formula is stated as
[tex]V_d= V_a + V_d_/_a[/tex]
Mathematically
[tex]V_d =844.8 \uparrow +( 844.8\frac{\sqrt{3} }{2} \uparrow + \frac{844.8}{2} \uparrow)[/tex]
[tex]V_d= (1576.4 \uparrow + 422.4\uparrow)[/tex]
[tex]V_d= 1632.028in/s[/tex]
If two ___ forces are applied to an object in opposite directions, the object does not move, or moves at a ___ , this means the forces are ___. If to ___ forces are applied to an object in opposite directions, the object does move, this means the forces are ___.
Answer:
Equal and opposite
Constant speed
Balanced
Unequal and non-opposite
Unbalanced
Explanation:
Balanced forces can be defined as forces which are equal in size but opposite in direction.
Now, these forces do not cause a change in motion because when they act on an object at rest, such an object will not move. For example, when attempt to push against a wall, the wall will push back with an equal but opposite force and neither you nor the wall will move.
While unbalanced forces are those that cause a change in the motion of an object.
Thus, these forces are said not to be equal and opposite.
in which part of the circulatory system can the exchange of gases and nutrients take place?
Number 1a and b and number 2(everything)
Answer:
Explanation:
The density of a substance is the ratio of its mass to its volume. Its unit of measurement is kg[tex]m^{-3}[/tex].
i.e density, ρ = [tex]\frac{mass}{volume}[/tex]
1a. To determine the density of the acetic acid, Rachael needs to know the mass and volume of the acid.
i. Measure the mass of the given beaker using the mass balance.
ii. Transfer the acetic acid into the beaker, and measure the new mass using the mass balance.
iii. Subtract the mass of the beaker from the new mass to determine the mass of the acetic acid.
iv. Measure the volume of the acid on the scale of the beaker.
v. Divide the value of the mass by its volume to determine its density of the acetic acid.
b. Given that the density is 1.05 g/[tex]cm^{3}[/tex], and volume is 200 [tex]cm^{3}[/tex].
Then,
density = [tex]\frac{mass}{volume}[/tex]
1.05 = [tex]\frac{mass}{200}[/tex]
mass = 1.05 x 200
= 210 g
mass = 210 g
2. Length of titanium = 0.40 m
Area of titanium = 0.05 [tex]m^{2}[/tex]
mass = 90.0 kg
density = [tex]\frac{mass}{volume}[/tex]
But,
volume = area x length
= 0.05 x 0.4
= 0.02 [tex]m^{3}[/tex]
density of titanium = [tex]\frac{90}{0.02}[/tex]
= 4500 kg[tex]m^{-3}[/tex]
an unladen swallow flies 5 m/s how far has the bird traveled after 1 minute?
Answer: 300m
1 minute = 60s
the unladen swallow can fly: 60.5 = 300 (m)
Explanation:
two asteroids crashed the crash caused both asteroids to change speeds scientist want to use the change
Answer:
The force each one experienced
Explanation:
Hope this helps :)
During the contraction of the heart, 65 cm3 blood is ejected from the left ventricle into the aorta with a velocity of approximately 103 cm/s. The blood volume traverses the aortic arch, exiting with the same speed but opposite direction. Assume the mass density of the blood is 1060 kg/m3 blood, the aortic arch remains stationary, and that the heart rate is 59 bpm. What is the average force exerted by the blood on the wall of the aorta.
Answer:
The value [tex]F = 0.1396 \ N [/tex]
Explanation:
From the question we are told that
The volume blood ejected is [tex]V = 65 \ cm^3 = 65*10^{-6} \ m^3[/tex]
The velocity of the blood ejected is [tex]v = 103 \ cm/s = \frac{103}{100} = 1.03 \ m/s[/tex]
The density of blood is [tex]\rho = 1060 \ kg/m^3[/tex]
The heart beat is [tex]R = 59 \ bpm(beats \ per \ minute) = \frac{59}{60}= 0.9833\ bps[/tex]
The average force exerted by the blood on the wall of the aorta is mathematically represented as
[tex]F = 2 * \rho * V * R * v[/tex]
=> [tex]F = 2 * 1060 * 65*10^{-6} * 0.9833 * 1.03[/tex]
=> [tex]F = 0.1396 \ N [/tex]
Which of the following cars have the most kinetic energy
[tex]\huge\boxed{OptionA}[/tex]
_____________________________________DATA:Blue Car:mass = 4 kg
velocity = 5 m/s^2
Orange truck:Mass= 2kg
Velocity = 7m/s^2
Grey Car:mass = 6 kg
velocity = 4m/s^2
Green Car:Mass = 8 kg
Velocity = 3 m/s^2
_____________________________________SOLUTION:By the equation of kinetic energy,
K.E = [tex]\frac{1}{2} mv^2[/tex]
Where,
K.E is kinetic energy
m is mass
v is velocity
_____________________________________Kinetic energy of Blue car:
Directly substitute the variables in the equation,
K.E = [tex]\frac{1}{2}x4x5^2[/tex]
Simplify the equation,
K.E = 50 J
_____________________________________Kinetic Energy of Silver Car:
Directly substitude the variable in the equation,
K.E = [tex]\frac{1}{2}x6x4^2[/tex]
Simplify the equation,
K.E = 48J
_____________________________________Kinetic Energy of Green Car:Substitute the variables in the equation,
K.E = [tex]\frac{1}{2}x8x3^2[/tex]
Simplify the Equation,
K.E = 36J
_____________________________________Kinetic Energy of Orange Truck:Substitute the variable,
K.E = [tex]\frac{1}{2}x 2x7^2[/tex]
Simplify the equation,
K.E = 49J
_____________________________________As you can see that the highest value of kinetic energy is of Blue SUV thus it will be out answer.
_____________________________________Best Regards,'Borz'The space shuttle releases a satellite into a circular orbit 630 km above the Earth.
How fast must the shuttle be moving (relative to Earth's center) when the release occurs?
Answer:
7,539 m/s
Explanation:
Let's use this equation to find the gravitational acceleration of this space shuttle:
[tex]\displaystyle g=\frac{GM}{r^2}[/tex]We know that G is the gravitational constant: 6.67 * 10^(-11) Nm²/kg².
M is the mass of the planet, which is Earth in this case: 5.972 * 10^24 kg.
r is the distance from the center of Earth to the space shuttle: radius of Earth (6.3781 * 10^6 m) + distance above the Earth (630 km → 630,000 m).
Plug these values into the equation:
[tex]\displaystyle g=\frac{(6.67\cdot 10^-^1^1 \ Nm^2kg^-^2)(5.972\cdot 10^2^4 \ kg)}{[(6.3781\cdot 10^6 \ m)+(630000 \ m)]^2}[/tex]Remove units to make the equation easier to read.
[tex]\displaystyle g=\frac{(6.67\cdot 10^-^1^1 )(5.972\cdot 10^2^4 )}{[(6.3781\cdot 10^6)+(630000 )]^2}[/tex]Multiply the numerator out.
[tex]\displaystyle g=\frac{(3.983324\cdot 10^1^4)}{[(6.3781\cdot 10^6)+(630000 )]^2}[/tex]Add the terms in the denominator.
[tex]\displaystyle g=\frac{(3.983324\cdot 10^1^4)}{[(7008100)]^2}[/tex]Simplify this equation.
[tex]\displaystyle g=8.11045189 \ \frac{m}{s^2}[/tex]The acceleration due to gravity g = 8.11045189 m/s². Now we use the equation for acceleration for an object in circular motion which contains v and r.
[tex]\displaystyle a = \frac{v^2}{r}[/tex]a = g, v is the velocity that the space shuttle should be moving (what we are trying to solve for), and r is the radius we had in the previous equation when solving for g.
Plug these values into the equation and solve for v.
[tex]\displaystyle 8.11045189 \ \frac{m}{s^2} = \frac{v^2}{7008100 \ m}[/tex]Remove units to make the equation easier to read.
[tex]\displaystyle 8.11045189 = \frac{v^2}{7008100}[/tex]Multiply both sides by 7,008,100.
[tex]56838857.89=v^2[/tex]Take the square root of both sides.
[tex]v=7539.154985[/tex]The shuttle should be moving at a velocity of about 7,539 m/s when it is released into the circular orbit above Earth.
Please help! What kind of energy is produce by filament light?
Answer:
electrical to thermal and light
(may wanna change the answers)
and the one before that should be electrical to electrical i think
Explanation:
The FitnessGram Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. A single lap should be completed each time you hear this sound. Remember to run in a straight line, and run as long as possible.
HELP ASAP!! i’ll mark you the brainliest!!
Answer:
yes
Explanation:
Sadie rolls a marble down a ramp. When the marble reaches the bottom of the ramp, it then rolls across the floor. After a few seconds, the marble slows down, then stops. What caused the marble to stop? *
A Friction between the marble and the floor.
B Air pressure pushing down on the marble.
C The force of gravity pulling the marble down.
D Magnetic attraction between Earth and the marble.
One of the two rectangular components of a force is 20N and it makes an angle of 30
with the force. Find the magnitude of the other components.
Answer:
11.545NExplanation:
The the horizontal and vertical component be expressed as;
Fx = Fxos theta (horizontal compt)
Given Fx = 20N
theta = 30°
Get F:
20 = Fcos30
20 = 0.8660F
F = 20/0.8660
F = 23.09N
Get the magnitude of the other components. (vertical compt)
Fy = Fsin theta
Fy = 23.09sin30
Fy = 23.09(0.5)
Fy = 11.545N
Hence the magnitude of the other component is 11.545N
what energy conversion takes place when a solar cell is used to light a street lamp?
Answer:
Explanation:
Electrical energy is the correct answer
Answer:
Is B
Explanation:
2. Fossil fuel has been used more in the
existing world
Answer: fossil fuels are using more in the existing world because fossil fuels are of great importance because they can burned producing significant amount of energy prr unit mass the use of coal as a fuel prefates recorded history
Explanation:
Answer:
A fossil fuel is a fuel formed by natural processes, such as anaerobic decomposition of buried dead organisms, containing organic molecules originating in ancient photosynthesis[1] that release energy in combustion.[2] Such organisms and their resulting fossil fuels typically have an age of millions of years, and sometimes more than 650 million years.[3] Fossil fuels contain high percentages of carbon and include petroleum, coal, and natural gas.[4] Peat is also sometimes considered a fossil fuel.[5] Commonly used derivatives of fossil fuels include kerosene and propane. Fossil fuels range from volatile materials with low carbon-to-hydrogen ratios (like methane), to liquids (like petroleum), to nonvolatile materials composed of almost pure carbon, like anthracite coal. Methane can be found in hydrocarbon fields alone, associated with oil, or in the form of methane clathrates.
Coal, a fossil fuel
As of 2018, the world's main primary energy sources consisted of petroleum (34%), coal (27%), and natural gas (24%), amounting to an 85% share for fossil fuels in primary energy consumption in the world. Non-fossil sources included nuclear (4.4%), hydroelectric (6.8%), and other renewables (4.0%, including geothermal, solar, tidal, wind, wood, and waste).[6] The share of renewables (including traditional biomass) in the world's total final energy consumption was 18% in 2018.[7] Compared with 2017, world energy-consumption grew at a rate of 2.9%, almost double its 10-year average of 1.5% per year, and the fastest since 2010.[8]
Although fossil fuels are continually formed by natural processes, they are generally classified as non-renewable resources because they take millions of years to form and known viable reserves are being depleted much faster than new ones are generated.[9][10]
Most air pollution deaths are due to fossil fuel combustion products, it is estimated to cost over 3% of global GDP,[11] and fossil fuel phase-out would save 3.6 million lives each year.[12]
The use of fossil fuels raises serious environmental concerns. The burning of fossil fuels produces around 35 billion tonnes (35 gigatonnes) of carbon dioxide (CO2) per year.[13] It is estimated that natural processes can only absorb a small part of that amount, so there is a net increase of many billion tonnes of atmospheric carbon dioxide per year.[14] CO2 is a greenhouse gas that increases radiative forcing and contributes to global warming and ocean acidification. A global movement towards the generation of low-carbon renewable energy is underway to help reduce global greenhouse-gas emissions.
What is food called when it enters the pharynx?
A.Bile
B.bolus
C. Food
D. Feces
Answer:
its food this was easy
A piece of copper wire with thin insulation, 200 m long and 1.00 mm in diameter, is wound onto a plastic tube to form a long solenoid. This coil has a circular cross section and consists of tightly wound turns in one layer. If the current in the solenoid drops linearly from 1.60 A to zero in 0.120 seconds, an emf of 80.0 mV is induced in the coil. What is the length of the solenoid, measured along its axis
Answer:
N= 3
Explanation:
For this exercise we must use Faraday's law
E = - dФ / dt
Ф = B . A = B Acos θ
tje bold indicate vectors. As it indicates that the variation of the field is linear, we can approximate the derivatives
E = - A cos θ (B - B₀) / t
The angle enters the magnetic field and the normal to the area is zero
cos 0 = 1
A = π r²
In the length of the wire there are N turns each with a length L₀ = 2π r
L = N (2π r)
r = L / 2π N
we substitute
A = L² / (4π N²)
The magnetic field produced by a solenoid is
B = μ₀ N/L I
for which
B₀ = μ₀ N/L I
The final field is zero, because the current is zero
B = 0
We substitute
E = - (L² / 4π N²) (0 - μ₀ N/L I) / t
E = μ₀ L I / (4π N t)
N = μ₀ L I / (4π t E)
The electromotive force is E = 0.80 mV = 0.8 10⁻³ V
let's calculate
N = 4π 10⁻⁷ 200 1.60 / (4π 0.120 0.8 10⁻³)]
N = 320 10⁻⁷ / 9.6 10⁻⁶
N = 33.3 10⁻¹
N= 3
CUP 6. A wire has a diameter of 0.032 inches. The AWG rating of this wire is most likely to be O A. 20 O B. 14. O C. 12. O D. 18.
Answer:
A. 20
Explanation:
The AWG rating of the wire can be determined by applying the formula;
[tex]d_{i}[/tex] = 0.005 x [tex]92^{\frac{(36 - s)}{39}} }[/tex]
where [tex]d_{i}[/tex] is the diameter of wire in inches, and s is the diameter of wire in AWG.
Given that [tex]d_{i}[/tex] = 0.032 inches, then;
0.032 = 0.005 x [tex]92^{\frac{(36 - s)}{39}} }[/tex]
[tex]\frac{0.032}{0.005}[/tex] = [tex]92^{\frac{(36 - s)}{39}} }[/tex]
6.4 = [tex]92^{\frac{(36 - s)}{39}} }[/tex]
Find the log of both sides to have,
log 6.4 = log [tex]92^{\frac{(36 - s)}{39}} }[/tex]
log 6.4 = [tex](\frac{36 -s}{39})[/tex] log 92
[tex]\frac{log 6.4}{log92}[/tex] = [tex](\frac{36 -s}{39})[/tex]
0.410523 = [tex](\frac{36 -s}{39})[/tex]
36 - s = 0.410523 x 39
= 16.0104
⇒ s = 36 - 16.0104
= 19.9896
s = 20
Therefore, the AWG of the wire is 20.