The percentage of people with blood pressure between 120 mm and 160 mm is approximately(d) 78.8%.
To estimate the percentage of people with blood pressure below 120 mm, we need to calculate the z-score for that value:
z = (120 - 140) / 20 = -1
Using a standard normal table, we can find the proportion of the distribution below a z-score of -1, which is approximately 0.1587. However, since we want the percentage below 120 mm, we need to multiply this proportion by 100 and round to one decimal place:
0.1587 x 100 ≈ 15.9%
Therefore, the percentage of people with blood pressure below 120 mm is approximately 15.9%.
To estimate the percentage of people with blood pressure between 120 mm and 160 mm, we need to calculate the z-scores for both values:
z1 = (120 - 140) / 20 = -1
z2 = (160 - 140) / 20 = 1
Using a standard normal table, we can find the proportion of the distribution between these two z-scores, which is approximately 0.7887. To find the percentage between 120 mm and 160 mm, we need to multiply this proportion by 100 and round to one decimal place:
0.7887 x 100 ≈ 78.8%
Therefore, the percentage of people with blood pressure between 120 mm and 160 mm is approximately 78.8%.
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However, they did not measure stellar parallax—the stars did not appear to move back and forth at all over the course of a year. What is the most likely reason for this apparent lack of motion?A. The heliocentric model explains retrograde motion because Mars only appears to move backward as Earth passes it in its orbit around the Sun.B. The planets would usually move west to east through the stars, but they appear to reverse direction when they are on the part of the epicycle that has motion opposite to that of the larger circle.C. The starts must be so distant that their parallaxes are too small for the ancient Greeks to have been able to measure with their technology.D. The geocentric model is wrong because it falsely predicts that Mars should always move in the same direction with respect to the stars.
The stars must be so distant that their parallaxes are too small for the ancient Greeks to have been able to measure with their technology.
Option C.
What is parallax?
Parallax is the apparent shift in the position of an object when viewed from different locations. In the case of measuring stellar parallax, astronomers look at the apparent shift in the position of a star against the background of more distant stars as the Earth orbits the Sun.
However, the amount of parallax observed is related to the distance to the star, with more distant stars showing smaller amounts of parallax. The ancient Greeks did not have the technology to measure small angles accurately, and so they were unable to measure the small parallaxes of the distant stars.
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HS: Physics A [M]
riptiv
All changes
9. A car is traveling at constant speed v across a flat road. First the road curves in a circular arc
radius 2R, and then it curves in a circular arc of radius R. As the car travels from the first curve
the second curve, how is its centripetal acceleration affected?
Answer:
Uniform Circular Motion:
When a car goes around a circular curve, the velocity of the car definitely changes because of the change in the direction of the car. However, the speed of the car does not necessarily change and circular motion can be sustained by a constant speed. Explanation: i don't know dawg :)
A swimmer wants to cross a river, from point A to point B, as shown in the figure. The distance d1 (from A to C) is 159 m, the distance d2 (from C to B) is 121 m, and the speed vr of the current in the river is 5 km/hr. Suppose that the swimmer's velocity relative to the water makes an angle of θ = 45 degrees with the line from A to C, as indicated in the figure. To swim directly from A to B, what speed us, relative to the water, should the swimmer have?
The speed us the swimmer should have relative to the water is 7.07 km/hr.
What is the speed ?The speed is the rate at which an object or person moves from one place to another. It can be measured in terms of velocity, which is the rate of change of position over time. Speed can also be measured in terms of acceleration, which is the rate of change of velocity over time. Speed is typically measured in units such as miles per hour (mph), kilometers per hour (kph), or meters per second (m/s).
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The speed, Us of the swimmer relative to the water, is, Us = 4.02km/hour.
If the swimmer reported their pace in kilometers per hour, we must calculate our speed relative to the water.
Consequently, the swimmer's speed in relation to the water is
Us equals 4.02 km/h
It is possible to separate the swimmer's speed Us into its vertical and horizontal components.
Thus, Usx = -(Us Cos45°) is the formula for the horizontal component of speed, Us.
Because the speed, Us, is located on the negative x-axis, the above symbol is negative.
Additionally, Usy = Us Sin45° represents the vertical component of speed.
Additionally, the river's horizontal component of speed Vr is,
Cos0° + Vrx = Vr + 5km/h
Additionally, the river's vertical component of speed Vr is,
Sin0° = 0km/h, where Vry = Vr
This is true because the speed VR forms a horizontal angle of 0°.
As a result, V'x and V'y represent the total speed in the horizontal and vertical directions, respectively, at (5-UsCos45) and (UsSin45).
As a result, the amount of time needed to go from point A to point C is,
Ty = d1/(UsSin45) (UsSin45).
Furthermore, the time Tx needed to go from point C to point B is,
Tx = d2/(5 - UsCos45) (5 - UsCos45)
Though Tx = Ty.
Therefore,
UsSin45 d1/ = d2 (5 - UsCos45).
i.e 159 / (0.7071Us) = 121 / (5 - 0.7071Us) (5 - 0.7071Us).
the cross-product
85.56Us = 795 - 112.43Us
85.56Us + 112.43Us = 795
197.99Us = 795
Us = 795 / 197.99 for the speed.
Usual swimming speed in relation to water is,
Us equals 4.02 km/h.
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Complete question -
What are a list of the months of the year ?
The months of the year, in order, are:
January, February, March, April, May, June, July, August, September, October, November, December.
January: This is the first month of the year and is named after the Roman god Janus, who had two faces and was believed to look back on the old year and forward to the new one.
February: This is the shortest month of the year, with 28 days in a regular year and 29 days in a leap year. It is named after Februa, a Roman festival of purification.
March: This is the third month of the year and is named after Mars, the Roman god of war. It is associated with the beginning of spring in the Northern Hemisphere.
April: This is the fourth month of the year and is believed to be named after the Latin word "aperire," which means "to open," as this is the time of year when trees and flowers begin to bloom.
May: This is the fifth month of the year and is named after the Greek goddess Maia, who was associated with growth and fertility.
June: This is the sixth month of the year and is named after the Roman goddess Juno, who was the queen of the gods and the patroness of marriage and childbirth.
July: This is the seventh month of the year and is named after Julius Caesar, the Roman general and statesman who reformed the calendar and was born in this month.
August: This is the eighth month of the year and is named after Augustus Caesar, the first Roman emperor and the successor of Julius Caesar.
September: This is the ninth month of the year and is derived from the Latin word "septem," which means "seven," as it was originally the seventh month in the Roman calendar.
October: This is the tenth month of the year and is derived from the Latin word "octo," which means "eight," as it was originally the eighth month in the Roman calendar.
November: This is the eleventh month of the year and is derived from the Latin word "novem," which means "nine," as it was originally the ninth month in the Roman calendar.
December: This is the twelfth and final month of the year and is derived from the Latin word "decem," which means "ten," as it was originally the tenth month in the Roman calendar.
Each month has a varying number of days, ranging from 28 to 31. The months with 31 days are January, March, May, July, August, October, and December. The months with 30 days are April, June, September, and November. February has 28 days in a regular year and 29 days in a leap year.
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Volatile high energy stored in bonds easily combustible organic compound liquid at room temperature based on the provided chemical and physical properties of the unknown substance, it would be most useful as a(n).
Based on the provided chemical and physical properties, the unknown substance would be most useful as a fuel.
The substance is an easily combustible organic compound that is in liquid form at room temperature, and it contains a lot of volatile, high-energy bonds.
These properties make it an ideal fuel for a range of applications. The high energy content of the bonds means that the fuel can be used to power engines and generate heat, while the liquid form makes it easily transportable.
The combustible nature of the substance also makes it a suitable fuel for cooking and other activities that require a flame. The fact that it is in liquid form at room temperature also makes it easier to store and use.
The unknown substance is a versatile fuel that can be used for a variety of applications.
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Answer:
a
Explanation:
the chemical change in the physical change
what is the answer to 2(3xX543)+90y
The answer to this equation is not possible to calculate without knowing the value of x and y.
What is equation ?An equation is a mathematical statement that expresses the equality of two expressions. Equations are used to find unknown values, such as the number of solutions to a problem, and to describe the relationship between two or more variables. An equation is composed of two expressions connected by an equal sign (=). The two expressions must be the same, meaning that whatever value is on one side of the equation must be the same value on the other side. Equations can be used to describe a wide variety of real-world situations, such as the speed of a car, the cost of a house, or the force of a magnet.
This equation contains two variables, x and y. In order to calculate the answer, we would need to know the value of each variable.
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What is the average force of gravitation between Pluto and the Sun?
Answer:
5.3 x 10^13 N.
Explanation:
The force of gravity between two objects can be calculated using the equation:
F = G * (m1 * m2) / d^2
where F is the force of gravity, G is the gravitational constant (6.67 x 10^-11 N m^2/kg^2), m1 and m2 are the masses of the two objects, and d is the distance between their centers.
To calculate the average force of gravity between Pluto and the Sun, we need to know their masses and the average distance between them.
Pluto has a mass of approximately 1.309 x 10^22 kg, and the average distance between Pluto and the Sun is about 5.9 x 10^9 m.
Plugging these values into the equation, we get:
F = 6.67 x 10^-11 N m^2/kg^2 * (1.309 x 10^22 kg * 1.989 x 10^30 kg) / (5.9 x 10^9 m)^2
F = 5.3 x 10^13 N
So the average force of gravity between Pluto and the Sun is approximately 5.3 x 10^13 N.
7N
2 kg
17 N
Net Force:
Balanced or Unbalanced
Direction of Motion:
The net force is obtain as the effective force.
What is the net force?The question is unclear but I will try to explain the concept of the net force.
The net force is the sum of all the forces acting on an object. In other words, it is the overall force that is causing an object to accelerate or change its motion. If the forces acting on an object are balanced, then the net force is zero and the object will remain at rest or continue moving with a constant velocity.
If the forces are in the same direction, then the net force will be equal to their sum. If the forces are in opposite directions, then the net force will be the difference between them.
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which one of the following properties most fundamentally distinguishes mechanical waves from electromagnetic waves?
B is correct option. Mechanical waves and electromagnetic waves both transfer energy through space, but they differ in fundamental ways.
Mechanical waves require a medium for their transmission, whereas electromagnetic waves can travel through a vacuum. This is a fundamental difference between the two types of waves that affects their behavior and properties.
In a mechanical wave, energy is transferred through the vibration of particles in a medium, such as air, water, or a solid material. The motion of the particles in the medium creates regions of compression and rarefaction, which propagate as the wave moves through the medium. This means that mechanical waves cannot exist in a vacuum or in a medium that is not capable of transmitting the wave.
In contrast, electromagnetic waves are self-propagating and do not require a medium for their transmission. They consist of oscillating electric and magnetic fields that can travel through a vacuum or any other medium capable of transmitting them.
While the other characteristics listed in the options (crests and troughs, clearly defined wavelengths, and limited speed) are also properties of mechanical waves, they are not as fundamental as the requirement for a medium. The requirement for a medium is what separates mechanical waves from electromagnetic waves at the most fundamental level.
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Complete question: Which of the following characteristics separates mechanical waves from electromagnetic waves the most fundamentally? A. There are crests and troughs on mechanical waves. B. A medium is necessary for the transmission of mechanical waves. C. The wavelengths of mechanical waves are clearly defined. D. The speed of mechanical waves is limited.
A ladder rests against a vertical wall. There
is no friction between the wall and the ladder.
The coefficient of static friction between the
ladder and the ground is µ = 0.464 .
(USE THE PICTURE TO DETERMINE THE ANSWER)
Identify the set of equations which is correct.
ANSWER CHOICES:
1. A1, B2, C3
2. A2, B2, C1
3. A1, B1, C1
4. A1, B2, C2
5. A1, B1, C2
6. A2, B1, C3
7. A2, B1, C2
8. A1, B2, C1
9. A1, B1, C3
10. A2, B1, C1
PART TWO
Determine the smallest angle θ for which the
ladder remains stationary.
Answer in units of â¦
The correct answer is option 4: A1, B2, C2
What is the force of friction in this question?A1: The force of friction acting on the ladder is given by:
f_friction = µ * N
where µ is the coefficient of static friction and N is the normal force acting on the ladder, which is equal to the gravitational force acting on the ladder.
B2: The gravitational force acting on the ladder can be expressed as:
f_gravity = m * g
where m is the mass of the ladder and g is the acceleration due to gravity.
C2: The component of the gravitational force acting parallel to the wall can be expressed as:
f_parallel = f_gravity * sin(θ)
where θ is the angle between the ladder and the wall.
The ladder will remain stationary as long as the force of friction acting on it is equal to or greater than the component of the gravitational force acting parallel to the wall. Setting these two forces equal to each other, we get:
f_friction = f_parallel
µ * N = m * g * sin(θ)
The smallest angle θ for which the ladder remains stationary is given by:
sin(θ) = µ * N / (m * g)
θ = sin^-1 (µ * N / (m * g))
Note that the value of µ * N / (m * g) must be less than or equal to 1 for the ladder to remain stationary.
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How many hours in 480 minutes?
480 minutes is equal to 8 hours.
Any specific period of time that is used to measure or represent duration on a regular basis is referred to as a unit of time.
The second, which is specified as about 9 billion oscillations of the caesium atom, is the fundamental unit of time in the International System of Units and, by extension, throughout the majority of the Western world.
There are 60 minutes in one hour. To convert minutes to hours, we can use the following formula:
Time in hours = Time in minutes ÷ 60
So, to find the number of hours in 480 minutes, we can plug in the values into the formula:
Time in hours = 480 minutes ÷ 60
Time in hours = 8 hours
Therefore, there are 8 hours in 480 minutes.
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Using Models The moon in its orbit around
Earth behaves like a ball at the end of a string
being swung above your head. Explain the
forces involved.
Answer: A gravitational pull is keeping the ball in place and not letting it go flying into the air. so simple answer is gravity
When a twirling ice skater brings her arms inward, her angular velocity?
Answer:
Explanation:
When she moves her arms inward, she spins faster. Her moment of inertia decreases, so her angular velocity must increase to keep the angular momentum constant.
L = Iω, so if I decreases, ω has to increase because L has to be conserved.
how to convert Hz to rad/s?
Answer:
Below
Explanation:
Hz is cycles per second....each cycle is 2 pi
so multiply Hz * 2 pi to get R/s
example
12 Hz 12 * 2pi = 24 pi rad/s = 75.4 Rad/s
when you whirl a can overhead by a string in a circular path, what is the direction of the force exerted on the can?
The force exerted on a can that is whirled overhead by a string in a circular path is a centripetal force, and its direction is toward the center of the circle.
What is the force exerted and the direction of center of circle?
When you whirl a can overhead by a string in a circular path, the direction of the force exerted on the can is toward the center of the circle. This force is known as the centripetal force and is required to keep the object moving in a circular path.
The centripetal force is given by the equation:
F = m * a
where F is the centripetal force, m is the mass of the object (the can), and a is the centripetal acceleration, which is given by:
a = v^2 / r
where v is the velocity of the object and r is the radius of the circular path.
In this case, the force exerted on the can is the tension in the string pulling the can toward the center of the circle. The direction of the force is always towards the center of the circle, regardless of the direction of motion of the object.
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.
Answer: Towards the center of the circle
Explanation: Whirling a can overhead makes it go towards the center.
A frequency distribution usually has equal bin widths. True or False?
True, A frequency distribution usually has equal bin widths.
What is frequency distribution?
In frequency tables or charts, frequency distributions are displayed. The exact number of observations that fall into each range may be seen in frequency distributions, as well as the proportion of observations that do. The distribution in the latter case is known as a relative frequency distribution.
What is frequency distribution formula?
The formula for the square root of the frequency distribution is expressed as: C = n, where n is the total number of observations of the data that has been distributed. C (number of classes) = 1 + 3.3 logn, where (log is base 10)
Hence True is a correct answer.
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You start at the origin and walk 33 meters East 71 meters West, and 62 meters East. What is the distance that you traveled? What is displacement?
Answer:
166 meters. Displacement is the movement of something from one place/position to another. Unless the type of displacement you're talking about is “the occupation by a SUBMERGED body or part of a body of a volume which would not otherwise be occupied by a fluid”.
Explanation:
33 + 71 + 62 = 166
The distance you traveled does not depend upon where, is about how much.
What will happen to the molecules over time?
Over time, the molecules will undergo various processes, such as diffusion, collision, and chemical reactions. These processes can cause the molecules to change their physical and chemical properties, as well as their spatial arrangement.
For example, diffusion can cause molecules to spread out and move from areas of high concentration to areas of low concentration. Collision can cause molecules to bounce off each other and change their direction of movement. Chemical reactions can cause molecules to form new substances with different properties.
Overall, the behavior of molecules over time is determined by the laws of physics and chemistry, and can be observed and studied using various experimental techniques.
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Which of these is NOT a force discussed in this chapter?
a. the tension force
b. the normal force
c. the thrust force
d. the orthogonal force.
Answer:
d. the orthogonal force.
Explanation:
The other three forces, the tension force, the normal force, and the thrust force, are commonly discussed in introductory physics courses.
What is the mass of a
dog that weighs 382 N?
[?] kg
The mass of a dog that weighs 382N is 38.94kg
How to calculate mass?Weight of a substance refers to the force on an object due to the gravitational attraction between it and the Earth (or whatever astronomical object it is primarily influenced by).
The mass can be calculated from the weight using the following formula:
Weight = mass × acceleration due to gravity.
Acceleration due to gravity on Earth is 9.81 m/s²
382N = m × 9.81m/s²
m = 38.94kg
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What is the formula for moment of inertia of semi circle?
The formula for moment of inertia of a semicircle is I = πr4 / 4. To find the moment of inertia of a semicircle, the moment of inertia of a full circle is calculated first. The result is then divided by half to derive the area moment of inertia of a semicircle.
The moment of inertia of a semicircle can be calculated using the formula: I = [tex](1/2) * mr^2[/tex]
where I is the moment of inertia, m is the mass of the semicircle, and r is the radius of the semicircle.
The moment of inertia of a semicircle is often used in calculations related to rotational motion, such as when analyzing the behavior of a rotating object or calculating the torque required to accelerate a semicircular object.
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Which material would you expect to have the greatest angle of repose, and so form the more stable slopes? O dry sand O rough, angular stones O smooth, well-rounded stones O saturated sand
The slopes that are formed by angular, ragged stones are more stable because they have the largest angle of repose.
What does the phrase "angle of rest" mean?1. In physics, the angle formed by the plane de contact between both bodies and the horizontal so when upper body is just about to slide: the angle whose tangent represents the frictional resistance of the two bodies.
What does "angle of repose" mean in pharmacy?One aspect of inter particulate friction, or the resistance to particle movement, is angle of repose. The USP describes it as the consistent, three-dimensional angle (relative to the horizontal base) acquired by a cone-shaped pile of material created using any of a number of different techniques.
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How many Mikrometer are in a Millimeter ?
A millimeter (mm) is made up of 1,000 micrometers (µm). That is, one millimeter equals 1,000 micrometers or [tex]10^{-3}[/tex] meters.
Micrometers are typically used to measure very tiny distances, notably in microscopy, whereas millimeters are commonly used to measure greater distances, such as an object's length or breadth.
It is crucial to note that the micrometer is also known as a micron, therefore the conversion may be represented as 1,000 microns in a millimeter at times. Regardless matter whether you use micrometers or microns, the conversion is the same: a millimeter has 1,000 of them.
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why are near- infrared telescopes located on mountaintops and ultraviolet telescopes in earth orbit?A. the primary infrared blocker, water vapor, is mostly in the lower atmosphere and the primary ultraviolet blocker, ozone, is located high in the atmosphere, far above mountaintops.B.there would be some chromatic aberrationC. light gathering power and resolving power.D. the primary lenses of refracting telescopes.
To minimise atmospheric interference brought on by water vapour and ozone, respectively, near-infrared telescopes are situated on mountaintops and ultraviolet telescopes in Earth's orbit.
Because of option A, near-infrared telescopes are situated on mountaintops and ultraviolet telescopes are positioned in Earth's orbit. The majority of incoming radiation at both ends of the spectrum is absorbed by the atmosphere of the Earth, with water vapour and ozone serving as the main absorbing materials for near-infrared and ultraviolet wavelengths, respectively. Astronomers can get clearer observations of infrared sources by mounting near-infrared telescopes atop mountaintops, which reduces the amount of atmospheric interference. The opposite is also true; by positioning ultraviolet telescopes in Earth's orbit, it is possible to detect sources that would otherwise be hidden by the atmosphere while avoiding the majority of atmospheric interference. This is also the rationale for why further telescopes that focus on other wavelengths of the electromagnetic spectrum, such as X-rays and gamma rays.
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Commercial concentrated aqueous ammonia is 28% nh3 by mass and has a density of 0. 90 g/ml.
The molarity of the aqueous ammonia solution is 0.0165 mol/mL.
The concentration of ammonia in aqueous ammonia solution can be expressed as a mass percentage or as a molarity. The molarity of a solution is defined as the number of moles of solute per liter of solution.
To find the molarity of the aqueous ammonia solution, we first need to find the mass of ammonia in a given volume of solution, and then convert that mass to moles.
Given that the concentration of ammonia is 28% by mass and the density of the solution is 0.90 g/mL, we can calculate the mass of ammonia in a volume of 1 mL of solution:
Mass of ammonia in 1 mL is
=> (28 g/100 mL) * (1 mL)
=> 0.28 g
Now that we know the mass of ammonia, we can convert it to moles using the formula:
Moles = Mass / Molecular weight
The molecular weight of ammonia (NH3) is 17 g/mol, so we have:
Moles = 0.28 g / 17 g/mol
=> 0.0165 mol/mL.
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A student with a mass of 100 kg kicks a 1. 5 kg soccer ball with a force of 450 n. According to newton's second law of motion, what is the acceleration of the ball?.
0.3m/s² is the acceleration of the ball.
What is stated by Newton's second law of motion?
The formal formulation of Newton's second law of motion is as follows: The acceleration of an item caused by a net force is inversely proportional to the mass of the object and directly proportional to the magnitude of the net force in the same direction.
Newton's second law provides a precise explanation of the modifications that a force can make to a body's motion. According to this, a body's momentum changes at a rate that is equal to the force acting on it over time in both magnitude and direction.
F = ma
Mass of ball = 1.5kg = 1500g
Force = 450N
a =?
a = F/m = 450/1500
a = 0.3m/s²
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Which color of the light has the longest wavelength?
A. Red
B. Blue
C. Green
D. Violet
Red color of the light has the longest wavelength. The correct answer is A.
Red light has the longest wavelength of all the colors in the visible light spectra.
Wavelengths of red light range from 620-750 nm (nanometers), while the other colors have shorter wavelengths. Blue light has a wavelength of 450-495 nm, green light has a wavelength of 495-570 nm, and violet light has a wavelength of 380-450 nm.
The longer the wavelength, the lower the energy of the light. This is why red light is often associated with warmth and heat, as it has lower energy than other colors of light. Conversely, blue and violet light have the shortest wavelengths and therefore have the highest energy.
Red light has the longest wavelength of all the colors in the visible spectra.
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Which one of the following properties most fundamentally distinguishes mechanical waves from electromagnetic waves? 0 Mechanical waves have crests and troughs. Mechanical waves require a medium for propagation. O Mechanical waves have well-defined wavelengths. © Mechanical waves move at a finite speed.
Energy is transported by mechanical waves perpendicular to wave motion. Energy is carried parallel to the wave motion by electromagnetic waves.
What characteristic separates electromagnetic waves in general from mechanical waves?Whether or not the waves require a medium for propagation determines one of their characteristics. This characteristic is also the basis for the main distinction between magnetic and electric waves. While electromagnetic waves can travel without a medium, mechanical waves can not.
What distinguishes electromagnetic waves from mechanical waves?In contrast to mechanical waves, electromagnetic waves can travel without a medium. This implies that microwaves can pass not only through solid objects like air and rock but also through empty space.
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If a bowling ball weighing 3,630 g is accelerating down the alley at a rate of 4 m/s2, then what is the net force applied to the bowling ball?
Answer:
[tex]\huge\boxed{\sf F = 14.52\ N}[/tex]
Explanation:
Given data:Mass = m = 3,630 g = 3.63 kg
Acceleration = a = 4 m/s²
Required:Force = F = ?
Formula:F = ma
Solution:Put the given data in the above formula.
F = (3.63)(4)
F = 14.52 N[tex]\rule[225]{225}{2}[/tex]
Suppose an asteroid orbiting the Sun had an orbital period of 7.5 years. What would its orbital radius be? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a. 3.8 AU b 20.5 AU с 422 AU d 56.3 AU e 2.7 AU
The orbital radius of the asteroid would be approximately 3.8 AU.
What is Kepler's third law?We can use Kepler's third law to calculate the orbital radius of the asteroid. Kepler's third law states that the square of the orbital period of a planet is proportional to the cube of its semi-major axis. Mathematically:
[tex]T^2[/tex] ∝ [tex]a^3[/tex]
where T is the orbital period and a is the semi-major axis.
Rearranging the equation, we get:
[tex]a = (T^2)^(1/3)[/tex]
Substituting T = 7.5 years, we get:
[tex]a = (7.5 years)^2/3 = 3.79 AU[/tex]
Therefore, the orbital radius of the asteroid would be approximately 3.8 AU.
Answer: a. 3.8 AU
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