The circuit can be simplified by noting that the two resistors in the middle are in parallel with each other. By using the formula for the equivalent resistance of two resistors in parallel .
Thus, we can redraw circuit with three resistors in series, each with a resistance of twice the individual resistor. When a voltage source is connected in series to a series of resistors, voltage drops across each resistor are additive. Since voltage source is 9 volts and there are three resistors in series, each with a resistance of 2 times individual resistor, total voltage drop across resistors is 6 volts. Therefore, the voltage drop across the far-right resistor, which is last resistor in series, would be 3 volts.
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3. the coefficient of friction between a soccer ball and a court is 0.52, and its mass is 425 gm. how much horizontal force is required to make the shoe slide?
The horizontal force that is required to make the shoe slide is 2.1658N.
Horizontal force = static friction
Static friction = uMg
u is coefficient of friction
g = acceleration due to gravity
M is the mass of the body that is .0425 kg.
Force required = (0.52 x 0.425 x 9.8) N
= 2.1658N
A horizontal force is a force that operates in a direction parallel to the horizon. The cycle's speed tends to slow down due to an opposing force called air resistance force, which acts in the opposite direction. Both the applied force and the air resistance force are considered horizontal forces when the direction is taken into account. Jumps and horizontal medicine ball throws can help increase the horizontal force produced. The Standing Long Jump, Standing Triple Jump, and horizontal jumps over hurdles or boxes are some of these jumps.
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Select the correct answer.
Why does ice float on water?
A.
The temperature of ice is lower than the temperature of water.
B.
The temperature of water and ice are the same.
C.
The density of ice is less than the density of water.
D.
The density of ice is greater than the density of water.
Answer:
C.
The density of ice is less than the density of water.
The ice float on water because the density of ice is less than the density of water.
What is Density?The density of a material describes how dense it is in a given area. A substance's density is determined by its mass per unit volume. Density is essentially a measure of how tightly something is packed.
It is a particular physical quality of a specific thing. Discovering the density principle was done by the Greek scientist Archimedes. If you are familiar with the formula and the required units, calculating density is simple. Alternatively to the symbol, the letter D can be used to denote density.
ρ=m/v where,
ρ is the density,
m= mass of object and,
v is the volume of the object.
Hence, the density of ice is 917 kg/m³, which is less than the density of water which is 997.7 kg/m³ and due to this reason the ice floats on water.
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Four identical charges (+2μC each ) are brought from infinity and fixed to a straight line. The charges are located 0.40 m apart. Determine the electric potential energy of this group.
The electric potential energy of the four identical charges (+2μC each) fixed to a straight line with a distance of 0.40 m is 1.44 × 10^-5 J.
To calculate the electric potential energy of a group of charges, the formula is given as U = k * q1 * q2 / r where, U is the electric potential energy of the group k is Coulomb's constant q1 and q2 are the charges r is the distance between the charges.
Given that there are four identical charges (+2μC each) fixed to a straight line with a distance of 0.40 m. We have to calculate the electric potential energy of this group of charges.
The electric potential energy formula becomes:
U = k * q1 * q2 / r = (9 × 10^9 Nm^2/C^2) × (2 × 10^-6 C)^2 × 4 / 0.40 m
U = 1.44 × 10^-5 J.
Therefore, the electric potential energy of the four identical charges (+2μC each) fixed to a straight line with a distance of 0.40 m is 1.44 × 10^-5 J.
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place the following spectral types of stars in order from coolest to hottest.
O-type stars are the hottest, with a surface temperature of more than 25,000 K. The temperature of a star, as previously stated, is a crucial factor that influences its behavior, lifespan, and other characteristics.
The spectral classification of stars is one of the most essential indicators of their temperatures. The temperature of a star also influences its color. In order from coolest to hottest, the spectral types of stars are: M, K, G, F, A, B, and O.M-type stars have a surface temperature of less than 3,500 K. The surface temperature of K-type stars is between 3,500 and 5,000 K. The surface temperature of G-type stars ranges from 5,000 to 6,000 K. F-type stars have a surface temperature of around 7,000 K. The surface temperature of A-type stars is around 9,000 K. B-type stars have a surface temperature of around 11,000 K. The spectral classification of a star is based on its color, which can reveal information about its temperature, composition, and other features.
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Behaviors in deer such as herding and male deer using antlers to compete for females increase the chances of successful reproduction.
True or False
Answer:
True
Explanation:
The reproductive success of any species is the capability to produce their offspring per breeding lifetime or event.
Most of the species have to attract their partners by their physical capability and build up so that the mother can choose her partner in order to breed the best kind of off spring.
In the context, in case of deer, the size of the their antlers as well as behavior in herding is considered as the best chances for a successful reproduction to compete among the males and find their breeding mate.
Thus the answer is TRUE.
why does warm, moist air start to uplift in the initial stages of thunderstorm development?'
Warm, moist air starts to uplift in the initial stages of thunderstorm development because of a combination of different lift mechanisms.
One of these is convective lift, which occurs when warmer air rises due to its buoyancy. This is because warm air is less dense than cooler air, and so it is more easily displaced by the cooler air. Another lift mechanism is orographic lift, which is the result of air being forced to rise as it moves over a mountain or hill. Finally, frontal lift occurs when a cold front moves into an area of warm, moist air, forcing it to rise. All of these lift mechanisms can combine to cause warm, moist air to be lifted and form a thunderstorm.
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Question 11(Multiple Choice Worth 4 points)
(05.03 LC)
HELP ASAP!!! WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What most likely happens when water vapor cools?
It changes into gas.
It changes into liquid.
Its temperature increases.
Its temperature remains constant.
Which of the following provide electrical resistance in a simple circuit? *
a battery
a wall outlet
a voltage source
a light bulb
Answer:
A light bulb
Explanation:
Sorry of it wrong
consider a 10 kg object free-falling from a cliff with an initial speed of 0 m/sec. what will the speed of the object be after 1 sec and after 2 sec?
The speed of the object after 1 second and 2 seconds is 9.8 m/s and 19.6 m/s respectively.
The equation of motion to be used for calculation of velocity is -
v = u + at, where v and u are final and initial velocity, a is acceleration and t refers to time. Keep the value for each case to find the final velocity. The value of a will be acceleration due to gravity which is 9.8 m/s².
After 1 second
v = 0 + 9.8 × 1
v = 9.8 m/s.
After 2 seconds
v = 0 + 9.8 × 2
v = 19.6 m/s.
Hence, the required velocities are 9.8 and 19.6 m/s.
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a window of a car is found to be covered with 0.6cm of ice. if the area of the window is 1 m2, and the ice is at -12 degrees celsius, what is the minimum heat required to melt all the ice? take the density of ice to be 900 kg/m3, the specific heat capacity of ice to be 0.5 cal/g*k, and the latent heat of fusion to be 80 cal/g. answer in kcal.
The total heat required to melt all the ice is 46.44 kcal.
To melt the ice, we need to first raise its temperature to 0 degrees Celsius, at which point it will start to melt. The mass of the ice on the window is given by the formula
m = (density)(volume) = (900 kg/m3)(0.6 cm)(1 m2) = 0.54 kg.To raise the temperature of this ice to 0 degrees Celsius, we need to transfer a certain amount of heat to it. The heat required is given by the formula
Q = (mass)(specific heat capacity)(temperature change) = (0.54 kg)(0.5 cal/g*K)(12 K) = 3.24 kcal.Once the ice has reached 0 degrees Celsius, it will start to melt. The heat required to melt the ice is given by the formula
Q = (mass)(latent heat of fusion) = (0.54 kg)(80 cal/g) = 43.2 kcal.Therefore, the total heat required to melt all the ice is 3.24 kcal + 43.2 kcal = 46.44 kcal.
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The USDA recommends that fresh pork be cooked until its internal temperature is at least
a. 145F
b. 130F
c. 140F
d. 155F
The USDA (United States Department of Agriculture) recommends that fresh pork be cooked until its internal temperature is at least 145°F (63°C). (Option A)
This temperature recommendation applies to all cuts of pork, including pork chops, roasts, and ground pork. This temperature ensures that harmful bacteria, such as salmonella and E. coli, are destroyed and that the pork is safe to eat.
It is important to use a meat thermometer to accurately measure the internal temperature of the pork and to check several places to ensure that the entire piece of meat has reached the recommended temperature. Letting the pork rest for a few minutes after cooking allows the internal temperature to rise by a few degrees and helps to ensure that the meat is fully cooked.
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a nuclear power plant produces an average of 3100 mw of power during a year of operation. Find the corresponding change in mass of reactor fuel over the entire year.
The change in mass of reactor fuel over the year is approximately 34.4 kg.
The corresponding change in mass of reactor fuel over the entire year can be calculated using Einstein's famous equation E=mc². First, we need to convert the power output of the nuclear power plant from megawatts to joules per second. 3100 megawatts is equal to 3.1 x 10¹² joules per second. Next, we need to determine how much energy is produced over the entire year. There are 31,536,000 seconds in a year, so the total energy produced is 9.81 x 10¹⁹ joules. Finally, we can use E=mc² to solve for the corresponding change in mass of reactor fuel. Therefore, the nuclear power plant would consume this amount of fuel over the entire year of operation.
To find the change in mass of reactor fuel in a nuclear power plant, we'll use the formula E=mc², where E is energy, m is mass, and c is the speed of light. The plant produces 3,100 MW, which equals 3.1 x 10^12 Joules per year (since 1 MW = 1 million Joules and we multiply by seconds in a year). The speed of light, c, is 3 x 10^8 m/s. Rearrange the formula to m=E/c². Substituting the values, we get m = (3.1 x 10^12 J) / (9 x 10^16 m²/s²). This gives m ≈ 34.4 kg. Therefore, the change in mass of reactor fuel over the year is approximately 34.4 kg.
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heyy i don't understand this question may u help me pls?
Answer:
What question?
Explanation:
A high-voltage direct-current generating station delivers mw of power at kv to a city. The city is represented by resistance and each wire of the transmission line round-trip between the station and city is represented by resistance. The distance between the two locations is km and the transmission lines are made of cm diameter copper wire. Determine (a) how much power is consumed by the transmission line and (b) what fraction of the power generated by the generating station is used by the city
(a) The power consumed by the transmission line is calculated by multiplying the square of the current flowing through it by the resistance of the transmission line.
(b) The fraction of power used by the city is calculated by dividing the power consumed by the city by the power generated by the generating station.
To calculate the power consumed by the transmission line, we need to first find the current flowing through the line using Ohm's Law. We can then use the resistance of the line and the current to calculate the power consumed by the line. The power consumed by the city is simply the product of the voltage and the current flowing through the city's resistance. To find the fraction of power used by the city, we divide the power consumed by the city by the total power generated by the generating station. The distance between the two locations and the diameter of the copper wire are important factors that affect the resistance of the transmission line.
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How long will it take for the plutonium to no longer exist?
It will take 8 years for the plutonium to no longer exists.
Plutonium is extremely uncommon. On Earth, there are only traces of it. Currently, NASA only has roughly 77 pounds of plutonium-238 available. Other radioactive isotopes can also be used as a heat source for an RTG, but plutonium-238 is a particularly effective one.
It decays more rapidly as it ages due to its half-life. Therefore, even when they are not consuming any of it, their supply is gradually running out. It will only take 8 years for NASA to run out of plutonium and the prospect of finding more in time for their next deep space mission is dim.
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write any two conditoons at which a body of certain mass become weightless
A body of a certain mass could become weightless in the following two conditions:
1. In microgravity
2. In neutral buoyancy
Cheers,
qxxi
1. A 5 kg block is pulled across a table by a horizontal force of 40 N with a frictional force of 8 N
opposing the motion. Calculate the acceleration of the object.
The acceleration of the block is 6.4 m/s².
To calculate the acceleration of the block, we need to consider the forces acting on it.
The applied force is 40 N, and since it is the only horizontal force in the direction of motion, it is the net force acting on the block.
The frictional force opposing the motion is 8 N.
The acceleration, we can use Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F = ma).
The net force is the difference between the applied force and the frictional force:
40 N - 8 N = 32 N.
Now, we can plug the values into Newton's second law:
32 N = 5 kg × a.
Solving for the acceleration (a), we get
a = 32 N / 5 kg
a = 6.4 m/s².
Therefore, the acceleration of the block is 6.4 m/s².
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The temperature scale that places zero at the point where all atomic and molecular motion ceases is:
Choose matching definition
Kelvin
Velocity
Fahrenheit
Celsius
The temperature scale that places zero at the point where all atomic and molecular motion ceases is Kelvin. This is known as the absolute temperature scale and is based on the theoretical concept of absolute zero, which is equivalent to -273.15 degrees Celsius.
The Kelvin temperature scale is often used in scientific applications, particularly in physics and chemistry. It is an absolute temperature scale that measures temperature based on the kinetic energy of particles in a substance. At absolute zero, the particles have no kinetic energy and therefore have a temperature of 0 Kelvin.
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Heart Rate During Aerobic Activity?
Answer:
It is recommended that you exercise within 55 to 85 percent of your maximum heart rate for at least 20 to 30 minutes to get the best results from aerobic exercise. The MHR (roughly calculated as 220 minus your age) is the upper limit of what your cardiovascular system can handle during physical activity.
(I think) ¯\_(ツ)_/¯
At a constant pressure, the volume of a gas varies as to the absolute temperature and at a constant volume the pressure of the gas varies directly with the absolute temperature. This is known as ____.
At a constant pressure, the volume of a gas varies as to the absolute temperature and at a constant volume the pressure of the gas varies directly with the absolute temperature. This is known as ideal gas law.
The statement describes two fundamental gas laws: Boyle's Law and Charles's Law. When combined, they form the ideal gas law.
According to Boyle's Law, the volume of a gas at constant temperature is inversely proportional to its pressure. It may be expressed mathematically as P₁V₁ = P₂V₂, where P₁ and V₁ are the beginning pressure and volume, and P₂ and V₂ are the final pressure and volume.
According to Charles' Law, the volume of a gas under constant pressure is exactly proportional to its absolute temperature. V₁ / T₁ = V₂ / T₂, where V₁ and T₁ are the beginning volume and temperature, and V₂ and T₂ are the final volume and temperature.
When these two laws are combined, we get the ideal gas law: PV = nRT, where P is pressure, V is volume, n is the number of moles, T is the absolute temperature, and R is the ideal gas constant. The connection between pressure, volume, temperature, and the quantity of gas molecules is described by this law.
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A specified volume of space contains an electric field for which the magnitude is given by E=E0cos(ωt). Suppose that E0 = 20 V/m and ω = 1.0 × 107 s−1. What is the maximum displacement current through a 0.40 m2 cross-sectional area of this volume?
Answer: \(0.708\ mA\)
Explanation:
Given
\(E_o=20\ V/m\)
\(\omega =10^7\ s^{-1}\)
Cross-sectional area \(A=0.40\ m^2\)
Current density is given by
\(J=\epsilon_o \dfrac{dE}{dt}\)
Displacement current
\(\Rightarrow I=JA\\\Rightarrow I=8.854\times 10^{-12}\times 20\times 10^7\times 0.4\\\Rightarrow I=0.708\times 10^{-3}\ A\)
The required value of the maximum displacement current of the given space is \(7.08 \times 10^{-4} \;\rm A\).
Given data:
The intensity of electric field is, \(E_{0}=20 \;\rm V/m\).
The angular frequency of electric field is, \(\omega=1.0 \times 10^{7} \;\rm s^{-1}\).
The cross-sectional area of space is, \(A =0.40 \;\rm m^{2}\).
In the given problem, the instantaneous electric field is given by \(E = E_{0} \times cos(\omega t)\)
So, the expression for the current density is,
\(J= \epsilon_{0} \times \dfrac{dE}{dt}\)
Here, \(\epsilon_{0}\) is the permittivity of free space. Solving as,
\(J= \epsilon_{0} \times \dfrac{d(E_{0} \times cos(\omega t))}{dt}\\\\J= -\epsilon_{0} \times E_{0} \times \omega \times sin(\omega t)\)
And the expression for the maximum displacement current is,
\(I = J \times A\)
And the maximum displacement current is possible only when, J is positive and J will be positive for \(sin(\omega t)=-1\).
Then solving as,
\(I = (-\epsilon_{0} \times E_{0} \times \omega \times sin(\omega t)) \times A\\\\I = (-8.85 \times 10^{-12} \times 20 \times (1.0 \times 10^{7}) \times (-1)) \times 0.40\\\\I = 7.08 \times 10^{-4} \;\rm A\)
Thus, we can conclude that the required value of the maximum displacement current of the given space is \(7.08 \times 10^{-4} \;\rm A\).
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What is the wavelength of sound wave in air that has a temperature of 24.6°C that has a frequency of 440.8 Hz?
A. 465.40 m
B. 0.78 m
C. 17.92 m
D. 0.75 m
1.1. Given the following forward transfer function: G(P) = 2/(s + 3) Assume that you have introduced proportional plus integral controller (G(c)) with gains of Kcp and Kci respectively within the closed loop system. Workout the values for Kep and Kci so that the peak time To is 0.2 sec and the settling time Ts is less than 0.4 sec
Considering the forward transfer function, to achieve a peak time of 0.2 sec and a settling time of less than 0.4 sec, the values of Kep and Kci should be approximately 0.189 and 9, respectively.
To determine the values of Kep and Kci for the given system, we can use the desired specifications of peak time (Tp) and settling time (Ts).
Given:
Forward transfer function: G(P) = 2/(s + 3)
Proportional plus integral controller: G(c) = Kcp + Kci/s
To achieve a peak time (Tp) of 0.2 sec, we can use the formula:
Tp = π / ωd
where ωd is the damped natural frequency. For a second-order system with a transfer function of the form G(s) = K / (\(s^{2}\) + 2ζωn s + ω\(n^{2}\)), ωd is given by:
ωd = ωn * sqrt(1 - ζ2)
From the given forward transfer function, we can see that ωn = 3. Substituting the values into the formula, we have:
0.2 = π / (3 * sqrt(1 - ζ2))
Solving for ζ, we find ζ = 0.283.
Now, to achieve a settling time (Ts) of less than 0.4 sec, we can use the following approximation for a second-order system:
Ts = 4 / (ζωn)
Substituting the values, we have:
0.4 > 4 / (0.283 * 3)
Simplifying, we find that 0.4 > 3.538 / ζ. Rearranging the equation, we have ζ > 3.538 / 0.4. Therefore, ζ > 8.845. Now that we have the values of ζ and ωn, we can determine the values of Kep and Kci using the following relationships:
Kep = 2ζ / ωn
Kci = ω\(n^{2}\)
Substituting the values, we have:
Kep = 2 * 0.283 / 3 = 0.189
Kci = \(3^{2}\) = 9
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two positive charges of 6.0 μc are separated by 0.50m. what force exists between the charges?
The force that exists between the charges is calculated as 1.296 * 10^-18 N.
What is electrostatic force?It is the force of attraction between two opposing charges, protons and electrons.
The electric force between charged bodies at rest is called electrostatic force or Coulomb force. Although the law was known earlier, but it was first published in 1785 by French physicist Charles-Augustin de Coulomb. It is the force of attraction between two opposing charges, protons and electrons.
Given, q1 = q2 = 6 *10^-6
and r = 0.5m
F= 1/4πc * q1 q2/r²
As 1/4πc = 9* 10^-9
= (9* 10^-9 * 6*10^-6*6*10^-6)/0.5²
= 1.296 * 10^-18 J
The force that exists between the charges is 1.296 * 10^-18 N.
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o
Question 4
1 pts
You jog around 180m track 4 times in 30 minutes. What is your average speed in
m/s? (Hint: Convert min to seconds first)
O 0.4 m/s
O 6 m/s
O 24 m/s
O O m/s
Answer:
0.4m/s
Explanation:
It is given speed so it is scalar.
distance covered in 1 round = 180m
therefore, distance covered in 4 rounds = 180*4 = 720m
time = 30 mins = 30*60 = 1800 seconds
average speed = total distance/total time taken
= 720/1800
= 0.4m/s
consider the following cases : i) a planet revolving in an elliptical orbit ii) a planet revolving in a circular orbit. the principle of conservation of angular momentum is applicable to which of these?
The principle of conservation of angular momentum is applicable to both a planet revolving in an elliptical orbit and a planet revolving in a circular orbit.
Does angular momentum conserve in elliptical and circular orbits?The principle of conservation of angular momentum states that the total angular momentum of a system remains constant unless acted upon by an external torque. Angular momentum is a property of rotating objects and depends on both the mass and distribution of mass in an object, as well as its rotational speed.
In the case of a planet revolving in an elliptical orbit, the planet experiences varying distances from the central body as it moves along its path. Despite these variations, the conservation of angular momentum still holds true. As the planet moves closer to the central body, its orbital speed increases to compensate for the decrease in distance, preserving the overall angular momentum of the system.
Similarly, for a planet revolving in a circular orbit, the conservation of angular momentum applies. In a circular orbit, the planet maintains a constant distance from the central body, and its orbital speed remains consistent to ensure that the angular momentum remains conserved.
Therefore, regardless of whether a planet is in an elliptical or circular orbit, the principle of conservation of angular momentum is applicable. This principle plays a crucial role in understanding the dynamics and stability of planetary motion.
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Given: NM 1 XZ
Prove: AXYZ- ANYM
N
Try 11
X
Z
M
We know that side NM is
to side
XZ. If we consider side NY the transversal for these
parallel lines, we create angle pairs. Using the
we can state
that YXZ is congruent to YNM. We know that angle
XYZ is congruent to angle
by the reflexive
property. Therefore, triangle XYZ is similar to triangle
NYM by the
similarity theorem.
F
The prove of Angle XYZ- Angle NYM is given below:
∠XYZ is congruent to ∠NYM - reflexive property. ΔXYZ is the same with Δ NYM,- AA (angle-angle) similarity theorem.What is the triangle about?Note that from the image given;
NM // XZNY = transversal line∠YXZ ≡ ∠YNMSince ∠XYZ is said to be congruent to ∠NYM it can be proven by the use of the reflexive property.
The reflexive property is one that informs that any shape is regarded congruent to itself.
Since ∠NYM has a different way to call ∠XYZ that uses a different vertexes, but the sides are made up of the two angles which are said to be the same.
Therefore , ∠XYZ ≡ ∠NYM are proved by the reflexive property.
Since ΔXYZ is the same with Δ NYM, it can be proven by the AA (angle-angle) similarity theorem.
We have 2 angles Δ XYZ and Δ NYM:
Note that ∠YXZ ≡ ∠YNM
∠XYZ ≡ ∠NYM
So, ΔXYZ is said to be the same to ΔNYM and it is proven by the AA similarity theorem.
Therefore, The prove of Angle XYZ- Angle NYM is given below:
∠XYZ is congruent to ∠NYM - reflexive property. ΔXYZ is the same with Δ NYM,- AA (angle-angle) similarity theorem.Learn more about triangles from
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Answer:
1. parrael
2. corresponding angles theorem
3. NYM
4. AA
Explanation:
just took it
Blocks A and B of masses M and 3M, respectively, are on a horizontal surface of negligible friction. A horizontal force FA is exerted on block A, as shown. If the force exerted by block B on block A has a magnitude F, the magnitude of FA is
a. 1/4 F
b. 3/4 F
c. F
d. 4/3 F
e. 4F
If there is no friction and block B pushes block A with a force of magnitude F, therefore FA will also have a magnitude F, according to Newton's third law of motion.
Newton's Third Law.According to Newton's third law, each force (action) in nature has an opposite and equal response. Whenever object B pulls on object A, item A pulls back on item B with an equal and opposing force.
Given :
Mass of Block A = M
Mass of Block B = 3M
Force exerted on block A is FA
Because both boxes are in contact.
Hence, force exerted by block A on block B is same that is FA
Force exerted by block B on block A has magnitude F (Given)
From Newton's third law of motion, the magnitude of FA is F Newton.
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If driving in fog, you should ______ All choices are correct use low-beam headlights use your defroster use your wipers Submit answer
When driving in fog, it is recommended to use low-beam headlights, use your defroster, and use your wipers. All of these choices are correct for enhancing visibility and maintaining safety in foggy conditions .By using low-beam headlights, the defroster, and the wipers, drivers can effectively combat the challenges posed by foggy conditions and ensure safer navigation on the roads.
Driving in fog can significantly reduce visibility, making it essential to take appropriate measures to enhance visibility and ensure safety on the road. One of the recommended actions is to use low-beam headlights instead of high beams. Low beams provide better illumination in fog by reducing the glare and reflection caused by the fog particles, improving visibility for both the driver and other road users.
Using your defroster is another important step. Foggy conditions often lead to moisture buildup on the windshield, which can further obstruct visibility. The defroster helps to clear the windshield by removing condensation or fog from the glass surface, allowing for a clearer view of the road ahead.
Additionally, using your wipers is necessary in foggy conditions to keep the windshield clear of any moisture, such as mist or light rain. The wipers help to remove water droplets or fog residue that may accumulate on the windshield, improving visibility and preventing any distortion or obstruction caused by water streaks.
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The magnetic field at the center of a 1.0-cm-diameter loop is 2.5 mT. What is the current in the loop
The current flowing through the loop is approximately 1.96 amperes.
Ampere's law states that the magnetic field around a closed loop is directly proportional to the current passing through the loop and inversely proportional to the distance from the center of the loop. By rearranging the formula, we can solve for the current:
B = (μ₀ * I) / (2 * π * r),
where B is the magnetic field, I is the current, μ₀ is the permeability of free space (a constant), and r is the radius of the loop.
In this case, we are given the magnetic field B = 2.5 mT and the diameter of the loop, which is equal to twice the radius (1.0 cm). We can convert the magnetic field to tesla by dividing by 1000 (1 T = 1000 mT). Thus, B becomes 0.0025 T, and the radius r is 0.5 cm.
Substituting these values into the rearranged Ampere's law equation, we have:
\(0.0025 T = (4\pi * 10^{-7} T m/A * I) / (2 * \pi * 0.5 cm).\)
Simplifying the equation, we cancel out the common factors and convert cm to meters:
\(0.0025 = (4\pi * 10^{-7}I) / 0.01.\).
Further simplification yields:
\(I = (0.0025 * 0.01) / (4\pi * 10^{-7}).\)
Evaluating the right side of the equation, we find:
I ≈ 1.96 A.
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