We have the given equation as [tex]\frac{7x}{(x+6)(3x+2)}[/tex] that we have to convert through partial fraction decomposition.
What is Partial Fraction?The partial fraction decomposition or partial fraction expansion of a rational fraction in algebra is the process of expressing the fraction as the product of a polynomial (possibly zero) and one or more fractions with a simpler denominator.
A rational fraction is defined as one that has a polynomial as both the numerator and the denominator.
Theory and solutionWe have to find the form of the partial fraction decomposition of the function.
The given rational function has two factors in multiplication form in the denominator.
Also, the degree of the numerator is less than the denominator. Hence, the form of partial fraction decomposition of the function is:
[tex]\frac{7x}{(x+6)(3x+2)}[/tex] = [tex]\frac{A}{x+6} + \frac{B}{3x+2}[/tex]
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In complete sentences please
Answer:
The topic of the graph is the age of people getting married. The x-axis shows the year and the y-axis shows the age of those getting married. The graph shows that as time has gone on, people have waited longer to marry. This is likely because they want to wait to find their true love before settling down, and there is a lot less pressure on people to get married now. Based on the statistics shown in the graph, I believe that in 10 years the average age of marriage will be between the age of 30 and 35.
A ball is thrown directly downward with an initial speed of 8.55 m/s, from a height of 30.4 m. after what time interval does it strike the ground?
The ball will reach the ground after 1.8 seconds.
We have a ball thrown directly downward.
We have to determine after what time interval does it strike the ground,
According to the question -
u = 8.55 m/s
S = 30.4 m
a = 9.8 m/[tex]s^{2}[/tex]
Using the Second Equation of Motion -
x = ut + [tex]\frac{1}{2} at^{2}[/tex]
Substituting the values -
30.4 = 8.55t + 4.9[tex]t^{2}[/tex]
4.9[tex]t^{2}[/tex] + 8.55t - 30.4 = 0
Solve this quadratic equation, you will get -
t = 1.8 seconds.
Hence, the ball will reach the ground after 1.8 seconds.
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if an astronaut can throw a certain wrench 14.0 m vertically upward on earth, how high could he throw it on our moon if he gives it the same starting speed in both places?
The formula that we will apply to get to the answer would be:
2as = v² - u²
Using this we will get the answer as 82.35425 m.
Formulation and calculationHere,
U= initial velocity
V= final velocity
S= displacement of the body
A= acceleration of the body/ acceleration due to gravity (as per the question)
Something that has not been mentioned here but is present in the original question is that the acceleration due to gravity has been given as 0.170g.
While throwing the wrench on earth,
v² - u² = 2as
⇒[tex]u = \sqrt{v^2 - 2as}[/tex]
⇒ u = [tex]\sqrt{0-2 * -9.81 * 14}[/tex]
⇒ u= 16.57347 m/s
Since the astronaut gives the same starting speed in both the places so the u on moon would be 16.57347 m/s
While throwing the wrench on moon,
v² - u² = 2as
s = [tex]\frac{v^2 - u^2}{2a}[/tex]
⇒ s = [tex]\frac{0^2 - 16.57347^2}{2 * (-9.81) * 0.17}[/tex]
⇒s = 82.35425 m
so, on moon, the wrench could be thrown a distance of 82.35425 m
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what is the definition of density? the measure of mass of a material within a given space. the measure of mass of a material within a given space., defragment, the volume of an object. the volume of an object., defragment, the weight of an object the weight of an object, defragment, the mass of an object.
the definition of density is: the measure of mass of a material within a given space
The density of an object is the relation that exist between the mass and the space that the object occupies. The general formula of the density is:
ρ = m/v
Where:
v= volumeρ= densitym= massFor example if we want to know which is the density of a body that has a mass of 100g and a volume of 150 cm³, applying the density formula we get:
ρ = 100 g/150 cm³
ρ = 0.666 g/cm³
What is density?It is a physical quantity that expresses the ratio of the body mass to the volume it occupies.
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As an airplane accelerates in level flight, what parameter must the pilot adjust to keep level and balance (lift = weight)?
As an airplane accelerates in level flight, pilot must adjust to keep level and balance at the angle of attack.
What is the type of lift in reference to airplane?When the air flows through the wingspan of an airplane, it generates a pressure difference between the upper and lower portions of wings. Due to this pressure difference, an upward force is generated that acts in upwards direction known as the aerodynamics lift.
In this case:
At the equilibrium condition, the upward lift generated by the airplane is equal to the weight of airplane. The lift generated depends upon area of the wind span, density, and velocity of the air; these values can not be changed by the pilot. But by changing the angle of attack parameter, the desired lift can be produced, and angle of attack can be changed easily by the pilot.
Therefore as an airplane accelerates in level flight, the parameter the pilot must adjust to keep it level and balance the lift to the weight is angle of attack.
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A brine solution of salt flows at a constant rate of l/min into a large tank that initially held l of brine solution in which was dissolved kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is kg/l, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach kg/l?.
which is 0.05 kg/L Just keep in mind that the concentration in the tank will fluctuate over time until it reaches the inflow concentration.
Chemistry involves creating and manipulating solutions frequently, yet a variety of concentration units are employed depending on the reaction or kind of analysis. Molality (M = moles solute/kg solution), mass% (mass solute/mass solution), and mass per volume concentrations are a few examples of frequent units.
After t minutes, the salt mass in the tank with a concentration of
0.02 kg/L is 2 kg.
According to the way the question is written, the tank's concentration is 0.02 kg/L, and its volume, which is independent of its input and outflow quantities, is 100 L. In light of this, multiplying the concentration by the volume will provide the amount of salt in the tank at the specified concentration.
(0.02kg/L)(100L) = 2kg
Just keep in mind that the concentration in the tank will fluctuate over time until it reaches the inflow concentration, which is 0.05 kg/L. The amount of time it will take for that to happen can be predicted by an equation, but that is not the issue being addressed here; rather, it is how much salt will be in the tank at time t when the tank concentration is
0.02 kg/L.
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The complete question is:
In a huge tank that initially stores 100 L of brine solution with 0.5 kg of salt dissolved in it, a brine solution of salt flows at a steady rate of 8 L/min. The interior of the tank is kept thoroughly stirred, and the solution drains at the same rate. Determine the mass of salt in the tank after t minutes when the concentration of salt in the tank reaches 0.02 kg/L if the salt concentration in the brine entering the tank is 0.05 kg/L.
bees often work together for the greater good of the hive. sometimes they can get excess charge on them. four pairs of bees, which can be represented as identical, conducting spheres, bump into each other in the hive. rank the bees in the order of the size of the magnitude of charge transfer. assume that since the bees are identical, they will have the same amount of charge after making contact. (enter your answer in decreasing order of the size of the magnitude of charge transfer. use only ">" or "=" symbols. do not include any parentheses around the letters or symbols.)
it goes as follows- B> C> A> D
Bees frequently cooperate for the benefit of the colony. They occasionally may have an excessive charge on them. In the hive, four pairs of bees collide with one another. These bees can be visualized as identical conducting spheres. Sort the bees according to the size of the charge transfer's magnitude. Bees live in hives with a distinct social structure. Three varieties of bees, each with a specific job, are present in each hive. The female workers gather food and take care of the hive, while the male drones fertilize the eggs laid by the queen. Every type of bee is modified for its specific job. As they get older, the workers' tasks change.
As we can see, there are four pairs of bees, conducting spheres, and it appears that B is higher than C, which is higher than A, which is lower than D.
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8
2 points
Select the two words that correctly complete this statement.
The mass number of an atom is affected by the
Neutron
Proton
Electron
and the
0
Answer:
neutron and proton are the answer
Through what total distance (in m) has the object moved between t = 0 and t = 18 s?
Distance covered by the box is 135m.
What are equation of motion?Equations of motion in physics are equations that explain how a physical system behaves in terms of how its motion changes over time. The behaviour of a physical system is described in further detail by the equations of motion as a collection of mathematical functions expressed in terms of dynamic variables.
The following are the three equations of motion:
First Equation of Motion : v = u + a t.Second Equation of Motion : s = u t + 1 2 a t 2.Third Equation of Motion : v 2 = u 2 + 2 a s.the theoretical question is complete but the diagram is missing, its added in the attachment.
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a 26.9-g mass is suspended 1.79 cm above a nonconducting flat plate, directly above an embedded charge of q. a) if the mass has the same charge, q, how much must q be so that the mass levitates (just floats, neither rising nor falling)?
For mass to levitate charge must be 9.692×10⁻⁸ C.
For mass to levitate,
mg=Fe ( Fe here refers to electrostatic force)
mg=(kq₁q₂/r²)
here q₁=q₂,
q²=(mgr²/k)
q²=( 26.9×10⁻³×9.81×(1.79×10⁻²)²)/9×10⁹
q²=93.947×10⁻¹⁶
q = 9.692×10⁻⁸ C
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a person jogs eight complete laps around a 400-m track in a total time of 15.1 min .calculate the average speed, in m/s .
The average speed in m/s of a person that jogs eight complete laps around a 400m track in a total time of 15.1 min is 0.44m/s.
How to calculate average speed?Average speed of a moving body can be calculated by dividing the distance moved by the time taken.
Average speed = Distance ÷ time
According to this question, a person jogs eight complete laps around a 400m track in a total time of 15.1 min. The average speed is calculated as follows:
15.1 minutes in seconds is as follows = 906 seconds
Average speed = 400m ÷ 906s
Average speed = 0.44m/s
Therefore, the average speed in m/s of a person that jogs eight complete laps around a 400m track in a total time of 15.1 min is 0.44m/s.
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The solubility of co2 in soda when the soda is canned under a pressure of 4.5 atm will:_________
The solubility of CO₂ in soda when the soda is canned under a pressure of 4.5 atm will 129.03 moles L⁻¹
According to Henry's law, the amount of a specific gas that dissolves in a liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid at a particular temperature.
Only at moderate pressure and temperature does Henry's law apply. iii. Henry's law is not followed by the gases reacting with the solvent. Ammonia or HCl, for instance, react with water and do not follow this rule.
Henry's law states that P=Ks S is the solubility in moles. Henry's law is L1 K. P stands for continuous pressure in atm.
Change the values in the preceding equation to:
S = Kp = 4 / 3.1*10²
= 129.03 moles L⁻¹
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What is Earth's natural form of visible light and what color is it?
Answer:
La luz visible es una onda electromagnética, que consiste en oscilaciones eléctricas y campos magnéticos que viajan por el espacio. La frecuencia de la onda determina el color: 4×1014 Hz es la luz roja, 8×1014 Hz es la luz violeta, y entre estos en el rango de 4-8×1014 Hz están todos los otros colores del arco iris
Explanation:
Answer:
Sunlight is the earth's natural form of visible light it is typically referred to as white light.
A cold drink initially at 39 f warms up to 42 f in 4 min while sitting in a room of temperature 72 f. how warm will the drink be if left out for 15 min?
If the cold drink will be left out for 15 minutes its temperature would be 72 F.
The formula for Newton’s Law of Cooling is given in the adjoining image.
Applying the given values in the above equation,
T- T1 = (TS - T1) e^-kt
42 -72 = (39-72) e^-2k
- 30/ -33 = e^-2k
K = 0.045
Putting k = 0.045 and t = 15 minutes
T comes out to be 72 F.
Hence, if the cold drink will be left out for 15 minutes its temperature would be 72 F.
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I went for a walk the other day. i went four avenues east (0.80 miles), then twenty-four streets south (1.20 miles), then one avenue west (0.20 miles), and finally eight streets north (0.40 miles). a. what distance did i travel? b. what's my resultant displacement (magnitude and direction relative to due east)?
By using vector
a. the distance traveled is 2.6 miles
b. the resultant displacement is s = ( 0.6 i - 0.8 j ) miles
the magnitude is |s| = 0.6 miles
We need to know about vectors to solve this problem. Vector has magnitude and also direction. Displacement is included in vector. It can be written as
s = sx i + sy j + sz k
where s is displacement, sx is displacement on x-axis, sy is displacement on y-axis and sz us displacement on z-axis.
From the question above, we know that
east = positive x
south = negative y
west = negative x
north = positive y
s1 = 0.8 i
s2 = -1.2 j
s3 = -0.2 i
s3 = 0.4 j
The distance traveled is
s = s1 + s2 + s3 + s4
s = 0.8 + 1.2 + 0.2 + 0.4
s = 2.6 miles
The resultant displacement is
s = s1 + s2 + s3 + s4
s = 0.8 i -1.2 j -0.2 i + 0.4 j
s = ( 0.6 i - 0.8 j ) miles
The magnitude is
|s| = √sx²
|s| = √0.6²
|s| = 0.6 miles
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Why does a feather drift back and forth as it falls ?
(I’m confused I think it has something to do with terminal velocity though in my mind)
Answer:
you are very most correct
Explanation:
it does have something to do with terminal velocity and because the weight is so light of it any tiny gust of wind can push it back and forth and because wind is never stable thats why it moves side to side
An astronaut who weighs 700 n on earth is in empty space, very far from any other objects. approximately what is the mass of the astronaut?
the mass of the astronaut will be 70KG, the mass stays the same everywhere.
What is space?The infinite three-dimensional expanse of space is where things and events have relative positions and directions. While modern physicists typically consider it to be a portion of an unbounded four-dimensional continuum known as spacetime, physical space is frequently conceptualized in classical physics as having three linear dimensions. It is believed that grasping the idea of space is essential to comprehending the physical cosmos. Philosophers dispute on whether it is a thing in and of itself, a connection between entities, or a component of a conceptual framework. Mathematicians started looking at non-Euclidean geometries in the 19th and 20th centuries, when space is thought of as curved rather than flat. Space around gravitational fields deviates from Euclidean space, according to Albert Einstein's theory of general relativity.
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it is known that the electric force of repulsion between two electrons is much stronger than the gravitational attraction. for two electrons at a distance d apart, calculate the ratio of the size of the electrostatic repulsion to that of the gravitational attraction.
The ratio of the size of the electrostatic repulsion to that of the gravitational attraction is 4.17×[tex]10^{42}[/tex]
if an arrow is shot upward on mars with a speed of 66 m/s, its height in meters t seconds later is given by y
By using uniform motion, the maximum height of arrow is 585.326 meters.
We need to know about the uniform motion to solve this problem. The uniform motion is an object's motion under acceleration. It should follow the rule
vt = vo + a . t
vt² = vo² + 2a . s
s = vo . t + 1/2 . a . t²
where vt is final velocity, vo is initial velocity, a is acceleration, t is time and s is displacement.
From the question above, we know that
vo = 66 m/s
vt = 0 m/s
gmars = 3.721 m/s²
By using the second equation, we can calculate the maximum height
vt² = vo² + 2a . s
0² = 66² - 2g . y
2 . 3.721 y = 4356
y = 585.326 meters
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What is a chemical change?
A. The appearance of an object changes, but its makeup remains the same.
B. One kind of matter changes into a different kind of matter with different properties. C. the process by which particles leave a liquid and become a gas.
Answer:
B. one kind of matter changes into a different kind of matter with different properties
11 A feather of mass 10 g falls from rest from a height of 3 m and takes 2s to hit the ground. Find the air
resistance on the feather.
The air resistance on the feather is 20.2275 x [tex]10^9[/tex]N.
Air resistance is the force the air applies to objects moving through it. Scientists frequently refer to this force as drag or drag force. Usually, this force is utilized to slow down the object's speed by acting in the opposite direction.
The moving body is subject to the frictional force of air resistance. Air resistance slows a moving body down. The body experiences higher air resistance the more it moves.
Given:
Mass, m = 10g
Height, h = 3m
Time, t = 2s
Force constant, k = 8.99 x [tex]10^9 Nm^2[/tex]
To find:
Air resistance, Fa = ?
Formula:
[tex]Fa = kv^2[/tex]
Calculations:
Speed, v = h/t
v = 3/2
v = 1.5m/s
Fa = 8.99 x [tex]10^9[/tex] x 1.52
Fa = 20.2275 x [tex]10^9[/tex]N
Result:
The air resistance on the feather is found to be 20.2275 x [tex]10^9[/tex]N.
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A certain european automobile has a gas mileage of 19 km/l. part a what is the gas mileage in miles per gallon?
The correct answer is 44.6 miles/gallon.
Finding the complete mileage and fuel consumption of a car over the course of the entire journey is necessary to answer this type of query. We must thus calculate the value for each mile separately using the provided data in order to avoid getting the incorrect answer by just adding the value of the gallons.
The number of miles an automobile can go on one gallon of fuel is known as MPG, or miles per gallon. A car's fuel efficiency is mostly measured by its MPG; the greater the MPG, the more efficient the vehicle is.
Speed of the automobile = 19 km/L
Use the following conversion factor to convert km/l into miles/gallon
19(km×0.621miles/km)/(l×0.264gallon/L)
=44.6 miles/gallon
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Olivia was riding her bike at a speed of 4m/s when she began rolling down a hill. The hill caused her to accelerate at a rate of 2m/s 2 until she reached the end of the hill 45m later. How fast was she going when she made it to the bottom of the hill?
The speed of Olivia when she made it to the bottom of the hill is 14m/s.
Kinematics is the study of mechanical points, bodies, and systems in motion without taking into account the forces acting on them or the corresponding physical qualities.
Kinematics equations of motion define the fundamentals of an object's motion, such as its position, velocity, or acceleration over time. These three equations of motion control how an item moves in one, two, and three dimensions.
Kinetics considers physical forces as well as material characteristics such as mass stiffness and tensile or compressive strength. These characteristics can be used to take a theoretical model from kinematics and use physics and thermodynamics to determine how to construct a workable, dependable, and functional real-world system.
Given,
Initial velocity, u = 4m/s
Acceleration, a = 2m/s-2
Displacement, s= 45m
we know that,
[tex]v^{2}= u^{2} + 2as[/tex], where v= final velocity
substituting the value in the above equation, we got
[tex]v^{2}[/tex] = [tex]4^{2} + 2(2)(45)[/tex]
v = [tex]\sqrt{196}[/tex]
v = 14 m/s
Thus, the speed of Olivia going down the hill is 14m/s.
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how research is important on gathering necessary information
Thank you !
. Electromagnetic induction is used by electric transformers to modify the voltage of current flow. Transformers may change the voltage in two different ways. What are the two ways?
Transformers may change the voltage in two different ways which are
Step up; Using step-up transformersStep down; Using step-down transformersThis is further explained below.
What is electromagnetic induction.?Generally, Electric transformers are devices that can change the direction and speed of the flow of current in an electrical circuit. They do this by adjusting the voltage of the existing flow of current through the use of electromagnetic induction.
In conclusion, There are two distinct methods by which transformers may alter the voltage, and they are
Step up; Using step-up transformersStep down; make use of transformers that scale down the voltageThe step-up transformer is usually used for the transmitting of electric charge through a lengthy distance where power drop might be experienced, while the step-down is used to moderate said transmitted charge to a consumer.
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A glass rod that has been charged to 14.0 nc touches a metal sphere. afterward, the rod's charge is 7.0 nc . what kind of charged particle was transferred between the rod and the sphere?
The charged particles that transferred between the glass rod and the metal sphere were electrons.
The rod has lost some of the charges it had earlier as the remaining count of charges is less than the previous one.Before analysing the type of the charge it is worthy to know about the conductive properties of both the materials.Glass is insulative while metal is conductive. Conductive materials in the sense have free electrons in abundance compared to insulative materials that conduct electricity within them. Glass, in comparison, does not conduct charges dynamically but rather keeps them stationary where those were originated. Electrons are more dynamic than protons.In this case, the metal sphere is neutral at the beginning that contained equal amounts of negative(electrons) and positive(protons) within it. Once the rod is taken close and eventually touched the sphere the more dynamic electrons flow into the rod nullifying the charges the rod had earlier.Therefore, it can be concluded that the type of charges the rod had were positive ones(protons) and the charges moved between them were electrons from the sphere to the rod.Otherway around is impossible.Finally, the sphere contains an amount of positive 7.0 nC charge while the rod contains the remainder of 7.0 nC on the parts which did not touch the sphere.
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a certain freely falling object, released from rest, requires 1.45 s to travel the last 27.0 m before it hits the ground.
By using uniform motion, the speed before hitting the ground is 23.00 m/s.
We need to know about the uniform motion to solve this problem. The uniform motion is an object's motion under acceleration. It should follow the rule
vt = vo + a . t
vt² = vo² + 2a . s
s = vo . t + 1/2 . a . t²
where vt is final velocity, vo is initial velocity, a is acceleration, t is time and s is displacement.
From the question above, we know that
vo = 0 m/s
t = 1.45 s
y = 27 m
g = 9.8 m/s²
By using the second equation, we can calculate the speed before hit the ground.
vt² = vo² + 2a . s
vt² = 0² + 2g . 27
vt² = 2 . 9.8 . 27
vt² = 529.2
vt = 23.00 m/s
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When a gas undergoes a quasi-static isobaric change in volume from 10.0 to 2.0 l, 15 j of work from an external source are required. what is the pressure of the gas?
When a gas undergoes a quasi-static isobaric change in volume from 10.0 to 2.0 l, 15 j of work from an external source are required then the pressure of the gas is
Work done is given as
W=PdV
15 = P ×( 20-10)
P = 1.5 bar
Define pressure.The force delivered perpendicularly to an object's surface per unit area across which that force is dispersed is known as pressure (symbol: p or P). The pressure relative to the surrounding air is known as gauge pressure, also written gage pressure[a].
Pressure is expressed using a variety of units. Some of these result from dividing a unit of force by a unit of area; the pound-force per square inch (psi), which is equivalent to one newton per square meter (N/m2) in the SI, is the standard unit of pressure in the imperial and U.S.
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If she drove back home using the same path she took out to the university and arrives 7.7 h after she first left home, what was her average speed for the entire trip, in kilometers per hour?
The average speed = (2 × the length of the path to the university in km) / (7.7 h)
The exact length of the path to the university is not given in the question but it is not unanswerable, therefore, consider that distance to be L measured in kilometres.If the distance is given in meters you need to convert it to kilometres as the question asks in that unit.The definition of the average speed is the key to the answer to this question which is given by
average speed = total distance covered [tex]\div[/tex] total time elapsed
So, the total distance covered is the addition of the distance of the trip to the university from home and the distance covered the way back home which is twice the distance to the university from home.And the total time taken to cover that distance is measured as 7.7 h and it can be thought of as follows as well.time to go - time to come = total time taken = 7.7 h
Therefore, simple substitution to the above average speed formula yields the required answer as follows,[tex]\begin{aligned}\\ \text{average speed} & =\small \frac{2\times L (km)}{7.7 \, h}\\\\&=\small \frac{2L}{7.7} \,km/h\\\end{aligned}[/tex]
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A sine wave has a rms value of 208 v. what is the peak value? group of answer choices
A sine wave has a rms value of 208 v, the peak value is 294.15v.
What is rms?The RMS value of a set of values (or a continuous-time waveform) is the square root of the arithmetic mean of the squares of the values, or square of the function that defines the continuous waveform. In physics, RMS current value can also be defined as the "value of the direct current that dissipates same power in a resistor".
Physical scientists often use the term root mean square as a synonym for standard deviation when it can be assumed input signal has zero mean, that is, referring to the square root of mean squared deviation of a signal from a given baseline or fit. This is useful for the electrical engineers in calculating "AC only" RMS of a signal. Standard deviation being the RMS of a signal's variation about the mean, rather than about 0, DC component is removed (that is, RMS(signal) = std e v (signal) if the mean signal is 0).
Mean power, or root mean square (RMS) power handling, refers to how much continuous power speaker can handle. The peak power handling value refers to the maximum power level that speaker is capable of utilizing in short bursts.
Therefore,
Peak value= rms[tex]\sqrt{2}[/tex]
=294.15v
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