The length of the trajectory of the function f(t) = (2t , 1, [tex]e^{2} + e^{-t}[/tex]) is 3/2
Calculationlength = [tex]\int\limits^b_a {\sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2 + (\frac{df}{dt})^2 } \, dx[/tex]
=[tex]\int\limits^{ln2}_0 {e^{t}+ e\\^{-t} } \, dt[/tex]
=(2+1) - (1/2+1)
=2-1/2 =3/2
What is a vector?In mathematics and physics, the term “vector” is used informally to describe certain quantities that cannot be described by a single number or by a set of vector space elements.
A vector example is what?A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity’s mathematical or geometrical representation.
Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.
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A car traveling in a straight line with an initial velocity of 10 m/s accelerates at a rate of 4. 1 m/s2to a velocity of 28 m/s. What is the distance covered by the car in this process? State your answer to two decimal places
Answer: 83.41m
Explanation:
v^2=vo^2+2a(x-xo)
x=?
xo=0
a=4.1m/s^2
v=28m/s
vo=10m/s
784=100+2(4.1)(x-0)
684=8.2x
x=83.4146341463
x=83.41m
you're welcome
A bullet is fired horizontally 0.58 meters off the ground. Assuming gravity is 9.8 m/s2, how long (t) was the bullet in the air?
Answer: well
Explanation:
Assuming the bullet fired is a 32-gram .458 Winchester Magnum then it will take from 3.386 seconds to cover 1500 meters at 20∘C to 3.404 seconds to cover 1474.6 meters at 0∘C. You cannot assume there is no air resistance without the result being incorrect by about 500 meters.
If the density of an object is 9.331 x 10−2 lbs/cubic inch, what is its density in g/cm3?
A substance's density is defined as its mass per unit of volume. Density is most frequently represented by the symbol ρ, however Latin letter D may also be used.
If the density of an object is 9.331 x 10−2 lbs/cubic inch, what is its density in g/cm3?
9.331 x 10−2 lbs/cubic inch = 258 281 190,85 g/m³
To calculate the density:
Determine an object's weightFind out an object's volume.Weight to volume ratio.Alternately, switch the unit.The following is the density formula:
D = m/v, where D = Density, m = mass, v = volume.
Write down the data and the density equation, solve for the mass, add the density to the volume, then multiply the result to get the density in grams.
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Draw Water Molecules Required Using circles and motion lines to represent water molecules, draw a model of water on the molecular level. Be sure to show that water molecules are: • Randomly arranged. • Close together because they attract each other Moving
Water is a colorless, transparent chemical that makes up the majority of the earth's oceans, lakes, and streams. It is a crucial fluid that is essential to the continued existence of life on Earth.
The chemical formula for water is H2O. Two hydrogen atoms and one oxygen atom are held together by covalent bonds to make it up. The surface of the earth is made up of 71% of this liquid.
The boiling point of water is 100 degrees Celsius.
The freezing point of water is zero degrees Celsius. Water takes a very long time to freeze (or even boil), which is essential for the survival of our ecosystem.
Water becomes denser as it cools up to 4°C. Water then becomes less dense, though.
Therefore, Ice floats on water.
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Your question is incomplete but the above content might help.
when is the ideal time to take a resting heart rate
According to doctors and health experts, resting heart rate should be taken before doing any physical activity. It is ideal to take your resting heart rate first thing in the morning.
The resting heart rate of an individual is of great importance in a medical examination as it is indicative of various infections or heart-related problems, if any, present in the individual.
The resting heart rate of any healthy individual falls between the range of 60 to 100 beats per minute. A resting heart rate below 60 and above 100 beats per minute, without any direct reason such as heavy exercise and physical exertion might be indicative of a serious developing heart condition; and the particular individual should consult a doctor.
The ideal time to take a resting heart rate is during resting time. It should be taken first thing in the morning before even coming out of bed. Resting heart rate should not be taken immediately after exercising or a workout.
Therefore, the ideal time to take resting heart rate is early in the morning before leaving the bed and doing any sort of physical activity.
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An accelerometer is a device that uses the extension
a spring to measure acceleration in terms of Earth's gravitational acceleration (g). What is
the approximate acceleration if this accelerometer spring is extended just 0.43 centimeters?
Answer:
your question explains that an accelerometer is a device that uses the extension spring to measure acceleration in terms of Earth's Gravitational accelerations. So if this device is extended just 0.43 centimeters the possible accelerations is letter B. 0.80 g
Calculate the speed in m/s of a skateboarder who accelerates from rest for 3 seconds down a ramp at an acceleration of 5m/s2
Answer: 15m/s
Explanation:
a change in position relative to a starting point
Rate of acceleration for a 5 kg grocery cart that’s being pushed with 50 N
Rate of acceleration for a 5 kg grocery cart that’s being pushed with 50 N is 10 m/sec^2. The value of acceleration can be calculated with the help of following formula Fnet = m . a
What is the calculation of the above problem?Fnet is the net force acting on the shopping cart
m is the mass of the grocery cart
a is the acceleration of the shopping cart
So on using the formula we get
Fnet = m . a
So on putting the values we get
Fnet = 50 N
m = 5kg
a = ?
50 = 5.a
On calculating we get the value of acceleration
a = 10 m/sec^2
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
The pictures show four wavelengths of sound. Which line shows the lowest frequency?
A. W
B. X
C. Y
D. Z
Answer: x
Explanation:
the closer the waves are to each other the higher the frequency
Answer: X
Explanation: i took the test
19. Name one physical property and one chemical
property of wood.
HELPPP
Answer:
malleability&flammable.
Explanation:
To hammer a horseshoe a blacksmith heats it until it is red hot. the blacksmith the plunges it into cold water. a) what happens to the temperature of the horseshoe and the temperature of the water? b) how have these changes in temperature taken place?
When the horseshoe is heated until it's red hot and when it is plunged into cold water the temperature of the horseshoe decreases and the temperature of the water increases. These changes take place by the Principle of Calorimetry.
The principle of Calorimetry states that whenever a hot body comes in contact with a cold body the hot body loses heat and the cold body gains heat. The amount of heat lost by the hot body is equal to the amount of heat gained by the cold body.
When the horseshoe is heated red hot, its temperature increases, and the temperature of cold water is low. When the horseshoe is plunged into the cold water it loses its heat and its temperature decreases. On the other hand, the cold water gains the heat lost by the horseshoe and its temperature increases.
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How could you test to see if your specimen will grow and how does that relate to cell theory
The correct answer is Every living thing is formed of cells. When an old cell dies, a new cell is created.
All living things are primarily composed of cells, which serve as both the basic structural and organisational unit of all living things. According to the biological notion known as "cell theory," all cells are descended from previously existing cells. In the middle of the nineteenth century, it was initially put forward. All living things are composed mostly of cells, which also serve as the fundamental unit of reproduction. The cell theory is based on the following three basic postulates:
Every living thing is made up of one or more cells.The fundamental unit of structure and organisation in organisms is the cell.New cells are created from pre-existing cells.To learn more about cell theory refer the link:
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A vector has a magnitude of 20
meters due east and a second vector
has a magnitude of 20 meters due
west. What is the resultant of these
two vectors?
Answer:
V1x = 20 one to write x-component of vector 1
V2x = -20 " 2
Vx = V1x + V2x = 20 + (-20) = 0
In December 2020, SpaceX Falcon 9 was launched into orbit at the Kennedy Space Center in Cape Canaveral. Explain how Newton's three laws are at work when the SpaceX Falcon 9 was launched into orbit? (50 Points; and will mark Brainiest!)
Answer:Put to the test by seeing the force between the rocket and ground as well as the gravitational pull
Explanation:
hope it helps
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Why should we learn atomic theory? If it is probably incorrect in some way and will undoubtedly change, why do we spend time learning about it?
Answer: The atomic theory is important because it describes the composition of the atom and the properties of the subatomic particles as well as their behavior.
Explanation:
Even if our grasp of atomic theory may continue to develop throughout time, learning about it is still important for a number of reasons.
Thus, Atomic theory gives the fundamental ideas for comprehending matter behaviour and interactions between atoms and molecules, which forms the basis of modern chemistry.
It serves as the cornerstone of contemporary chemistry and provides insight into a number of chemical processes.
The development of atomic theory throughout millennia has been shaped by the efforts of numerous scientists. It has roots in antiquity.
Thus, Even if our grasp of atomic theory may continue to develop throughout time, learning about it is still important for a number of reasons.
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If Janie puts her hand on a
cold metal doorknob, how will
thermal energy move??
Answer:
B. Heat moves from her hand to the door knob
Explanation:
This is because heat flows from hot to cold objects.
Answer:
B. Heat moves from her hand to the doorknob.
Explanation:
A straight wire segment carries 0.25a. what length would it need to be to exert a 4.0-mn force on a magnet that produces a uniform magnetic field of 0.015t that is perpendicular to the wire?
A straight wire segment that carries 0.25a, would need 1.10m to produce a uniform magnetic field.
Where is the homogenous magnetic field?A uniform magnetic field is the solution. The magnetic field is considered to be uniform if its strength is the same at all of the area’s equally spaced points. It is represented by a parallel set of equally spaced lines.
What is a magnetic field’s uniform and non-uniform state?A magnetic field that receives the same magnetic forces in all directions is said to have a uniform magnetic field. The magnetic field that experiences unequal forces from various directions is said to have a non-uniform magnetic field.
Give an example of a uniform magnetic field.Helmholtz coils are available for purchase in order to provide a consistent magnetic field. The constant magnetic fields enable calibration in any scenario.
CalculationI = 0.25A
B = 0.015 J
F = 4.0 mN
F = I (dl x B)
4 x 10^(-3) = 0.25 x l x 0.015
⇒ l = (4 x 10^(-3)) / 0.015 x 0.25
≈ 1.1 m
Thus, the length required would be 1.1m
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A boat sailed for 7 hours at the speed of 80 km per hour it changed its speed to 95 km per hour for the next 6 hours how far had the boat sailed in kilometers
The boat had sailed 1130km.
How to find how far the boat had sailed?Initial Boat travel time = 7 hours.
The boat's initial speed is 80 km/h
The boat's current speed is 95 km/h.
Boat travel time at present = 6 hours.
Total nautical miles traveled =?
Solution:
Speed = distance / time.
The distance = Speed * Time
1. Distance = 80 km/h x 7 hours
Distance = 560 km
2. Distance = 95km/h x 6hours
Distance = 570 km
Hence, total distance = 560km + 570km
= 1130km
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five charges are placed in a closed box. each charge (except the first) has a magnitude which is twice that of the previous one placed in the box. all charges have the same sign and (after all the charges have been placed in the box) the net electric flux through the box is 7 × 107 n · m 2 /c. what is the magni
The magnitude of the charge is q = 13.423 µC.
What is point charge?If the magnitude of an electric charge for a body is very small compared to the distance between them, they are referred to as point charges. As a result, the charge is thought to be concentrated at that location.
Let the first charge be q.
So
q1 = q
q2 = 2q
q3 = 4q
q4 = 8q
q5 = 16q
Total charge Q = q1 + q2 + q3 + q4 + q5 = 31q
Flux f = 4.7 × 10^7 N · m2/C
According to gauss law
Flux f = Q/(permittivity of free space)
4.7 × 10^7 = 31q/(8.854*10^-12)
q = 1.3423*10^-5
= 13.423*10^-6 C
= 13.423 µC
The smallest possible charge q = 13.423 µC
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what is displacement vs speed
Answer:
Displacement is the vector difference between the ending and starting positions of an object. It may be very different from the distance the object has travelled along the way. Velocity is the rate at which displacement changes with time.
Explanation:
Ik this is super simple so I’m just gunna look it up if no body responds but what’s the formula for the Area of a triangle
The answer is:Area=1/2×b×h
Answer:
A= b×h ÷ 2
Explanation:
The Area of a triangle formula is the Base multiplied by the Height, then divided by 2
THE FIRST PERSON TO GIVE ANSWERS GETS BRAINLIEST
PLEASE HELP URGENT
Answer:
number 1
Explanation:
using the formula of momentum
velocity × mass
number 1 gives more momentum hence will easily move the system
All gases exhibit ideal behavior in low pressure situations because when the pressure is very low, the gas particles are.
Gases move slower at temperatures not pressures.
What happens to gas at low pressure?The average kinetic energy of the gas particles falls as the temperature rises. Because of this, a greater percentage of gas molecules lack the kinetic energy needed to repel intermolecular forces generated by nearby atoms.As air pressure drops, the air spreads out or expands more widely. There is a consequent drop in temperature.The temperature of a gas is directly proportional to its pressure for a constant volume of gas in a sealed container, according to the pressure law.The amount of oxygen available to breathe likewise reduces when the pressure drops. At very high altitudes, the oxygen levels and air pressure are so low that individuals can get sick or possibly pass away.All gases exhibit ideal behavior in low-pressure situations because when the pressure is very low, the gas particles are:
Far apart and rarely interacting
- gases move slower at temperatures, not pressures.
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Bill is driving a very old car with a hood designed to be rigid in a crash. linda is driving a new car with a hood
designed to crumple in a crash. both have the same mass and are wearing seatbelts. in a head-on collision at the
same speed with a stationary wall, which driver will experience greater force?
Bill will experience the greater force.
What is mass?Mass is a physical body's total amount of matter. It also serves as a gauge for the body's inertia or resistance to acceleration (change in velocity) in the presence of a net force. The strength of an object's gravitational pull to other bodies is also influenced by its mass.The kilogram is the SI unit of mass (kg). In science and technology, a body's weight in a given reference frame is the force that causes it to accelerate at a rate equal to the local acceleration of free fall in that frame.For instance, a kilogram mass weighs around 2.2 pounds at the surface of the planet. However, the same kilogram mass would weigh just about 0.8 pounds on Mars and about 5.5 pounds on Jupiter.An object's mass is a crucial indicator of how much stuff it contains. Weight is a measurement of an object's gravitational pull. It is influenced by the object's location in addition to its mass. As a result, weight is a measurement of force.Bill is driving a very old car with a hood designed to be rigid in a crash. Linda is driving a new car with a hood designed to crumple in a crash. Both have the same mass and are wearing seatbelts. in a head-on collision at the same speed with a stationary wall, which driver will experience greater force:
Bill will experience the greater.
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Q1.
Figure 1 shows a car travelling at a constant speed on a straight, level road
Figure 1
6
Figure 2 shows a free body diagram for the car.
Figure 2
Normal contact force
Forward
force
Air resistance
Weight
(a) Explain how the free body diagram shows that the resultant force on the car is zero.
The lengths of the arrows that show the forces that act on the car are equal hence no net force acts on the car.
What is the free body diagram?The free body diagram is the image that shows us the forces that are acting on a body. We know that the greater the magnitude of the forces that act on a body, the longer the line that shows the force that acts on a body, the greater the magnitude of the force.
Now we have the free body image of the car. If we look at the forces that act in the vertical direction which are the weight and the normal reaction we can see that those forces are balanced since the arrows are of equal length. The forces that acts in the horizontal direction, forward force and air resistance also have lines of equal length which show that the forces are balanced.
Since the lengths of the arrows that show the forces that act on the car are equal in length, the forces are balanced and there is no net force that acts on the car.
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a bullet is shot horizontally from shoulder height (1.55 m) with an initial speed of 210 m/s. how much time elapses before the bullet hits the ground? how far does the bullet travel horizontally?
The ratio of displacement to time is known as velocity. The bullet needs 0.553 seconds before it touches the ground.
Consider the vertical motion of bullet
We have equation of motion s = ut + 0.5 at²
Initial velocity, u = 0 m/s
Acceleration, a = 9.81 m/s²
Displacement, s = 1.5 m
Substituting
s = ut + 0.5 at²
1.5 = 0 x t + 0.5 x 9.81 xt²
t = 0.553 s
Time elapsed before the bullet hits the ground is 0.553 seconds.
b) Consider the horizontal motion of bullet
We have equation of motion s = ut + 0.5 at²
Initial velocity, u = 200 m/s
Acceleration, a = 0 m/s²
Time, t = 0.553 s
Substituting
s = ut + 0.5 at²
s = 200 x 0.553 + 0.5 x 0 x 0.553²
s = 110.6 m
The bullet travels horizontally 110.6 m.
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How much force is needed to stop a 100-kg football player if she negatively accelerates (decelerates) at 20 m/s2? responses 5 n 5 n 20 n 20 n 200 n 200 n 2000 n 2000 n
The amount of force required to stop a 100-kg football player if she negatively accelerates (decelerates) at 20 m/s² is 2000N.
How to calculate force?Force is a physical quantity that denotes ability to push, pull, twist or accelerate a body and which has a direction.
The force required to accelerate a body can be calculated by multiplying the mass of the body by the acceleration as follows:
Force = mass × acceleration
According to this question, a 100-kg football player negatively accelerates (decelerates) at 20 m/s², the force needed can be calculated as follows:
F = 100kg × 20m/s²
F = 2000N
Therefore, the amount of force required to stop a 100-kg football player if she negatively accelerates (decelerates) at 20 m/s² is 2000N.
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An object with a negative acceleration can
have a positive velocity
Answer:Is it possible to have positive acceleration with a negative velocity?
Explanation:An object which moves in the positive direction has a positive velocity. If the object is slowing down then its acceleration vector is directed in the opposite direction as its motion (in this case, a negative acceleration).
A car accelerates from a velocity of 100ms-1 to a final velocity of 20ms-1 in 10 seconds.Find it's deceleration.
The deceleration of the car from a velocity of 100ms-1 to a final velocity of 20ms-1 in 10 seconds is 8ms-2.
We are aware that acceleration refers to an object's rate of increase in speed, and deceleration refers to an object's rate of decrease in speed.
Because it must be reported as a magnitude and a direction, acceleration is a vector. Negative and positive signs are used to denote the direction in circumstances of one-dimensional motion. Negative indicators indicate that the object is slowing down.
The unit of measurement is the meter per second square, or ms-2.
We know that
v= u + at,
where,
v= final velocity
u= initial velocity
t= time
a= acceleration
According to the question,
u= 100ms-1
v= 20ms-1
t= 10s
a=?
so, v = u + at
substituting the values in the equation, we get:
20 = 100 + 10a
a= -8 ms-2
Here, the negative sign shows that the car is decelerating,
Thus, deceleration is 8ms-2.
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