To plot data points for the four Galilean moons of Jupiter using the provided measurements, organize the data in a table, assign axes (time on the x-axis, distance on the y-axis), and plot the data points for each moon. Label the points and analyze the graph for patterns.
To plot data points for the four Galilean moons of Jupiter using the provided measurements, you can follow these steps:
Organize the measurements: Arrange the 18 measurements in a data table with columns representing the relevant parameters such as time, distance, or any other quantity you have measured.
Identify the data for each moon: Determine which measurements correspond to each of the four Galilean moons (Io, Europa, Ganymede, and Callisto). Typically, the measurements would include the time and distance of each moon relative to Jupiter.
Assign axes: Decide which variables you want to plot on the x-axis and y-axis. For example, you may choose to plot the distance of the moon from Jupiter on the y-axis and the time on the x-axis.
Plot the data points: For each moon, plot the corresponding data points on the graph. Use the time measurements on the x-axis and the distance measurements on the y-axis. Repeat this process for all four moons.
Label the data points: Add labels or markers to each data point to indicate which moon it represents (e.g., "Io," "Europa," etc.). This will make it easier to identify the data points for each moon.
Title and label the axes: Provide a clear title for the graph and label the x-axis and y-axis with the appropriate units.
Add a legend (optional): If necessary, include a legend that explains the symbols or colors used for each moon.
Analyze the graph: Examine the plotted data points to identify any patterns or trends related to the motion or positions of the Galilean moons.
By following these steps, you should be able to plot the data points for the four Galilean moons of Jupiter based on the given measurements.
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what causes a desktop to make a screeching sound and horizontal interference lines on the screen, then frozen computer
A desktop computer making a screeching sound accompanied by horizontal interference lines on the screen and subsequent freezing is often caused by hardware or software issues.
The screeching noise may result from a failing component, such as a hard drive or a cooling fan. Overheating or dust accumulation could contribute to these failures. Additionally, a faulty power supply or graphics card may cause interference lines and freezing, as they are responsible for rendering the visual output and supplying adequate power to the system.
Software issues, such as corrupt drivers or system files, can also trigger similar symptoms. Outdated or incompatible graphics drivers may produce interference lines and freezing, as they struggle to handle the display output correctly. Malware or viruses might cause erratic system behavior, including screeching sounds, visual distortions, and freezing.
To resolve the issue, first ensure that the system is clean and well-ventilated to prevent overheating. Check the hardware components for visible signs of wear or damage, and consider replacing them if needed. Update drivers and software, perform a thorough virus scan, and repair or reinstall the operating system if necessary to rule out software-related problems.
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A physics teacher designs a rather unusual demonstration of simple harmonic motion which utilizes a combination of a 4. 0 kg mass and two identical springs mounted on a smooth horizontal table. Each spring has a force constant of 75 n/m and an unstretched length of 0. 25 m. The motion is started by releasing the mass from point a, where both springs have lengths of 0. 5 m. One cycle is carried out as the mass moves from a to b to c to b to a. From the information given, find the speed of the mass as it passes through the central point b. 139 mls.
The speed of the mass as it passes through the central point b is 139 m/s. To find this, we need to use the concept of conservation of mechanical energy.
As the mass moves from a to b, it loses potential energy and gains kinetic energy. At point b, all the potential energy is converted into kinetic energy, so we can equate the potential energy at point a with the kinetic energy at point b.
Using the formula for potential energy of a spring (PE = 0.5 * k * x^2), where k is the force constant and x is the displacement, we can find the potential energy at point a. The potential energy at point b is zero because the spring is unstretched. Equating these two energies and solving for the speed at point b gives us a speed of 139 m/s.
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A 0.48 kg circus monkey is about to be shot from a cannon as part of his thrilling circus act. Draw a free body diagram labeling the forces acting on him at the moment he is launched from the cannon. F_(Net= ) 86N
Newton's 1st Law:
object in motion will...
and an object at rest will...
unless...
This is also referred to as the Law of Inertia.
Inertia:
Answer:
an objext in motion will stay in motion and an object at rest will stay at rest unless impacted by a new force
a drill log represents information about ______. multiple choice question. the quality of the groundwater rock layers and presence or absence of water the direction of flow of the groundwater
A drill log represents information about the quality of the groundwater rock layers and the presence or absence of water.
A drill log is a record or documentation of the geological information obtained during the process of drilling a well or borehole.
It provides valuable information about the subsurface conditions, including the quality of the groundwater rock layers and the presence or absence of water.
Drill logs typically include details such as the depth at which different rock layers or formations were encountered, the composition and characteristics of the rock layers, and any indications of water presence, such as water levels, flow rates, or water-bearing formations.
By examining a drill log, hydrogeologists and geologists can assess the quality and potential yield of groundwater sources in a particular area.
It helps in understanding the geological formations, stratigraphy, and hydrogeological properties of the subsurface, which are crucial for various applications such as water resource management, well design, and groundwater exploration.
In summary, a drill log provides essential information about the quality of groundwater rock layers and the presence or absence of water, offering valuable insights into the hydrogeological characteristics of a specific location.
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how much does a change in mass affect the kinetic energy of two balls of comparable diameter?
Answer:
Mass and kinetic energy have a positive relationship, which means that as mass increases, kinetic energy increases, if all other factors are held constant.
In this state, Kinetic energy is equal to half of the product mass and velocity. SI unit is joules. So it's if the mass is doubled then the kinetic energy also gets doubled.
Solar energy and hydroelectric energy are important sources of energy. Find out more about either one of these forms of energy. What is being done to make it a more efficient source of energy, and where it is being used in the United States?
Answer:
Question: Find out more about either one of these forms of energy
Answer:
Solar energy: This is energy generated from the sunlight, and it can be converted to other energy that can be useful. Solar energy from the sun considered a clean source of electricity can be converted to a usable electricity source or stores the light in batteries for thermal use. This energy conversion is possible through the use of solar panels attached to where the conversion would take place so as to capture the light from the sun.
Question: What is being done to make it a more efficient source of energy
Answer:
1. When using solar energy to power homes, it is more efficient to have panels on a green roof because of the characteristics of this roof not to reflect or lose more light from the sun.
2. Improvements on the type of solar cell to use for instance that are cheaper and could maximize the energy from the sun are all ways that make it more efficient.
3. Since solar panels don't produce energy at night, usage of batteries that could store electricity during the day or when the sun is not obscured would make solar more efficient.
Question: where it is being used in the United States?
Answer:
1. California
2. Nevada
3. New York
4. Texas
A man with a mass of 60 kg rides a bike with a mass of 13 kg. What is the force needed to accelerate the bike at 0.90 m/s2?
A. 65.7
B.657
C.75.6
D.756
Question 12 (True/Faise Worth 5 points)
The presence of free electrons makes a material a good insulator.
O True
O False
In the United States, electricity use per capita has been approximately constant over the last two decades. However, despite per-capita use not significantly changing, total electricity use in the United States each year continues to rise. What could account for this increase?
Total electricity use in the United States has continued to rise despite per capita use remaining constant. This is likely due to factors such as population growth, economic growth, shifts in industry and technology, and changes in lifestyle and behavior.
There are several factors that could account for the increase in total electricity use in the United States over the last two decades, despite per capita use remaining constant. Some possible explanations include:
1. Population growth: Even if per capita electricity use remains the same, an increase in the total population will lead to an increase in total electricity consumption.
2. Economic growth: As the economy grows, there is an increase in demand for goods and services that require electricity, such as manufacturing, transportation, and data centers. This increase in demand can lead to an increase in total electricity consumption.
3. Shifts in industry and technology: There have been significant changes in the structure of the US economy in the last two decades, with a shift away from manufacturing towards service industries. Additionally, advances in technology have led to the proliferation of electronic devices and the increasing use of data centers. These changes have contributed to an increase in total electricity consumption.
4. Changes in lifestyle and behavior: Even though per capita electricity use has not significantly changed, there may be changes in lifestyle and behavior that have led to an increase in overall electricity consumption. For example, the increased use of air conditioning, larger homes, and more electronic devices can contribute to higher energy use.
It's important to note that the factors contributing to the increase in total electricity use are likely to be complex and multifaceted. However, by understanding the underlying causes of this increase, policymakers and energy experts can work to develop strategies to manage and reduce energy consumption in the United States.
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Which unit abbreviation is a measurement of force?
A. m/s
B. m/s²
C. N
D. N/s
The unit abbreviation that represents a measurement of force is C. N, which stands for Newton.
What is newton unit?ewton is the force unit derived from the International System of Units (SI). It is named after Sir Isaac Newton, widely acknowledged as one of the most influential scientists of all time. The force required to accelerate a mass of one kilogram at a rate of one meter per second squared (m/s2) is referred to as one Newton.
Choice A, m/s, addresses an estimation of speed or speed (meters each second), while
choice B, m/s², addresses an estimation of speed increase (meters each second squared), which is connected with force, however not the unit of power itself.
Choice D, N/s, addresses an estimation of the pace of progress of power after some time, which is certainly not a generally involved unit in physical science.
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A 0.1 kg toy train car moving at 1.0 m/s runs into a stationary car with a mass of 0.15 kg. At what speed do they move off together?
The toy train and the car move off together at speed of 0.4 m/s.
What is law of conservation of momentum?
According to the law of momentum conservation, momentum is only modified by the action of forces as they are outlined by Newton's equations of motion; momentum is never created nor destroyed inside a problem domain.
From conservation of momentum, we get:
Total initial momentum = total final momentum
0.1 kg × 1.0 m/s + 0.15 kg × 0 m/s = ( 0.1 kg + 0.15 kg) × v
v = (0.1/0.25) × 1.0 m/s
v = 0.4 m/s.
Hence, they move off together at speed of 0.4 m/s.
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b. Determine the velocity of the hoop at the bottom of the ramp
conservation.
mgh = 1/2 mv² + 1/2 MR² w²
The velocity of the hoop at the bottom of the ramp is given by v = R√(gH/2R).
Velocity of a hoopWe can use the principle of conservation of energy to find the velocity of the hoop at the bottom of the ramp. The total initial energy of the hoop and cylinder is equal to the total final energy of the system at the bottom of the ramp. Assuming that there is no slipping, the kinetic energy of the hoop and cylinder will be rotational, and we can write:
1/2 Iω^2 = 1/2 mv^2
where I is the moment of inertia of the hoop, ω is its angular velocity, m is the mass of the hoop and cylinder, and v is the velocity of the hoop at the bottom of the ramp.
The moment of inertia of a thin hoop of mass M and radius R is given by:
I = MR^2
The moment of inertia of a uniform cylinder of mass M and radius R is given by:
I = 1/2 MR^2
Using these values, we can write:
1/2 MR^2 ω^2 = 1/2 mv^2
Solving for v, we get:
v = ωR√(g/2)
where g is the acceleration due to gravity. The angular velocity of the hoop at the bottom of the ramp can be found by equating the gravitational potential energy lost by the hoop to its rotational kinetic energy at the bottom of the ramp. The gravitational potential energy lost by the hoop is given by:
ΔU = MgH
where H is the height of the ramp. The rotational kinetic energy of the hoop at the bottom of the ramp is given by:
1/2 Iω^2
Equating these two expressions, we get:
MgH = 1/2 MR^2 ω^2
Solving for ω, we get:
ω = √(2gH/R)
Substituting this value into the expression for v, we get:
v = R√(gH/2R)
Therefore, the velocity of the hoop at the bottom of the ramp is given by v = R√(gH/2R).
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Very low temperature molecular clouds emit most of their light in which part of the electromagnetic spectrum?
The radio region of the electromagnetic spectrum is where molecular clouds with extremely low temperatures emit the majority of their light.
To find the answer, we need to know more about the molecular clouds.
What is molecular clouds?Only within molecular clouds can stars actually form. Because the internal forces operating "outward" to prevent a collapse must be greater than the gravitational force acting to collapse the cloud, this is a natural result of their high densities and low temperatures.At 10 K, molecular clouds are extremely cold. Clouds that are diffuse are usually 100 K. Depending on the abundances of heavy elements that provide the cooling radiation, HII areas have T 8000 K.Thus, we can conclude that, the radio region of the electromagnetic spectrum is where molecular clouds with extremely low temperatures emit the majority of their light.
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A box with a weight of 100 N rests on a horizontal floor. The coefficient of static friction is = 0,40 and the coefficient of kinetic friction = 0,30. Determine the frictional force acting on the box if a horizontal force is applied with a magnitude of: a) O N; b) 20 N; C) 40 N; d) 60 N
A 0.15 kg baseball reaches a batter with a speed of 32.0 m/s. If a 0.94 kg bat, moving with a speed of 41.0 m/s, hits the baseball, what is the speed of the baseball right after the elastic collision? Assume the bat speed does not change.
A batter is struck with a baseball that weighs 0.15 kg at a speed exceeding 32.0 m/s. When a 0.94 kilogram bat. After a collision, the baseball's final speed was 24 m/s.
What is speed and what is its unit?The pace at which a distance changes over time is referred to as speed. It has a dimension of time-distance. As a result, the fundamental unit of time and indeed the basic unit pf distance are combined to form the Special name of speed.
How do find speed?Speed indicates how quickly thing or an individual are moving. If you know how far something has traveled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time.
Briefing:Mass of baseball, m=0.15kg,
Mass of bat, M=1.4kg,
Initial speed of baseball, u=-32 m/s,
Initial speed of bat, U=41 m/s
Final speed of bat, V=35 m/s,
Linear momentum, mu+MU = mv+MV
(0.15" " kg×-32" " m/s)+(1.4" " kg×41" " m/s)
=(0.15" " kg ×v)+(1.4" " kg×35" " m/s)
-4.8+57.4 = 0.15v+49
0.15v = 3.6
v=(3.6)/(0.15)
v=24m/s
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is the interquartile range a resistant measure of spread? give an example of a small data set that supports your answer.
Yes, the interquartile range (IQR) is a resistant measure of spread.
What is an interquartile range?IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.
Mathematically, interquartile range (IQR) is the difference between quartile 1 (Q₁) and quartile 3 (Q₃):
IQR = Q₃ - Q₁
What is an outlier?An outlier is also referred to as anomalous data and it can be defined as a numerical value that is either unusually too small or large (big) in comparison with the overall pattern of the numerical values contained in a data set.
In Statistics and Mathematics, the interquartile range (IQR) is a measure of spread that is very resistant to an outlier.
For example, given the following data set:
1, 2, 3, 4, 5, 6, 7.
Median = 4.
First quartile, Q₁ = 2.
Third quartile, Q₃ = 6.
Thus, the interquartile range (IQR) for the above data set is given by:
IQR = Q₃ - Q₁
IQR = 6 - 2
IQR = 4.
In this context, we can infer and logically deduce that the interquartile range (IQR) is truly a resistant measure of spread.
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How
did the solar system begin? ( use complete sentences ) will mark b
What is the air density atop of Mount Everest on a summer day (at a pressure of 3.30 x 104 N/m2 and a temperature of -190C)
The air density Difference = 0.829 kg/ \(m^{3}\)
Elaborating the question :
Ideal gas equation : PV= nRT
R = 8.314J/mol/k
n =\(\frac{m}{MW}\) where , n = moles of gas
m = mass of gas
MW = molecular weight
PMW =pRT
p = air density , T = -19 + 273k = 254k
p = \(\frac{PMW}{RT}\)
p = 3.30 × \(10^{4}\) ×0.0188kg ÷ 8.314 ×254 k
p = 0.450kg/m³
Density of air under standard condition = 1.28kg/m³
difference = 1.28 - 0.45 = 0.829kg/m³.
What is air density ?
Air density is defined as the mass of air per unit volume, whereas the specific volume is defined in terms of unit mass of dry air.The density of air or atmospheric density, denoted ρ, is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature and humidity.
Question is incomplete , missing part is given below :
What is the air density atop of Mount Everest on a summer day (at a pressure of 3.30 x 104 N/m2 and a temperature of -190C)? How is it different from the density of air in standard conditions (at a pressure of 1.01 x 105 N/m2 and a temperature of 200 C the air density is1.28 kg/m3). The molar mass of air is 28.8g/mole.
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A frog jumps vertically upward from a 20m tall building with an initial velocity of 8.1m/s. How high above the ground will the frog reach?
Answer:
Explanation:
Consider the initial position of the frog (20 m above ground) as the reference position. All measurements are positive measured upward.
Therefore,
u = 10 m/s, initial upward velocity.
H = - 20 m, position of the ground.
g = 9.8 m/s², acceleration due to gravity.
Part (a)
When the frog reaches a maximum height of h from the reference position, its velocity is zero. Therefore
u² - 2gh = 0
h = u²/(2g) = 10²/(2*9.8) = 5.102 m
At maximum height, the frog will be 20 + 5.102 = 25.102 m above ground.
Answer: 25.1 m above ground
Part (b)
Let v = the velocity when the frog hits the ground. Then
v² = u² - 2gH
v² = 10² - 2*9.8*(-20) = 492
v = 22.18 m/s
Answer: The frog hits the ground with a velocity of 22.2 m/s
In 2000, a 20-year-old astronaut left Earth to explore the galaxy; her spaceship travels at 2.5 x 10^8 m/s. She returns in 2040. About how old will she appear to be?
Answer:
42.11 years old
Explanation:
Given that:
In 2000, a 20-year-old astronaut left Earth to explore the galaxy; her spaceship travels at 2.5 x 10^8 m/s. She returns in 2040
To find her age we use:
\(\Delta t_m=\frac{\Delta t_s}{\sqrt{1-\frac{v^2}{c^2} } }\\\)
Δtm is time interval for the observer stationary relative to the sequence of
events = 2040 - 2000 = 40 years
Δts is is the time interval for an observer moving with a speed v relative to the sequence of event
v = velocity = 2.5 x 10^8 m/s
c = speed of light = 3 x 10^8 m/s
\(\Delta t_s=\Delta t_m}{\sqrt{1-\frac{v^2}{c^2} } }\\\Delta t_s=40\sqrt{1-\frac{(2.5*10^8)^2}{(3*10^8)^2}}\\\Delta t_s=22.11\ yr\)
Here age in 2000 is 20 year, therefore when she appear she would be 20 year + 22.11 year = 42.11 years old
Ellie conducts an investigation to determine if size or weight affect how fast objects fall. Her investigation includes repeatedly dropping a basketball and a golf ball at the same time. After many trials, she determines that both balls land at the exact same time.
Why would Ellie's investigation be valid?
It is based on evidence.
It uses objects that move.
It proves her predictions are correct.
It includes her opinion.
Answer: The answer is A
Explanation: I have the same exact question as you and i took a quiz with this exact question and it said that was the answer and i also took a quizlet with this question and it also said the answer was A hope this helped :)!
The repetition of the experiment allows to support the results, therefore the correct answer is:
based on experimental evidence
The theory is a set of rules, principles and knowledge that are developed from models and experiments that are carried out repeatedly, finding similar results in any given case.
In this case, Ellie repeated each experiment several times, finding results that lead to the result that the two balls hit the ground at the same time, therefore her conclusions are supported by experimental evidence.
In conclusion the conclusions of the experiment of dropping the balls the correct answer is: it is based on the experimental evidence
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Why are infrared waves located between microwaves and visible light on the electromagnetic spectrum?
Answer: The infra red waves is located between microwave and visible light based on their WAVELENGTH and FREQUENCY of occurrence.
Explanation:
Electromagnetic waves are those waves that do not require or need a material medium for its propagation, but they are able to travel through a vacuum. They exhibit or show all properties associated or connected with light. They are undeflected in electric and magnetic fields. These electromagnetic waves are arranged in order of their FREQUENCY and WAVELENGTHS which is known as ELECTROMAGNETIC SPECTRUM.
FREQUENCY is defined as the number of cycles which the wave completes in one second and is measured in Hertz(Hz). While WAVELENGTH is defined as the distance between two successive crests or troughs of waves which is measured in meter (m).
The electromagnetic spectrum is made up of the following rays which is arranged from the biggest wavelengths to the smallest:
--> Radiowaves
--> microwave :
--> infrared rays:
--> visible light:
--> ultraviolet rays
--> x-rays and
--> Gamma rays.
According to the arrangement of the spectrum above, the microwave has a higher wavelength and frequency than the infrared rays, while the visible light has a lower wavelength and frequency than the infrared rays.
on a whim, you are trying to stand in a cart attached to a strong spring. the spring is compressed and then released, and you oscillate back and forth, trying to maintain your balance. there is a sand bag in the cart.
The effect that this will have on the amplitude of your oscillation.is b.) The amplitude of oscillation will decrease.
What is the amplitude?The amplitude of an oscillating system is the magnitude of change in the oscillating variable with each oscillation. Sound waves in air, for example, are oscillations in atmospheric pressure, and their amplitudes are proportional to the pressure change during one oscillation.
When a wave travels through a medium, it loses energy as it moves. As the distance between the wave and its source grows, it spreads out over a larger and larger area. As the wave spreads through the medium, it loses energy and its amplitude decreases.
In this case, at the point of equilibrium, the cart and the skater will have maximum kinetic energy. By dropping the same bag, the energy is reduced. The amplitude of an oscillating pendulum decreases with time because of friction due to air
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On a whim, you are trying to stand in a cart attached to a strong spring. The spring is compressed and then released, and you oscillate back and forth, trying to maintain your balance. There is a sand bag in the cart.
At the instant you pass through the equilibrium (x=0) location of the spring, you drop the sandbag onto the ground, out of the cart.
Question: If you drop the sand bag out of the cart right at the equibrium location, what effect will that have on the amplitude of your oscillation? (choose correct choice):
a.) The amplitude of oscillation will increase.
b.) The amplitude of oscillation will decrease.
c.) There will be no effect on the amplitude.
Things that are electrically charged attract the little bits of paper. The T tape and the B tape are both charged, and the bits of paper are considered neutral. Describe a procedure that you could use to determine if a known object is charged or neutral.
The procedure that can be used to determine if a known object is charged or neutral is take the known object and rub it against a piece of wool or fur. This rubbing should cause the object to become charged electrically. Touch the charged object to a suspended bit of paper. If the paper is attracted to the object, the object is charged. If the paper remains stationary, then the object is neutral.
Electrically charged objects are objects that possess either a positive or negative charge. These charges are usually acquired due to the gain or loss of electrons.The ability of charged objects to attract bits of paper is due to the principle of electrostatics, which states that opposite charges attract while like charges repel.The T tape and B tape are both electrically charged, and as a result, they attract the neutral bits of paper. On the other hand, if a known object is neutral, it will not attract the bits of paper.
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PLEASE HELLPPP ILL GIVE BRAINLY
which part of the United States would have generally cooler temperatures due to the effects of currents?
A ) East Coast
B ) Gulf Coast
C ) West coast
D ) Central States
Answer:
West coast
Explanation:
i think this is the ans
discuss your observations regarding the velocity and acceleration of a ball undergoing the projectile motion of a basketball shot.
A ball undergoing a projectile motion of a basketball shot has two components of velocity, 1) horizontal component and 2) vertical component
When a ball undergoes a projectile motion at θ° angle, it possesses two components of velocity, Horizontal component = vcosθ and vertical component = vsinθ. Vertical components always subjected to acceleration due to gravity in downward direction, whereas horizontal component does not have any acceleration. So it remains constant throughout the whole journey.
Time taken by the ball to reach at height, T = (vsinθ)/g
Total time to return to the ground is 2T = 2vsinθ/g
Horizontal range of the ball, R = vcosθ × 2T
= 2vsinθ(vcosθ)/g
= v²sin2θ/g
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Your friend wants to lose weight around the belly. Your friend is planning to do crunches every day to lose the weight, but is not planning on doing any other exercises. Do you think this strategy will be effective? Why or why not? What can your friend do to increase the pace of weight loss? Explain your answer. Please hurry I need a paragraph!!!
But I will put it in my own words so it won't be plagerism!
Answer:
i don't think it will work
Explanation:
because in order to lose weight, you have to do more than one stretch because weight loss takes multiple steps and not just one exercise, it would also involve you to eat healthy and to increase the pace, your friend could go running, do yoga, eat healthier, drink more water, and do more than just a core workout and etcetera.
what is the form of energy absorbed when matter changes state
Answer:
This energy, called the heat of fusion or heat of melting, is absorbed by the particles as potential energy as the solid changes to a liquid
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Explanation:
Changing states of matter occur when matter loses or absorbs energy. When a substance absorbs energy, the atoms and molecules move faster and that increases kinetic energy, which causes particles to push even farther, to a point that they change its form. This energy is usually considered heat or thermal energy.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hope I helped!!!
GL :)
Solve this problem using system of linear equationsA chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand contains 12% vinegar. The chef wants to make 210 milliliters of a dressing that is 11% vinegar. How much of each brand should she use? First brand=( ) MillilitersSecond brand=( )Milliliters
Let's call x the vinegar.
• The first brand contains 7% vinegar, this can be expressed as ,0.07x,.
,• The second brand contains 12% vinegar, this can be expressed as ,(210-x)*0.12, because the total amount is 210 mL.
,• The chef wants to make 210mL which is 11% vinegar, this is going to be the other side of the equation.
Let's express the equation.
\(0.07x+(210-x)\cdot0.12=0.11\cdot210\)Now we solve for x.
\(\begin{gathered} 0.07x+25.2-0.12x=23.1 \\ -0.05x=23.1-25.2 \\ x=\frac{-2.1}{-0.05} \\ x=42 \end{gathered}\)Therefore, the chef needs 42 mL for the first brand and 168 mL for the second one.