The correct answer is rate of acceleration will be reduced by 3.
Newton's law states that the force acting on an object is inversely proportional to its rate of acceleration. This means that if an object's mass remains constant, its acceleration will fluctuate in accordance with its applied force, and vice versa.
A vector number called acceleration can be used to describe how quickly an object changes its velocity. If an object is constantly altering its velocity, it is still accelerating.
By Newton's law.
F=ma
The force is F.
m is the object's mass.
A represents acceleration.
The mass will triple if
a'=1/3×F/m
a'=a/3
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when a body moves in a simple harmonic motion, its acceleration at the ends of its path is: group of answer choices zero less than at equilibrium more than g maximum
When a body moves in a simple harmonic motion, its acceleration at the end of its path is more than that of the acceleration at equilibrium.
The acceleration of the body moving in Simple Harmonic Motion(SHM) is given by,
Acceleration = ω^2 A
Here w is the angular velocity of the body and A is the amplitude.
A is the maximum distance of the body from the equilibrium position.
When the body is at an equilibrium position, its amplitude is equal to zero.
Hence, acceleration = ω^2 x 0 = 0
When the body is at the end of its path, its amplitude is equal to A.
Hence, acceleration = ω^2 x A
Therefore,
when a body moves in a simple harmonic motion, its acceleration at the end of its path is more than that of the acceleration at equilibrium.
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to find the total field you have to sum over all dq’s corresponding to each increment of length dx’. summing of infinitesimals is called integration. set up the integral over the length of the line of charge, including correct limits and integration variables.
A to find the total field you have to sum over all d's corresponding to each increment of length dx'. Summing of infinitesimals is called integration.
What is integration?Combination is the computation of a vital. Integrals in math's are utilized to find numerous helpful amounts like regions, volumes, relocation, and so on. Researchers who predicted the idea of a basic, was the old Greek researcher Endous of Cnidus, who lived around 408-355 years BC. At the point when we talk about integrals, it is connected with typically unmistakable integrals. The endless integrals are utilized for antiderivatives. Vital conditions are arranged by three distinct divisions, making eight various types: Essential conditions are significant in numerous applications. The positive indispensable of a capability f (x) with lower cutoff and maximum breaking point b might be characterized as the distinction where F (x) is an antiderivative of the capability f (x).
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How does the atmosphere affect life on earth? Include both positive and negative effects.
The Earth's atmosphere blocks the sun's rays as they travel toward us. The atmosphere's layers act as a filter, allowing just the radiation needed to support life to pass through while blocking the dangerous radiation from reaching the Earth's surface. Our globe is warmed by the sun's energy as it travels through the atmosphere, supplying light energy for photosynthesis and powering the biogeochemical cycles in the Earth's systems. The object that cannot pass through, on the other hand, is reflected back into space.
The global temperature does, however, increase as more heat is trapped by the atmosphere. Global warming is the name of this occurrence.
Global warming is the phenomenon that results in a change in our climate. Natural calamities like wildfires, flooding, and severe storms occur more frequently when this happens.
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light strikes a 5.0-cm thick sheet of glass at an angle of incidence in air of 50°. the sheet has parallel faces and the glass has an index of refraction 1.50.
The correct answer is a) r = 30.7, b) r = 50 c) 0.822 cm
(a)
According to Snell's laws :
The incident ray, the refracted ray, and their normal boundaries between the two media all lie on the same plane.
i = 50o
Using Snell's Law
ni × sin(i) = nr × sin(r)
1.0 × sin(50) = 1.5 × sin(r)
r = 30.7
(b)
The Angle of refraction will be same as Angle of incidence, i = 50
So,
Final Angle of refraction, r = 50
(c)
Thickness, t = 5.0 cm
Difference = t × [sin(50) - sin(30.7)]
x = 5.0 × [sin(50) - sin(30.7)]
x = 1.28 cm
The ray is displaced by , = 1.28 × sin(90 - 50) cm
= 0.822 cm
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What make race condition bad? name and briefly desribe two distince factors needed for a race
when two computer program processes, or threads, attempt to access the same resource at the same time and cause problems in the system and it makes race condition bad.
Which of the following conditions can result in a race condition?When race conditions develop. When two threads access a shared variable at the same time, a race condition occurs. The first thread reads the variable, and the second thread reads the variable's value. A race condition is an undesirable situation that occurs when a device or system attempts to perform two or more operations at the same time, but the operations must be performed in the correct sequence due to the nature of the device or system.A race condition is a program condition in which the behavior is dependent on the relative timing or interleaving of multiple threads or processes. One or more of the possible outcomes may be harmful, resulting in a bug. This is referred to as nondeterministic behavior.
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a motorcycle travels down the street at a constant velocity of 25 m/s . assuming the motorcycle does not accelerate during the next 40 seconds it will travel..
the calculated displacement is 1000 m.
The equation a = v/t denotes acceleration (a), which is the change in velocity (v) over the change in time (t). This enables you to calculate the change in velocity in meters per second squared (m/s2). Since acceleration is a vector quantity, both its magnitude and its direction are included. The following equation can be used to determine distance from acceleration: D = v*t + 1/2*a*t2. where and is the acceleration, t is the passage of time, and v is the velocity.
Velocity= 25 m/s
time= 40 seconds
displacement= velocity x time
=25 x 40
=1000 m
the calculated displacement is 1000 m.
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A girl rides her bike up a steep hill 2.4 kilometers in 8 minutes. What is her speed?
Answer:
0.3km/min
Explanation:
2.4/8=24/80=3/10=0.3
As officer konstantin explains, when driving at 60 mph, in four seconds, you've traveled?
when driving at 60 mph, in four seconds, you've travelled 107.29 m
What is speed?Speed is the distance travelled per unit. Mathematically, it can be expressed as:
Speed = distance / time
How to convert 60 mph to m/sWe'll begin by converting 60 mph to m/s. This can be o btained as follow:
1 mph = 0.44704 m/s
Therefore,
60 mph = (60 mph × 0.44704 m/s) / 1 mph
60 mph = 26.8224 m/s
How to determine the distanceThe distance travelled can be obtained as follow:
Time = 4 sSpeed = 26.8224 m/sDistance =?Speed = distance / time
Cross multiply
Distance = speed × time
Distance = 26.8224 × 4
Distance = 107.29 m
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There are 9 different positions on a baseball team. if a team has 13 players how many different line-ups can the team make? the team can make different line-ups.
The team can make different line-ups in 13!(13−9)!=13!4! ways.
For the first spot in the lineup, there are 13 possibilities, for the second spot there are 12 possibilities, continuing in this fashion there are 5 possibilities for the ninth spot in the lineup. So there are
13 × 12 × • • • × 5 = 259459200
possibilities.
To write it succinctly
13!(13−9)!=13!4!
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train cars are coupled together by being bumped into one another. suppose two loaded train cars are moving toward one another, the first having a mass of 168000 kg and a velocity of 0.291 m/s, and the second having a mass of 117000 kg and a velocity of -0.128 m/s. (the minus indicates direction of motion.) what is their final velocity?
Their final velocity would be 0.118 m/s
Calculation
M1= 168000kg, V1= 0.291 m/s
M2= 117000kg, V2 = 0.128 m/s
According to conservation of momentum,
M1V1 + M2V2 = V(M1+M2)
⇒V = [tex]\frac{168000 * 0.291-117000*0.128}{168000+117000}[/tex]
=[tex]\frac{48888-14976}{285000}[/tex]
=0.118 m/s
Thus, the trains will finally get to the velocity of 0.118 m/s
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If a fisherman applies a horizontal force with magnitude 43.5 nn to the box and produces an acceleration of magnitude 3.30 m/s2m/s2, what is the mass of the box?
The mass of the box which the fisherman applies a horizontal force is 13.18 Kg
To solve this exercise, the formula and procedure to be applied are:
F = m * a
Where:
m = massF = Forcea = accelerationInformation about the problem:
a= 3.30 m/s2F= 43.5 N1 N = kg * m/s²m = ?Applying the force formula and isolating the mass, we get:
F = m * a
m = F/a
m = 43.5 Kg * m/s² / 3.30 m/s2
m = 13.18 Kg
What is force?It is the physical magnitude that expresses the effort necessary to move the mass of one kilogram with an acceleration of one meter per second squared, this is expressed in units of the international system in Newton.
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how would an observer on train a, which is moving at nearly the speed of light, view a clock on train b, which is moving at the same speed and in the same direction?
According to Special Relativity
two objects in relative motion always see the other moving through time slower.
Special Relativity describe how time and space are affected by motion at a constant velocity (especially very fast velocities)describes how mass and energy are inter related. whereas General Relativity states the geometric theory of gravitation developed by Albert Einstein, incorporated and extended the theory of special relativity to accelerated frames of reference and introducing the principle that gravitational and inertial forces are equivalentspace time are part of the same wholeathe speed of light is the same for all observers regardless the motion of the source or observerreference frame is a perspective from which the position and motion of a system can be describedTo know more about Special Relativity visit : https://brainly.com/question/7203715
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Given that mhmh = 1.007825 uu , is the mass of a hydrogen atom 1h1h greater than, less than, or equal to 1/12 the mass of a 12c12c atom? select the correct answer and explanation.
A ¹²C atom's mass is exactly 1u, or 1/12 of its mass. As a result, the mass of an atom of hydrogen is larger than one-twelfth the mass of an atom of ¹²C.
What is atomic mass ?
Atomic mass is the amount of matter that makes up an element's atom. It is written as a multiple of 1.992646547 x 10^-23 gram, or one-twelfth of of the mass of the carbon-12 atom, which is given an atomic mass of 12 units.
A ¹²C atom's mass is equal to one-twelfth of the unified atomic mass unit.
1u = 1/12 m ¹²C
Additionally, since 1 mole is equal to 6.022x10^23 atoms, the unified atomic mass unit is equal to the mass (in grams) of 1 mole of a substance. Accordingly, the unified atomic mass unit in grams is:
1u = 1 g/ mol x 1mol / 6.022 x 10^23atoms = 1.66 x 10^-27 kg
From this definition, we can determine the mass of a 1H atom in relation to a ¹²C atom:
m¹H = 1.67 x 10 ^ -27 kg
As a result, a 1H atom has a mass that is larger than 1/12 that of a ¹²C atom.
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Question:
Given that mH = 1.007825 u, is the mass of a hydrogen atom 1H greater than, less than, or equal to 1/12 the mass of a 12C atom? Select the correct answer and explanation. Given that = 1.007825 , is the mass of a hydrogen atom greater than, less than, or equal to 1/12 the mass of a atom? Select the correct answer and explanation. 1/12 of the mass of a 12C atom is greater than 1 u. Therefore, the mass of the hydrogen atom is greater than 1/12 of the mass of a 12C atom. 1/12 of the mass of a 12C atom is less than 1 u. Therefore, the mass of the hydrogen atom is less than 1/12 of the mass of a 12C atom. 1/12 of the mass of a 12C atom is exactly 1 u. Therefore, the mass of the hydrogen atom is less than 1/12 of the mass of a 12C atom. 1/12 of the mass of a 12C atom is exactly 1 u. Therefore, the mass of the hydrogen atom is greater than 1/12 of the mass of a 12C atom. 1/12 of the mass of a 12C atom is exactly 1 u. Therefore, the mass of the hydrogen atom is equal to 1/12 of the mass of a 12C atom.
An empty vial weighs 63.28 g. if the vial weighs 436.33 g when filled with liquid mercury (d = 13.53 g/cm3), what volume of mercury is in the vial?
The volume of mercury is in the vial 28.71 cm³
Once you are aware of the mass of the mercury, you may calculate the volume of the vial by using the density of the mercury to determine its mass.
You are aware that the vial including the mercury weighs 439.31 g.
The vial weighs vial=50.90 g.
This indicates that the mercury will have a mass of mercury=439.31 g
50.90 g=388.41 g.
You now are aware that the density of mercury is 13.53 g/cm3.
The mass of 1 cm³ of mercury is 13.53 g.
Your sample will have a volume of 388.41g/1 cm³/13.53g = 28.71 cm.
Four sig figs, the number of sig figs you have for the mass of the empty vial, is the answer, which is rounded to four sig figs.
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a river flows toward the east. because of your knowledge of physics, you head your boat 53 degrees west of north
Velocity of the current is 2.7 m/s and the velocity of the boat relative to the water is 4.8 m/s.
Define the velocity?The pace at which a moving object's location changes as seen from a specific frame of reference and as measured by a specific time standard is known as its velocity. In kinematics, the area of classical mechanics that studies how bodies move, velocity is a fundamental idea.
Given:
[tex]West\;of\;north\;angle,\;\alpha=56\;^{\circ}[/tex]
[tex]Velocity\;of\;boat\;relative\;to\;shore,\;V_{b} = 4 m/s[/tex]
From the right angle triangle ABC, (see the attached figure)
[tex]sin\;\alpha=\frac{V_{b} }{V_{b,c} }[/tex]
[tex]V_{b,c}=\frac{V_{b} }{sin\;\alpha}[/tex]
Substitute the known values in the above equation,
[tex]V_{b,c}=\frac{4}{sin\;56^{\circ}}[/tex]
By solving the above equation, We get
[tex]Velocity\;of\;boat\;relative\;to\;water,V_{b,c}=4.8\;m/s[/tex]
[tex]cos\;\alpha=\frac{V_{c} }{V_{b,c} }[/tex]
[tex]V_{c}={V_{b,c}}\times{cos\;\alpha}[/tex]
Substitute the known values in the above equation,
[tex]V_{c}={4.8}\times{cos\;56^{\circ}}[/tex]
By solving the above equation, We get
[tex]Velocity\;of\;current,\;V_{c}=2.7\;m/s[/tex]
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A 30-g car rolls from a hill 12 cm high and is traveling at 154 cm/s as it travels along a 275 cm horizontal track. What is the momentum of the car?.
The momentum of the car, given the data d from the question is 0.0462 Kg.m/s
What is momentum?Momentum is defined as the product of mass and velocity. It is expressed as
Momentum = mass × velocity
With the above formula, we can determine the momentum of the car. Details below
How to determine the momentum of the carThe momentum of the car can be on rained as follow:
Mass of car = 30 g = 30 / 1000 = 0.03 KgVelocity of car = 154 cm/s = 154 / 100 = 1.54 m/sMomentum of car = ?Momentum = mass × velocity
Momentum of car = 0.03 × 1.54
Momentum of car = 0.0462 Kg.m/s
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According to the law of multiple proportions, if 12 g of carbon combine with 16 g of oxygen to form co, the number of grams of carbon that combine with 16 g of oxygen in the formation of co2 is ________.
Answer: Carbon and oxygen combine together to give two compounds carbon dioxide (CO 2) and carbon monoxide (CO) Thus the ratio of different weights of oxygen (32 and 16) combining with a fixed weight of carbon (12) is 32 : 16 i.e. 2 :1, which is simple whole number ratio. Illustration 2:
Explanation:
A moving average can be used to smooth:__________
1) cyclical variation
2) seasonal variation
3) irregular variation
4) all responses are correct
A moving average can be used to smooth:3) irregular variation
What is irregular variation ?
Irregular with the aid of its call says “wrong”. these are those variations which aren't predictable. They do now not observe some pattern which may be expected. It totally follows in opposition to the rules. It includes the pandemic, endemic, other sicknesses spread, environmental disasters, and irregular variation. greater particularly, floods, earthquakes, draughts, and many others comes under the umbrella of irregular variations.
In time series, we do no longer make any estimation of parameters or speculation checking out. The simplest purpose is to find the versions/trends in facts. this alteration may be everyday or irregular. ordinary variations includes linear, seasonal, and cyclic variations. whereas, abnormal variations are all rest of the variations that aren't blanketed with the aid of the everyday versions. those irregular variations are never predictable. We don't have any facts about the length of this alteration, whether it's miles short time period or long time variation. moreover, irregular variations are stationary variations.
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The passage of a current of 0.750 a for 25.0 min deposited 0.369 g of copper from a 4 solution. from this information, calculate the molar mass of copper.
The passage of a current of 0.750A for 25.0 min deposited 0.369 g of copper from a solution. From this information, the molar mass of copper is 63.3u.
How to calculate the molar mass of copper?
First we will convert the time from mins to sec,
Hence,
Time = 25min = 25*60 sec
Current = 0.75A
Electricity passed is given by:
[tex]Q=I\times T \\Q=0.75 \times25\times60\\Q=1125C[/tex]
The reaction that will take place is:
[tex]Cu^{2+}+2e^_- } \rightarrow Cu[/tex]
Hence, there are 2 atoms of copper.
We know, Faraday's number is 96500, and as there are 2 atoms of copper, therefore, the value of Z = 96500*2.
We are given that the deposited mass is 0.369g
Hence, the molar mass of copper will be:
[tex]M=\frac{2\times 96500 \times 0.369}{1125}=63.3u[/tex]
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If a car accelerates from a stand still to 60 km/s in 10 seconds what is its acceleration
Answer:
I think it's 6 km/s^2
Explanation:
We know that velocity is 60 km/s and time is 10 seconds.
We need to find acceleration, so we need to use a=v/t.
Add in your numbers into the equation giving you a=60 km/s divided by 10s.
Your units for acceleration are km/s^2
Your answer should end up being 6 km/s^2
Hope I'm right and if I'm wrong I hope my physics teacher doesn't see this...
Consider two vectors A⃗ and B⃗ and their re- sultant A⃗ + B⃗ . The magnitudes of the vectors A⃗ and B⃗ are, respectively, 13.9 and 5.9 and they act at 53◦ to each other.
B⃗
A⃗ + B⃗
A⃗
Find the magnitude of the resultant vector A⃗ + B⃗ .
Use the dot product identity,
[tex]\vec x \cdot \vec y = \|\vec x\| \|\vec y\| \cos(\theta)[/tex]
where [tex]\theta[/tex] is the measure of the angle between the two vectors [tex]\vec x,\vec y[/tex]. Note that
[tex]\vec x \cdot \vec x = \|\vec\| \|\vec x\| \cos(0) = \|\vec x\|^2[/tex]
Applying the identity to [tex]\vec x = \vec y = \vec A + \vec B[/tex] and using the distributive and commutative properties of the dot product, we get
[tex](\vec A + \vec B) \cdot (\vec A + \vec B) = (\vec A \cdot \vec A) + 2 (\vec A \cdot \vec B) + (\vec B \cdot \vec B)[/tex]
which is equivalent to
[tex]\|\vec A + \vec B\|^2 = \|\vec A\|^2 + 2\|\vec A\|\|\vec B\| \cos(\theta) + \|\vec B\|^2[/tex]
Now, we're given [tex]\|\vec A\| = 13.9[/tex], [tex]\|\vec B\| = 5.9[/tex], and [tex]\theta=53^\circ[/tex], so that
[tex]\|\vec A + \vec B\| = \sqrt{13.9^2 + 2\cdot13.9\cdot5.9\cos(53^\circ) + 5.9^2} \approx \boxed{18.1}[/tex]
a student is provided with a battery-powered toy car that the manufacturer claims will always operate at a constant speed. the student must design an experiment in order to test the validity of the claim. which of the following measuring tools can the student use to test the validity of the claim? select two answers.
Correct question is -
A student is provided with a battery-powered toy car that the manufacturer claims will always operate at a constant speed. The student must design an experiment in order to test the validity of the claim. Which of the following measuring tools can the student use to test the validity of the claim?
a. Photogates placed at the beginning, end, and at various locations along the track that the car travels on.
b. A meterstick to measure the distance of the track that the car travels on.
c. A motion detector that is oriented perpendicular to the direction that the car travels.
d. A mass balance to determine the mass of the car
a. Photogates positioned at the beginning, give up, and at numerous locations along the music that the car travels on.
b. A meterstick to degree the distance of the track that the automobile travels on.
Physics may be described as the field or branch of technology that normally offers with nature and residences of count, motion and electricity with admire to space, pressure and time.on this scenario, a student is provided with a battery-powered toy vehicle that the manufacturer claims will continually function at a consistent speed. The student have to layout an test so as to check the validity of the declare.
consequently, to check the validity of the declare, the student must use the following measuring tools;
a. Photogates placed at the beginning, cease, and at diverse places alongside the song that the automobile travels on. This tool is normally used to degree time with admire to the price of change of the interruption or block of an infra-pink beam.b. A meterstick to measure the space of the track that the car travels onsubsequently, with those two gadgets the student can successfully measure or determine the validity of the declare.
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What is the acceleration of a car moving along a straight road that increases its speed from 0 to 100 km/h in 10 s?.
The acceleration of a car moving along straight road that increases its speed from 0 to 100 km/h in 10 s is 10 km/h-s.
What is acceleration?The rate at which an object's velocity with the minimum time changes is called an accelerator in mechanics. They were the vector quantities and accelerations.
Acceleration has dimensions of velocity (L/T) divided by time, i.e. L T−2. SI unit of acceleration is the meter per second squared (m s−2); or "meter per second per second", as the velocity in meters per second changes by the acceleration value, every second
The direction of net load acting on an item affects the direction of its acceleration.
Average acceleration = (change in velocity)/(time it takes)
The acceleration of a car moving along straight road that increases its speed from 0 to 100 km/h is:
car's acceleration = (100 km/h)/(10 s) = 10 km/h/s
Thus, acceleration of a car moving along a straight road that increases its speed from 0 to 100 km/h in 10 s is 10 km/h-s.
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if the water in a lake is everywhere at rest, what is the pressure as a function of the distance from the surface?
The pressure as a function of the distance from the surface is 101325 + 10055.25h
One must go h = 10.1 m down before the pressure is 1 atm greater than the pressure at the surface.
What are the pressure and absolute pressure?In order to determine absolute pressure, a complete vacuum is used. In contrast, gauge pressure is the amount of pressure that is measured in relation to atmospheric pressure, also referred to as barometric pressure. The average barometric pressure at sea level is 14.7 PSIA, while the absolute pressure of a complete vacuum is 0 PSIA.
The pressure at sea level = 1 atm = 101325 Pa
Density of sea water = 1025 kg/ m^(3)
Pressure due to fluid height = pgh
Absolute pressure = 101325 + 1025(9.81) h
= 101325 + 10055.25h
where h= 0 at sea level at increases downward
101325 = 1025(9.81)h
h = 10.1 m
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The complete question is:
"If the water in a lake is everywhere at rest, what is the pressure as a function of distance from the surface? The air above the surface of the water is at standard sea-level atmospheric conditions. How far down must one go before the pressure is 1 atm greater than the pressure at the surface?"
part b run the video frame-by-frame again. now describe the car’s velocity (speed and direction) over time.
Velocity is the direction in which an object is moving and serves as a measure of the pace at which its position is changing as seen from a particular point of view.
What do you mean by motion?Motion in physics is the phenomenon in which an object shifts in relation to time. Motion is quantitatively characterized in terms of the body's change in position with respect to the observer's frame of reference as well as the velocity, acceleration, and speed of the body. Kinematics is the area of physics that studies forces and how they affect motion, while dynamics is the area that studies motion in relation to its causes.
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In humans, genetic defects in the dna repair system result in the skin disorder -- xeroderma pigmentosum (xp). how do these defects create the phenotypes associated with the disorder?
At least eight different genes have inherited mutations that cause the disease xeroderma pigmentosum. More than half of all cases in the US have mutations in the XPC, ERCC2, or POLH genes.
What are mutations ?An alteration to an organism's DNA sequence is known as a mutation. Viral infection, mistakes in DNA replication during cell division, and exposure to mutagens are all ways in which mutations can develop.
Examples of inherited mutations include sickle cell disease, hemophilia, and cystic fibrosis. Additional mutations could happen naturally at any time during a person's lifetime. They're known as novel mutations. The damaged cells are small in number.
An alteration to an organism's DNA sequence is known as a mutation. Viral infection, mistakes in DNA replication during cell division, and exposure to mutagens are all ways in which mutations can develop.
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Ben wants to buy a new cell phone. Select the conditions that Ben should consider for this buying decision.
The number of sisters and brothers Ben has
The amount of money Ben has to spend
The price of the cell phone
Ben's age
a medicine ball has 10 J of energy and is thrown upward with a velocity of 2 m/s. what is its mass
what is the distance fallen for a ball in free fall 1 s after being dropped from a rest position? what is the distance for a 5- s drop?
The distance fallen for a ball in free fall 1s from a rest positon. Hence it falls 5m in 1s and 125m in 5s.
Initial velocity (u) = 0
Gravitational acceleration (g) (g) = 10 m/s2
Using equation of motion,
S=ut+1/2 at2
for t=1s, a=g , u=0
s=0×t + 1/2g ×1
s= 1/2 × 10
s= 5 m
t=5s,
s=0×t + 1/2g ×5×5
s= 1/2 × 10 × 25
s= 5 × 25
s= 125 m
What is a simple definition of distance?The distance between two points, objects, lines, etc. Remoteness is the quality of being physically separated from another thing or person.
a line is drawn in the universe.
To walk seven miles in one hour would be too time-consuming.
a big area:
A wide body of water encircled the ship.
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a vector has an x component of -22.5 units and a y component of 37.4 units. find the magnitude and direction of this vector.
The magnitude of the vector is 43.81 units and the direction of the vector is 120.89 degrees with a +x-axis counterclockwise.
What is the magnitude and direction of a vector?The length for a certain vector (let's say v) can be calculated by using the symbol |v|, which stands for the magnitude of a vector formula. In essence, this measurement represents the separation between the vector's starting and ending points. We apply the distance formula to get the vector's magnitude.
Its direction indicates where it points. Although vector direction can be expressed in a number of ways, degrees are the most frequent notation.
The magnitude of the given vector will be
[tex]\vec{r} &=x i+y j \\\vec{r}=-22.5 \hat{i}+37.6 \hat{j} \\{[\vec{r}] } &=\sqrt{(22.5)^2+(37.6)^2} \\&=43.81 units[/tex]
The direction of the vector will be
tanα=[tex]\frac{y}{x}\\[/tex]
[tex]=tan^{-1}(\frac{y}{x})\\=tan^{-1}(\frac{37.6}{22.5}\\=59.103 degree[/tex]
Therefore, the direction of the vector is 120.89 degrees with the +x-axis counterclockwise.
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