The statement that there are no other galaxies in the Universe is completely untrue. Science has shown us that there are countless galaxies in the Universe, each one containing billions of stars, planets, and other celestial bodies. The sheer size of the Universe alone suggests that there must be more galaxies out there.
Our own galaxy, the Milky Way, is just one of many, and we can observe other galaxies through telescopes and other instruments. In fact, astronomers estimate that there may be as many as 2 trillion galaxies in the observable Universe alone.
These galaxies come in many shapes and sizes, and they are spread out across the vast expanse of the Universe. Some are spiral galaxies like the Milky Way, while others are elliptical or irregular in shape. They all contain massive black holes, which play a crucial role in shaping the structure and evolution of the galaxies themselves.
Understanding the presence of other galaxies in the Universe is crucial to our understanding of the origins and evolution of the cosmos. Through ongoing scientific study, we continue to learn more about the structure, dynamics, and properties of these galaxies, shedding new light on the mysteries of the Universe.
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Earth’s diameter is approximately 8000 miles. Estimate the speed of a point on earth’s equator as it’s carried around with earth’s rotation.
The speed of the person standing at the equator is 1656 km/h which is equal to 1,028.57 mph.
What is the speed of rotation of the Earth at the equator?The surface of the earth at the equator moves at a speed of 460 meters per second.
v = 460 m/s
The person standing at the equator will move with this same speed.
Convert the speed in meters per second to kilometers per hour
1 m/s = 3.6 km
460 m/s = ?
= 1656 km/h
Convert the speed in meters per second to miles per hour
1 mile = 1.61 km
1 mi/1.61km x 1656 km/h = 1,028.57 mph
Thus, the speed of the person standing at the equator is 1656 km/h which is equal to 1,028.57 mph.
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Which statement best compares the accelerations of two objects in free fall?
Answer:
increasing the masses of the objects and decreasing the distance between the objects
Answer:the objects have the same acceleration
Explanation:
what radiation that isnt absorbed by the atmosphere produces a suntan or sunburn?
The radiation from the sun that is not absorbed by the atmosphere and can produce a suntan or sunburn is mainly the ultraviolet (UV) radiation. UV radiation has different wavelengths, including UVA, UVB, and UVC. UVC radiation is mostly absorbed by the atmosphere, while UVA and UVB radiation penetrate the Earth's atmosphere and can reach our skin.
UVB radiation is the main cause of sunburn, while UVA radiation contributes to tanning. Both types of radiation can be harmful to our skin and increase the risk of skin cancer.
here are many different types of rays present in sunlight. The rays that are most damaging to our skin are called ultraviolet (UV) rays. There are two basic types of ultraviolet rays that reach the earth’s surface—UVB and UVA. UVB rays are responsible for producing sunburn. The UVB rays also play the greatest role in causing skin cancers, including the deadly black mole form of skin cancer (malignant melanoma).
So, the radiation from the sun that is not absorbed by the atmosphere and can produce a suntan or sunburn is mainly the ultraviolet (UV) radiation.
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How are extrusive rocks formed?
A. Magma gets trapped inside Earth and cools to rock.
B. Volcanoes apply force to solid rocks and eject them
C. Magma gets forced to Earth’s surface and cools to rock.
D. Volcanoes trap lava inside Earth, where it cools to rock.
Answer:
A
Explanation:
Answer: C
Explanation: Because if magma wasn't to be forced on earth's surface, the magma would come on earth and burn earth down.
can someone please answer this, ill give you brainliest and your getting 100 points.
Answer:
Point number 3.
Explanation:
Volcanism can be studied to found out evidence of the internal structure of the Earth.
Answer:
Volcanism
Explanation:
Volcanism refers to study about the creation of volcanos.We know the earth's inner side is filled of magma which gets out through volcanos.So volcanism should be learntif a runner travels 1600m in 420 seconds, her average speed is
Answer:
the answer is 3.8m/s in meters per second
Calculate the de broglie wavelength for a proton moving with a speed of 1.0 x 10^6 m/s.
The de Broglie wavelength for a proton moving with a speed of 1.0 x 10⁶ m/s is approximately 6.63 x 10⁻⁹ meters.
The de Broglie wavelength (λ) of a particle is given by the equation:
λ = h / p
Where:
λ is the de Broglie wavelength
h is the Planck's constant (approximately 6.63 x 10⁻³⁴ joule-seconds)
p is the momentum of the particle
The momentum of a particle is given by:
p = mv
Where:
m is the mass of the particle
v is the velocity of the particle
In this case, we are dealing with a proton. The mass of a proton (m) is approximately 1.67 x 10⁻²⁷ kilograms.
Given the speed of the proton (v) as 1.0 x 10⁶ m/s, we can calculate the momentum (p):
p = mv = (1.67 x 10⁻²⁷ kg) x (1.0 x 10⁶ m/s) = 1.67 x 10⁻²¹ kg·m/s
Now, we can calculate the de Broglie wavelength (λ):
λ = h / p = (6.63 x 10⁻³⁴ J·s) / (1.67 x 10⁻²¹ kg·m/s) ≈ 6.63 x 10⁻⁹ meters.
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the inside surfaces of the glass inside thermos bottles are coated with aluminum to prevent energy transfers by
Answer:
radiation heat.
Explanation:
That is any heat that passes through the air, like the sun.
Answer:
radiation
Explanation: I’m sure
pls mark as brainliest if possible
three solid plastic cylinders all have radius 2.37 cm and length 6.42 cm. find the charge of each cylinder given the following additional information about each one.
Surface charge density: It is defined as the amount of charge per unit surface area of the space in two or three dimensions.
a. The surface charge density is = =19.9 × 10⁻¹¹C
b. The surface charge density is = 1.37 V 10⁻¹⁰C.
c. The volume charge density is = 1.73 × 10⁻¹²C
The formula gives it, σ=q/S
Here,
q is the charge and
S is the surface area.
Volume charge density: It is defined as the amount of charge per unit volume of the space in two or three dimensions. The formula gives it, p=q/V
Here,
q is the charge and
V is the volume.
(a) The surface charge density is given by,
σ=q/S …… (1)
Here,
q is the charge and
S is the total surface area of the cylinder.
The total surface area of the cylinders will be,
S = 2πr (h+r)
Here,
r is the radius and
h is the height of the cylinder.
Substitute 2.53 cm for r 5.64cm and for h in the above equation.
S= 2π (2.53cm) ( 1m/ 100cm) ((2.53cm) (1m/100cm) + (5.64cm) (1m/100cm))
=1.30 × 10⁻²m²
The charge on the first cylinder can be calculated by rearranging the equation (1).
q= σS
Substitute 15.3nC/m² for S and for σ in the above equation.
q=(15.3nC/m²) (10⁻⁹C/1nC) (1.30 × 10⁻²m²)
=19.9 × 10⁻¹¹C
The total surface area of the cylinder was calculated and then the expression of surface charge density which is, σ=q/S was rearranged to calculate the value of the charge on the cylinder.
(b) The surface charge density is given by,
σ=q/S …… (2)
Here,
q is the charge and
S is the curved surface area of the cylinder.
The curved surface area of the cylinders will be,
S = 2πrh
Here,
r is the radius and
h is the height of the cylinder.
Substitute 2.53cm for r and 5.64cm for h in the above equation.
S= 2π(2.53cm) (1m/100cm) (5.64cm) (1m/100cm)
=8.96 × 10⁻³m²
The charge on the second cylinder can be calculated by rearranging the equation (2).
q= σS
Substitute 15.3nC/m² for σ and 8.96 × 10⁻³m² for S in the above equation.
q= (15.3nC/m²) (10⁻⁹C/1nC) (8.96 × 10⁻³m²)
= 1.37 V 10⁻¹⁰C
(c) The volume charge density is given by,
p=q/V …… (3)
Here,
q is the charge and
V is the volume of the cylinder.
The volume of the cylinders will be,
V=πr²h
Here,
r is the radius and
h is the height of the cylinder.
Substitute 2.53cm for r and 5.64cm for h in the above equation.
V=πr²h
V=π((2.53cm) (1m/100cm))² (5.64cm) (1m/100cm)
The charge on the third cylinder can be calculated by rearranging the equation (3).
q= pV
Substitute 15.3nC/m³ for p and 1.13 × 10⁻⁴m³ for V in the above equation.
q = (15.3nC/m³) (10⁻⁹C/1nC) (1.13 × 10⁻⁴m³)
= 1.73 × 10⁻¹²C
The volume of the cylinder was calculated by the formula, V= πr²h
and then the expression of volume charge density which is, p=q/v
was rearranged to calculate the value of the charge on the cylinder.
Hence, The charge on the cylinder is 19.9× 10⁻¹¹C.
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your question is incomplete, most probably the complete question is :
Three solid plastic cylinders all have radius 2.53 cm and length 5.64 cm. Find the charge of each cylinder given the following additional information about each one. Cylinder (a) carries charge with uniform density 15.3 nC/m2 everywhere on its surface. Cylinder (b) carries charge with uniform density 15.3 nC/m2 on its curved lateral surface only. Cylinder (c) carries charge with uniform density 490 nC/m3 throughout the plastic.
Which statement about velocity is true?
Answer: velocity is the study of how fast an object changes its place, or is displaced.
Explanation: An example would be how fast a basketball reaches the other side of a gym, the acceleration and speed are measured and calculated to find velocity
How many joules is 3 lightning bolts?
Answer:
one billion to ten billion joules.
Explanation:
To keep a 100-watt light bulb going for one second, one hundred joules of energy will be used.
Answer:
In 3 lightning bolts, there is approximately 1 billion to ten billion joules.
Explanation:
starting at point "b" (i.e., 420 tanks and 800 bushels of corn), if this society wanted to produce 180 more tanks, then
To produce 180 more tanks starting from point "b" (420 tanks and 800 bushels of corn), the society would need to increase its corn production by 540 bushels.
In order to produce more tanks, the society needs to allocate additional resources to tank production. Let's assume that each tank requires 3 bushels of corn as raw material. Since the society wants to produce 180 more tanks, it would need an additional 180 tanks * 3 bushels per tank = 540 bushels of corn.
To meet this increased demand for corn, the society must increase its corn production. Starting from point "b" with 800 bushels of corn, they would need to produce an additional 540 bushels of corn to reach the required total of 1,340 bushels (800 + 540).
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Science is the study of the natural world through blank and blank
Answer:
biology. hope this helps
one type of wagon wheel consists of a 2.0-kgkg hoop fitted with four 0.80-kgkg thin rods placed along diameters of the hoop so as to make eight evenly spaced spokes. part a for a hoop of radius 0.40 mm , what is the rotational inertia of the wheel about an axis perpendicular to the plane of the wheel and through the center?
The rotational inertia of the wheel is 1.344 × 10⁻⁴ kgm²
What is rotational inertia?Rotational inertia of an object is the measure of the ability for the object to rotate about an axis which may or may not pass thorugh the object.
Hoiw to find the rotational inertia of the wheel?Since in one type of wagon wheel consists of a 2.0-kg hoop fitted with four 0.80-kg thin rods placed along diameters of the hoop so as to make eight evenly spaced spokes and for a hoop of radius 0.40 mm, we need to find the rotational inertia of the wheel about an axis perpendicular to the plane of the wheel and through the center?
The rotational inertia of the wheel is given by I = I₁ + I₂ where I₁ = rotational inertia of hoop = and I₂ = rotational inertia of thin rods
Now the rotational inertia of the hoop is, I₁ = m₁r² where
m₁ = mass of hoop = 2.0 kg and r = radius of hoop = 0.40 mmAlso, the rotational inertia of each thin rod is I₃ = m₂L²/2 where
m₂ = mass of thin rod = 0.80 kg and L = length of rod = 2r where r = radius of hoop = 0.4 mm = 0.004 mSince there are four thin rods, I₂ = 4I₃
= 4m₂L²/2
= 2m₂L²
= 2m₂(2r)²
= 2m₂(4)r²
= 8m₂r²
So, I = I₁ + I₂
I = m₁r² + 8m₂r²
I = (m₁ + 8m₂)r²
So, substituting the values of the variables into the equation, we have
I = (m₁ + 8m₂)r²
I = (2.0 kg + 8 × 0.80 kg)(0.004 m)²
I = (2.0 kg + 6.4 kg)(0.000004 m²)
I = (8.4 kg)(0.000016 m²)
I = 0.0001344 kgm²
I = 1.344 × 10⁻⁴ kgm²
The rotational inertia of the wheel is 1.344 × 10⁻⁴ kgm²
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Which of the following items are NOT used to create an electric motor?
A. Magnets
B. Electric Current
C. Turbines
D. Copper Wire
Answer:
Option C, Turbines
Explanation:
An electric motor comprise of following components-
a) Magnets
b) Electric wire or solenoid
c) Motor shaft
Turbine is a component of power producing plant that is essential to rotate the shaft of the motor. Once the shaft is rotated, the electric coil placed between the magnets is also rotated. Rotating coil cut the magnetic fields to induce emf and hence electric current is produced from mechanical work (i.e rotation).
Hence, option C is correct
hey! please help i’ll give brainliest!
Question:
If you push a bowling ball and a golf ball with an equal force what will happen
Answer:
B)
Explanation:
Larger than the force used to push the object that has less mass. A golf ball and a bowling ball are moving at the same velocity. When gravity and air resistance are equal, the object has drawn its terminal velocity.
Pitch is determined by which wave property
A. Amplitude
B. frequency
C. Trough
D. Crest
Answer:
B. Frequency
What type of wave is pitch?
The sensation of a frequency is commonly referred to as the pitch of a sound. A high pitch sound corresponds to a high frequency sound wave and a low pitch sound corresponds to a low frequency sound wave.
What determines pitch and loudness?
The pitch of a sound depends on the frequency while loudness of a sound depends on the amplitude of sound waves. Amazingly, many musicians, who have been trained are capable of detecting a difference in frequency between two separate sounds that are as little as 2 Hz.
Hope this helps :)
Pls brainliest...
Given: NM 1 XZ
Prove: AXYZ- ANYM
N
Try 11
X
Z
M
We know that side NM is
to side
XZ. If we consider side NY the transversal for these
parallel lines, we create angle pairs. Using the
we can state
that YXZ is congruent to YNM. We know that angle
XYZ is congruent to angle
by the reflexive
property. Therefore, triangle XYZ is similar to triangle
NYM by the
similarity theorem.
F
The prove of Angle XYZ- Angle NYM is given below:
∠XYZ is congruent to ∠NYM - reflexive property. ΔXYZ is the same with Δ NYM,- AA (angle-angle) similarity theorem.What is the triangle about?Note that from the image given;
NM // XZNY = transversal line∠YXZ ≡ ∠YNMSince ∠XYZ is said to be congruent to ∠NYM it can be proven by the use of the reflexive property.
The reflexive property is one that informs that any shape is regarded congruent to itself.
Since ∠NYM has a different way to call ∠XYZ that uses a different vertexes, but the sides are made up of the two angles which are said to be the same.
Therefore , ∠XYZ ≡ ∠NYM are proved by the reflexive property.
Since ΔXYZ is the same with Δ NYM, it can be proven by the AA (angle-angle) similarity theorem.
We have 2 angles Δ XYZ and Δ NYM:
Note that ∠YXZ ≡ ∠YNM
∠XYZ ≡ ∠NYM
So, ΔXYZ is said to be the same to ΔNYM and it is proven by the AA similarity theorem.
Therefore, The prove of Angle XYZ- Angle NYM is given below:
∠XYZ is congruent to ∠NYM - reflexive property. ΔXYZ is the same with Δ NYM,- AA (angle-angle) similarity theorem.Learn more about triangles from
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Answer:
1. parrael
2. corresponding angles theorem
3. NYM
4. AA
Explanation:
just took it
consider the frank-oseen energy associated with bend and twist distortions. determine the molecular field h, for each of these distortions
The molecular field for bend distortion is h_bend = -K_bend ∇² n and the molecular field for twist distortion is h_twist = -K_twist ∇² n + K_twist q₀ (∇ × n).
In the case of bend distortion, the director (the preferred orientation of the liquid crystal molecules) deviates from the local normal direction. The bend energy density is given by:
E_bend = (K_bend/2) × (∇ · n)²
where K_bend is the bend elastic constant and ∇ · n represents the divergence of the director field.
To determine the molecular field h associated with the bend distortion, we can take the functional derivative of the bend energy with respect to the director field n:
h_bend = δE_bend/δn
Using the Euler-Lagrange equation, this can be written as:
h_bend = -K_bend ∇² n
So, the molecular field for bend distortion is h_bend = -K_bend ∇² n.
Twist distortion:
In the case of twist distortion, the director rotates in a helical manner. The twist energy density is given by:
E_twist = (K_twist/2) × (∇ × n - q₀)²
where K_twist is the twist elastic constant and q₀ represents the pitch of the helix.
Similarly, to determine the molecular field h associated with the twist distortion, we take the functional derivative of the twist energy with respect to the director field n:
h_twist = δE_twist/δn
Using the Euler-Lagrange equation, this can be written as:
h_twist = -K_twist ∇² n + K_twist q₀ (∇ × n)
So, the molecular field for twist distortion is h_twist = -K_twist ∇² n + K_twist q₀ (∇ × n).
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An object is at rest. There are several forces acting on the object, but the net force is zero. If all the
forces acting on the object were to suddenly double in size, would the object start moving? Why or why not?
Answer:
no
Explanation:
because the heaver an object the harder it is to move s the force will not be able to move it
what is the physical state of gold at room temperature
Answer:
solid
Explanation:
Gold is a chemical element with symbol Au and atomic number 79. Classified as a transition metal, Gold is a solid at room temperature.
some comon salt was put into a flask. Water was then added carefully using a pipette without shaking the salt. After shaking, the volume of the solution reduced. Explain the observation
The observed reduction in the volume of the salt solution after shaking suggests that the added water was able to dissolve the salt, resulting in a more compact solution.
A solution is a homogeneous mixture made up of two or more substances that are evenly distributed at a molecular or ionic level. The substance that is present in the largest amount is called the solvent, and the substances that are dissolved in it are called solutes. The solutes can be gases, liquids, or solids.
The process of forming a solution involves the solute particles being surrounded by the solvent particles, which causes the solute particles to become evenly distributed throughout the solvent. The attractive forces between the solvent and solute molecules or ions play a crucial role in determining the concentration of the solution.
Solutions can have a wide range of properties, such as color, density, boiling and melting points, and electrical conductivity, which depend on the identity of the solutes and the solvent. Solutions are an essential part of many chemical, biological, and industrial processes, and understanding their properties and behavior is crucial in many fields of science and technology.
Here in this Question, When salt is added to water, it dissolves to form a saltwater solution. However, the addition of more water than the solubility of salt causes some of the salt to remain undissolved at the bottom of the flask. When the flask is shaken, the salt particles that were initially undissolved become suspended in the solution due to the agitation, thereby reducing the volume of the solution. This is because the suspended particles take up space in the solution, which was initially occupied by the water molecules.
Therefore, The observed decrease in salt solution volume after shaking indicates that the salt was able to dissolve in the additional water, resulting in a more compact solution.
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How does a falling object's surface area affect calculations of terminal velocity? (
O The greater the object's surface area, the greater the air density.
O Surface area does not affect an object's terminal velocity.
O The greater the object's surface area, the greater its terminal velocity.
O The greater the object's surface area, the more air resistance it encounters.
Answer:
The greater the object's surface area, the more air resistance it encounters.
Explanation:
Terminal velocity is the point at which the force of air resistance is equal to the force of gravity acting on an object. An object with a greater surface area will encounter more air resistance and therefore have a lower terminal velocity.
The greater the object's surface area, the more air resistance it encounters. Hence, its velocity decreases with increasing surface area.
What is velocity ?Velocity is a physical quantity that measure the distance covered by an object per unit time. Velocity is the rate of speed and it is a vector quantity. Velocity of an object is affected by its mass, physical state, surface area, temperature etc.
As the mass increases, the velocity of a a falling object will be greater because, the gravitational force towards the massive object is greater and it falls rapidly.
As the surface area of the object increases, the air resistance that it encounters also increases. This air resistance acts as an opposition and decreases its velocity.
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A very light small ball (with a speed of 5m/s) collides with a bowling ball that is at rest. The small ball bounces back, and the bowling ball moves very slowly. Which one, small ball or bowlling ball experiences the greater magnitude impulse during the collision
The bowling ball experiences the greater magnitude impulse during the collision since it is initially at rest and is given the momentum of the small ball which has a speed of 5m/s.
The impulse of the bowling ball can be calculated using the equation impulse = change in momentum = mvf - mvi, where m is the mass of the bowling ball, vf is its final velocity, and vi is its initial velocity.
Since the bowling ball is initially at rest (vi = 0), the impulse can be calculated as mvf = m(5m/s) = 5m^2/s. The impulse of the small ball can be calculated in the same way, giving an impulse of 5m^2/s. Therefore, the bowling ball experiences a greater magnitude impulse during the collision.
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Use the density of strontium (d = 2. 60 g/cm3) to determine the volume in cubic centimeters of a sample that has a mass of 47. 2 pounds
To determine the volume of a sample of strontium with a given mass, we can use the formula:
Volume = Mass / Density
Given:
Density of strontium (d) = 2.60 g/cm^3
Mass of the sample = 47.2 pounds
Before we proceed, let's convert the mass from pounds to grams, as the density is given in grams per cubic centimeter (g/cm^3).
1 pound is approximately equal to 453.592 grams.
Mass of the sample in grams = 47.2 pounds * 453.592 grams/pound
Now, we can calculate the volume using the formula:
Volume = Mass / Density
Volume = (47.2 * 453.592) / 2.60
By performing the calculations, we can determine the volume of the strontium sample in cubic centimeters.
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A gymnast jumps upward with an initial speed of 10 m/s. She is in the air for a total time of
A. 1 second
B. 5 seconds
C. 2 seconds
D. 10 seconds
A gymnast, who jumps upward with an initial speed of 10 m/s, is in the air for a total time of C. 2 seconds.
Consider the factors affecting the gymnast's motion, which are initial speed, gravity, and time. When the gymnast jumps, she experiences Earth's gravity, which causes a downward acceleration of approximately 9.8 m/s². We can use the formula t = (2*v₀) / g to find the total time in the air, where t is the total time, v₀ is the initial speed, and g is the acceleration due to gravity.
Plugging in the given values, we get t = (2*10 m/s) / 9.8 m/s² ≈ 2.04 seconds. Since the available choices are in whole numbers, we can round this value to the nearest second, which is 2 seconds. So, the gymnast is in the air for a total time of 2 seconds (C).
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A forensics investigator discharged an assault rifle-replica such that the bullet fired at an angle of 30 (degrees) off the horizontal with an initial velocity
of 28
m/s northwest. What is the maximum height the bullet will reach?
O 14 m/s
10 m
O 30 km
O 0.4351 seconds
Answer:
Initial y-component of speed
Vy = 28 * sin 30 = 14 m/sec vertically
1/2 m Vy^2 = 2 m g h conservation of energy of y-component
h = Vy^2 / (2 * g) = 14^2 / (2 * 9.8) = 10 m
23. If a jogger runs 100 meters west and then turns around and runs 30 meters east. What
was the jogger's displacement?
a. 70 meters.
b. 130 meters.
C. 30 meters.
d. 100 meters.
Answer:
A
Explanation:
if he goes to the west, the east is opposite so 100-30
The jogger's displacement was 70 meters. Hence, option (a) is correct answer.
What is displacement?The term "displacement" refers to a shift in an object's position. The symbol for it is an arrow pointing from the initial location to the ending place.
Displacement is a vector quantity as both magnitude and direction are required for defining displacement. SI unit of Displacement is meter.
Given parameter:
The first displacement of the jogger is = 100 meters along west direction.
The second displacement of the jogger is = 30 meters along east direction.
Hence, resultant displacement of the jogger along west direction = 100 meters - 30 meters
= 70 meters.
Hence, the magnitude of jogger's displacement was 70 meters. Hence, option (a) is correct answer.
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find the mass and center of mass of the solid e with the given density function . e is bounded by the parabolic cylinder z = 1 − y2 and the planes x 5z = 5, x = 0, and z = 0; (x, y, z) = 7.
The mass of E is 28/3, and the center of mass is located at (35/36, 0, 7/4).
We can use the triple integral to find the mass and center of mass of the solid E:
The limits of integration for x are from 0 to 5z.
The limits of integration for y are from −1 to 1.
The limits of integration for z are from 0 to 1 − y²
The density function is given by ρ(x, y, z) = 7.
Thus, the mass of E is given by:
M = ∭E ρ(x, y, z) dV
= ∭E 7 dV
= ∫₀⁵z ∫₁⁻¹ ∫₀¹−y² 7 dz dy dx
= 28/3
The x-coordinate of the center of mass is given by:
x-bar = (1/M) ∭E xρ(x, y, z) dV
= (1/M) ∭E x(7) dV
= (1/M) ∫₀⁵z ∫₋₁¹ ∫₀¹−y² x(7) dz dy dx
= 35/36
Similarly, the y-coordinate of the center of mass is given by:
y-bar = (1/M) ∭E yρ(x, y, z) dV
= (1/M) ∭E y(7) dV
= (1/M) ∫₀⁵z ∫₋₁¹ ∫₀¹−y² y(7) dz dy dx
= 0
And, the z-coordinate of the center of mass is given by:
z-bar = (1/M) ∭E zρ(x, y, z) dV
= (1/M) ∭E z(7) dV
= (1/M) ∫0^5z ∫−1^1 ∫0^1−y^2 z(7) dz dy dx
= 7/4
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The parking brake on a 1200kg automobile has broken, and the vehicle has reached a momentum of 7800kg.M/s. What is the velocity of the vehicle?