The appropriate flow rate of the plastic when the radius of each toy is 0.5 inch is 0.5236 cubic inches per second.
To find the appropriate flow rate of the plastic, we first need to find the volume of each toy. The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius.
When the radius of each toy is 0.5 inch, the volume of each toy is:
V = (4/3)π(0.5)^3 = 0.5236 cubic inches
Since the radius of each ball is increasing at a rate of 0.1 inch per second, the volume of each toy is increasing at a rate of:
dV/dt = (4/3)π(3r^2)(dr/dt) = (4/3)π(3(0.5)^2)(0.1) = 0.0524π cubic inches per second
To produce 100 toys at a time, the total volume of plastic needed is:
100 toys x 0.5236 cubic inches/toy = 52.36 cubic inches
To find the average rate of change of volume over the 10 second interval, we need to know the starting radius of the first toy and the ending radius of the last toy produced during the 10 seconds.
Assuming that the first toy has a radius of 0.5 inch, the last toy produced after 10 seconds would have a radius of:
r = 0.5 + 0.1(10) = 1.5 inches
The volume of the last toy is:
V = (4/3)π(1.5)^3 = 14.1372 cubic inches
The total volume of plastic used to produce 100 toys over the 10 seconds is:
100 toys x (0.5236 + 0.0524π + 0.1047π + ... + 13.6133π + 14.1372)/2 = 888.64 cubic inches
The average rate of change of volume over the 10 second interval is:
dV/dt = (888.64 - 52.36) / 10 = 83.628 cubic inches per second
Finally, the average flow rate of the plastic over each 10-second production cycle is:
(888.64 - 52.36) / 10 = 83.628 cubic inches per second.
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The rarest type of stars are A. stars that are about 1 solar mass. B. stars that are more than 50 solar masses. C. stars that are about 10 solar masses. D. stars that are about 0.5 solar mass.
The rarest type of stars is those that are more than 50 solar masses.
How are stars categorized?
Stars are categorized on the basis of mass, spectral behavior, and temperature.
There are 7 spectral types of stars:
O-type (Blue) stars have more than 50 times the solar mass of the sun and are the rarest main sequence stars present in the universe. Their abundance is merely 0.000001% of known stars.Thus, the rarest type of stars are the O-type stars that have more than 50 times the solar mass of the sun.
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we observe stars orbiting at distances of 25000 light years from the centers of galaxy x and galaxy y for this orbital distance stars in galaxy x have higher orbital speeds tan stars in galaxy y what can we conclude
Galaxy X contains more total mass within 25,000 light-years of its center than Galaxy Y.
Light-yearsA light-year, a significant unit of length used to express astronomical distances, is roughly 9.46 trillion kilometers, or 5.88 trillion miles. A light-year is the distance that light travels in a vacuum in one Julian year, according to the International Astronomical Union. The name "light-year" is occasionally misunderstood as a unit of time since it contains the time measurement word "year". When expressing distances to stars and other distances on a galactic scale, the light-year is most frequently employed, especially in non-specialized situations and popular science publications. The parsec, which comes from astrometry and is the distance at which one astronomical unit subtends an angle of one second of arc, is the unit that is most frequently used in professional astronomy.
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A hydraulic system contains 3 pistons. The input piston has an area of 0.625 in2, one of the output pistons ( piston A ) has an unknown area and the other piston ( Output Piston ) has a diameter of 3.75 inches. If system pressure is 1,440 psi, and Piston A is supporting 20,000 lb, what is the area of Piston A
The area of Piston A is 13.88 in^2
What is a hydraulic system?
The hydraulic system functions by using pressurized fluid. The power of liquid fuel in hydraulics is significant and as a result, they are commonly used in heavy equipment.
Hydraulic system simply means a mechanical function that operates through the force of liquid pressure.
Here
A hydraulic system contains 3 pistons.
Pressure, P = 1440 psi
for piston A:
Area, A= 0.625 in^2
Force, F = 20,000 lb
We know that,
Force = Pressure x Area
F = P x A
Area ( piston A) = F / P
A = 20,000 / 1440
A = 13.88 in^2
Hence,
The area of Piston A is 13.88 in^2
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A billiard ball at rest is struck by another billiard ball of the same mass whose speed is 6.0 m/s. After an elastic collision the striking ball goes off at an angle of 25° with respect to its original direction of motion. Find the angle the struck ball makes with this direction and the final speeds of both balls.
The angle that the stuck ball makes with the direction of motion and the velocity of both the billiard balls are 65°, 2.6 m/s and 5.5m/s respectively.
To find the answer, we need to know about the linear momentum and angle made in elastic 2 dimensional collision.
What's the angle made by the struck billiard ball with the direction of motion of the 1st ball?In the two dimensional elastic collision between two objects, the scattered objects make 90° angle between them.So, here the angle between the two billiard balls after collision is 90°.As the one billiard ball is making 25° with the initial direction of motion, so the another struck billiard ball makes 90°-25°= 65°.What's the conservation of linear momentum along vertical direction?Let m = mass of each billiard balls, v = velocity of scattered billiard ball, u = velocity of struck billiard ballBefore collision there's no vertical component of momentum. So it's zero.From figure, the total momentum along vertical direction is m×v×sin25°-m×u×sin65°From conservation of linear momentum,0= m×v×sin25°-m×u×sin65°
v×sin25°=u×sin65°
v= 2.1u
What's the conservation of momentum along horizontal direction as shown in figure?Total momentum before the collision along horizontal direction = m × 6 m/sFrom the figure, total momentum after collision is m×v×cos25° + m×u×cos65°So, m×6 = m×v×cos25° + m×u×cos65°6= 2.1u× cos25° +u×cos65°
= 2.33u
u = 6/2.33 = 2.6 m/sAnd v= 2.1×2.6= 5.5 m/sThus, we can conclude that the angle that the stuck ball makes with the direction of motion and the velocity of both the billiard balls are 65°, 2.6 m/s and 5.5m/s respectively.
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Hydrostatic equilibrium in the Sun means that Choose one: A. energy produced in the core per unit time equals energy emitted at the surface per unit time. B. pressure balances the weight of overlying layers. C. the Sun absorbs and emits equal amounts of energy. D. the Sun does not change over time.
Answer: Hydrostatic equilibrium in the Sun means that pressure balances the weight of overlying layers.
Explanation: To find the answer, we have to know more about the Hydrostatic equilibrium in sun.
What is Hydrostatic equilibrium in sun?Hydrostatic equilibrium in sun means that, the sun is neither expanding not contracting.We can say that the forces that control the sun are precisely balanced.The structure of the sun is in such a way that it can balance the pressure outward and the force of gravity inward.This balance is known as hydrostatic equilibrium.Thus, we can conclude that, the Hydrostatic equilibrium in the Sun means that pressure balances the weight of overlying layers.
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How many outer-orbital electrons are found in an atom of:a) Na?b) P?c) Br?d) I?e) Te?f) Sr?
Answer:
Na=1P=5Br=7I=7Te=6Sr=2The requried number of outer-orbital electrons in an atom of Na is 1, P is 5, Br is 7, I is 7, Te is 6, and Sr is 2.
What is orbital?An orbital is a region of space around the nucleus of an atom where there is a high probability of finding an electron. The electrons in an atom are arranged in specific energy levels or shells, and each shell contains one or more subshells, which in turn contain one or more orbitals.
Here,
To determine the number of outer-orbital electrons in an atom, we need to look at the position of the element in the periodic table. The number of outer-orbital electrons is equal to the group number of the element for groups 1, 2, and 13 to 18. For groups 3 to 12, we need to subtract the group number from 10.
a) Na is in group 1, so it has 1 outer-orbital electron.
b) P is in group 15, so it has 5 outer-orbital electrons.
c) Br is in group 17, so it has 7 outer-orbital electrons.
d) I is in group 17, so it has 7 outer-orbital electrons.
e) Te is in group 16, so it has 6 outer-orbital electrons.
f) Sr is in group 2, so it has 2 outer-orbital electrons.
Therefore, the number of outer-orbital electrons in an atom of Na is 1, P is 5, Br is 7, I is 7, Te is 6, and Sr is 2.
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True or false: power output can be increased by increasing the rate at which work is done.
By speeding up the process of doing work, power production may be enhanced. The following statement is true.
Description:
Work is completed at a rate determined by power. It is the ratio of work to time. It may be calculated mathematically using the next equation.
Power = Work / Time
or, P = W / T
If the amount of effort/work increases and the amount of time decreases, power will grow. To complete a task in a short amount of time, a lot of force is used.
The Watt is the common metric unit of power. A quantity of power is one unit of labor divided by one unit of time, as the expression for power suggests. As a result, one Watt is equal to one Joule/second. The term "horsepower" is sometimes used to describe a machine's output of power for historical reasons. The equivalence of horsepower is around 750 Watts.Therefore it is concluded that the questioned statement is true.
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On the day Harvey is to present his dissertation, he wakes up with a severe headache. During the presentation, he feels no pain in his head. Fifteen minutes after the presentation is over, Harvey becomes aware of his headache again. Harvey's experience is best explained by
Gate-control theory
What is Gate-control theory?
According to the Gate Control Theory of Pain, the spinal cord has a system that allows pain signals to be amplified in the brain before being processed at the spinal cord itself, or attenuated there.
The mechanism that allows or prevents the passage of pain signals is known as the gate. The gate may be open or it may be closed, one of two possibilities:
When the gate is open, pain signals can enter and are delivered to the brain, where they are perceived as pain.If the gate is closed, pain signals will be prevented from ascending to the brain and won't be felt.The administration of a non-noxious (soothing or light rubbing) stimulus can help engage the gate control mechanism and alleviate pain in those who are exposed to painful (noxious) stimuli.
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Consider two celestial objects with masses m1 and m2 with a separation distance between their centers r. If the first mass m1 were to double and the second mass m2 were to triple, what would happen to the magnitude of the force of attraction
The new magnitude of the force of attraction will be 6 times the original force of attraction
How to determine the initial force Mass 1 = m₁Mass 2 = m₂ Gravitational constant = GDistance apart = rInitial force (F₁) = ?F = Gm₁m₂ / r²
F₁ = Gm₁m₂ / r²
How to determine the new force Mass 1 = 2m₁Mass 2 = 3m₂ Gravitational constant = GDistance apart (r) = rNew force (F₂) =?F = Gm₁m₂ / r²
F₂ = G × 2m₁ × 3m₂ / r²
F₂ = 6Gm₁m₂ / r²
But
F₁ = Gm₁m₂ / r²
Therefore
F₂ = 6Gm₁m₂ / r²
F₂ = 6F₁
Thus, the new magnitude of the force of attraction will be 6 times the original force of attraction
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two particles each having a mass of 5g and charge of 1.0×10^-7C stay in limiting equilibrium on a horizontal table with a separation of 10cm . The coefficient of friction between them and the table is same . Find the value of this coefficient.
The value of the coefficient is μ=0.18.
What is meant by Friction?A force that opposes this motion of the hands is activated when they brush against one another. The frictional force is the force resisting motion that is exerted in the direction that is counter to the direction that the hands are moving, and it is what creates heat energy.The force that prevents one solid item from moving across another is known as friction. Static, sliding, rolling, and fluid friction are the four main categories of friction.Many times, the uses of friction can be understood by imagining what would happen in their absence. You wouldn't be able to walk, operate a car, or grip anything if there was no friction. Pencils and pencils wouldn't function. Using brakes on a car or bicycle to halt requires friction as well.Find the value of this coefficient.
The particles are in equilibrium, meaning the net force on them is zero.
Thus, repulsion due to their charge = friction due to the table.
As the equilibrium is limiting, friction reaches its maximum value.
[tex]\frac{kQ^{2} }{r^{2} }[/tex]=μmg
[tex]k=9*10^{9} Nm^{2} C^{-2}[/tex]The electrostatic constant [tex]Q=10^{-7} C[/tex] is the charge, and r=0.1m is the distance between the charges.
[tex]\frac{(9*10^{2})(10^{-7})^{2} }{(0.1)^{2} }[/tex]=μ*[tex](5*10^{-3})(10)[/tex]
Therefore, The answer is μ=0.18.
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A bicycle with 20 -inch diameter wheels is traveling at 16 mi/h. Find the angular speed of the wheels in rad/min.
The angular speeds of the wheels is 1,647.28 rad/min
What is Angular Velocity?angular velocity is the speed at which the angle between two bodies changes as an item rotates or revolves around an axis.
The diameter of a bicycle, d = 20inches
Radius, r = 10 inches
The bicycle is travelling at 16 mi/h.
We need to find the angular speed of the wheels in rad/min.
We know that,
1 mi/h = 0.0166667 mi/min
It means,
16 mi/h = 0.26 mi/min
Also,
10 inch = 0.0001578356 miles
The angular speeds of the wheels is given by :
v = rω
ω = v/r
ω = 0.26/0.0001578356
ω = 1,647.28 rad/min
So, the angular speeds of the wheels is 1,647.28 rad/min
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Consider the following forces. (1) frictional (2) gravitational (3) tension (4) strong nuclear (5) normal (6) electroweak which of the forces listed are considered fundamental forces?
The forces listed are considered fundamental forces (2) gravitational (4) strong nuclear (6) electroweak.
Fundamental force, also called fundamental interaction, in physics, is any of the four primary forces—gravitational, electromagnetic, sturdy, and weak—that govern how gadgets or particles interact and how certain particles decay. All of the regarded forces of nature may be traced to those essential forces.
Now, physicists say they have discovered viable symptoms of a fifth essential force of nature. The findings come from studies performed at a laboratory near Chicago. The four fundamental forces govern how all of the objects and particles inside the Universe engage with each other.
The strong nuclear pressure pulled definitely and negatively charged quarks collectively to form undoubtedly charged protons and neutrally charged neutrons. The strong nuclear force also binds protons and neutrons within the nucleus of atoms. The weak nuclear force enabled complicated atoms to form through nuclear fusion.
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The electric field of an atom in an ionized helium atom, the most probable distance between the nucleus and the electron is r = 26.5 x 10-12m. what is the electric field due to the nucleus at the location of the electron?
The electric field due to the nucleus at the location of the electron is 4.101 × 10¹² N/C.
Given:
Distance between the electron and nucleus, r = 26.5 × 10⁻¹² m
Charge on an electron, Q = 1.6 × 10⁻¹⁹ C
Calculation:
We know that the Helium atom (He²⁺) has an atomic number Z = 2 and an atomic mass number A = 2 ( 2 protons + 2 neutrons). Thus the charge of a helium atom can be calculated as:
Q' = +2e = 2(+1.6 × 10⁻¹⁹ C) = 3.2 × 10⁻¹⁹ C
We know that the electric field on charge Q due to the nucleus is given as:
E = kQ' / r²
where E is the electric field
k is Coulomb's force constant
Q' is a charge ona Helium atom
r is the separation distance between the electron and nucleus
Applying values in the above equation we get:
E = (9×10⁹ Nm²/C²) (3.2 × 10⁻¹⁹ C) / (26.5 × 10⁻¹² m)²
= 4.101 × 10¹² N/C
Thus, the electric field on electrons due to the Helium nucleus is of magnitude 4.101 × 10¹² N/C.
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A block of mass 0.248 kg is placed on top of a light, vertical spring of force constant 5 025 N/m and pushed downward so that the spring is compressed by 0.090 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise
The maximum height above the point of release it rises is 8.82 m
What is spring force:
The force exerted by a spring on objects attached to its ends is proportional to the spring's change in length away from its equilibrium length.
F(spring) = k*x
here,
mass, m=0.240 kg
vertical spring constant, k = 5050 N/m
compression, x=0.090 m
When the spring is compressed, the spring potential energy is:
E = (k*x^2) / 2
substituting the values,
E = 5050* 0.090^2 / s
E = 20.91 J
This energy would be converted to kinetic, so the mass gains speed, which is then converted to gravitational potential energy once the mass reaches its highest point
E(p) = m*g*h
where, h is the maximum height
E(p) = E
m*g*h = 20.91
h = 20.91 / ( 9.8 * 0.248 )
h = 8.82 m
hence
The maximum height above the point of release is 8.82 m
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Rewrite the following sentence in the negative form >Each library contains 3000 brand new books
The SI unit of current is the ampere, which is defined as the flow of charge in units of _____ over a period of time measured in _____.
The SI unit of current is the ampere, which is defined as the flow of charge in units of coulomb over a period of time measured in seconds.
What is Current?Electrical charge carriers, often electrons or atoms deficient in electrons, travel as current. The capital letter I is a typical way to represent the current. The ampere, denoted by the letter A, is the common unit. An ampere is a unit of measure of the rate of electron flow or current in an electrical conductor. One coulomb of electrical charge (6.24 x 1018 charge carriers) traveling by a given place in one second is represented by one ampere of current.
Conventional current, also known as Franklin current, is thought by physicists to flow from relatively positive points to comparatively negative locations. The most prevalent charge carriers, electrons, are negatively charged. From somewhat negative to relatively good points, they move.
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The tub of a washing machine goes into its spin cycle, starting from rest and gaining angular speed steadily for 8.00 s, at which time it is turning at 6.00 rev/s. At this point, the lid of the washing machine is opened, and a safety switch turns it off. The tub then smoothly slows to rest in 11.0 s. Through how many revolutions does the tub rotate while it is in motion
Through 57 revolutions the tub rotate while it is in motion.
What is angular speed?
Angular speed is defined as the rate of change of angular displacement, It is a scalar measurement of rotating object.
It is expressed as follows: ω = θ / t.
Here,
Initially tub is at rest so,
ω(i) = 0 rev/s
ω(f) = 6 rev/s
time taken, t = 8 second
Now the total number of revolutions,
N = t * ( ω(i)+ ω(f) ) / 2
N1 = 8* ( 0+6 ) / 2
N1 = 24 rev
Now, when the lid is opened it's safety switch is off due to which it is uniformly decelerated and comes to rest in 11 s
N2 = 11* ( 0+6 ) / 2
N1 = 33 rev
So,
Total number of revolutions:
N = N1 + N2
N = 24 + 33
N = 57 revolutions
Thus,
Through 57 revolutions the tub rotate while it is in motion.
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A straight current-carrying wire carries a current I. If the magnetic field at a distance d from the wire has magnitude B, what is the magnitude of the magnetic field at a distance 2d from the wire
0.07 is the magnitude of the magnetic field at a distance of 2d from the wire
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Which has a higher reduction potential — silver or iron?
Answer:
Fe
Explanation:
Dựa vào dãy hoạt động hóa học của kim loại
A skydiver falls towards the earth. the attraction of the earth on the diver pulls the diver down. what is the reaction to this force?
There will be no reaction force acting on the object
Newton's second law is a quantitative description of the changes that a force can produce on the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it.
The motion of a free falling object can be described by Newton's second law of motion,
Force (F) = mass * acceleration
a = F / m
The net external force is just the weight of the object (F = W).
Substituting into the second law equation gives:
a = W / m = m * g / m = g .
The acceleration (change of velocity) of the object then becomes the gravitational acceleration.
On freely falling body their is no normal acting on that object
hence , there will be no reaction force acting on the object
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If the strength of a magnetic field at B is three units the strength of the magnetic field at A is ____?
If the strength of a magnetic field at B is three units the strength of the magnetic field at A, means that point B has three times more turns as compared to point A.
How strength of the magnetic field should be increased?We can increase the strength of the magnetic field by increasing the number of turns which increases the strength of the current flow.
So we can conclude that point B has three times more turns as compared to point A.
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The end point of a spring oscillates with a period of 2.0 s when a block with mass m is attached to it. When this mass is increased by 2.0 kg, the period is found to be 3.0 s. Find m.
Answer: The end point of a spring oscillates with a period of 2.0 s when a block with mass m is attached to it. When this mass is increased by 2.0 kg, the period is found to be 3.0 s. Then the mass m is 0.625kg.
Explanation: To find the answer, we need to know more about the simple harmonic motion.
What is simple harmonic motion?A particle is said to execute SHM, if it moves to and fro about the mean position under the action of restoring force.We have the equation of time period of a SHM as,[tex]T=2\pi \sqrt{\frac{m}{k} }[/tex]
Where, m is the mass of the body and k is the spring constant.How to solve the problem?Given that,[tex]T_1=2s\\m_1=m\\m_2=m+2kg\\T_2=3s[/tex]
We have to find the value of m,[tex]T_1=2\pi \sqrt{\frac{m}{k} } \\T_2=2\pi \sqrt{\frac{m+2}{k} } \\\frac{T_1}{T_2} =\sqrt{\frac{m}{m+2} }\\\frac{2}{3} =\sqrt{\frac{m}{m+2} }\\\\[/tex]
[tex]m=\frac{5}{8} =0.625kg[/tex]
Thus, we can conclude that, the mass m will be 0.625kg.
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What is the tangential speed of a lug nut on a wheel of a car if the lug nut is located 0.114 m from the axis of rotation; and the wheel is rotating at 6.53 rev/sec
The tangential speed of a lug nut on a wheel of a car will be 4.68 m/s
Given:
Distance of lug nut = 0.114 m
wheel is rotating at speed = 6.53 rev/sec
To Find:
tangential speed of a lug nut
Solution: Tangential velocity is the linear speed of any object moving along a circular path. A point on the outside edge of a turntable moves a greater distance in one complete rotation than a point near to the center
Vr = r.ω
(0114 m)(41.03 rad/s) = Vr
Vr = 4.68 m/s
Hence, tangential speed of lug nut on wheel of car is 4.68 m/s
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An 800-N box is pushed up an inclined plane. The plane is 4.0 m long and 2.0 m high. If it requires 3200 J of work to get the box to the top of the plane, what was the magnitude of the average friction force on the box? Group of answer choices 400 N 0 N Non-zero, but less than 400 N Greater than 400 N
The magnitude of the average friction force on the box is 400 N
What is energy conservation?
It is the principle by which the total energy remains constant in a system that is not subject to external influence.
It states that energy can neither be created nor be destroyed, It may be transformed from one form to another.
Here,
length of the plane, d = 4 m
height of the plane, h = 2 m
work done total, w = 3200 J
kinetic energy on top, KE = 0
Potential energy on top,
PE = weight x height
PE = 800 *2
PE = 1600 J
Now,
Total work done = KE + PE + W (friction)
W (friction) = 3200 - 1600
W (friction) = 1600 J
W (friction) = F (friction) x d
F (friction) = 1600 / 4
F (friction) = 400 N
Hence,
The magnitude of the average friction force on the box is 400 N
option A is correct
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Intelligence test. If you get it right ,you are a critical thinker. You were in the garden,there are 34 people in the yard. You killed 30. How many people are in the garden.
The riddle is solved by knowing that there is only one person left in the garden and that is you.
How many people are in the garden?We are told that there were a total of 34 people in the yard. We do not know if these people are in the garden or somewhere around the yard. The next information we have is that a total of 30 persons were killed.
Since you killed them in the garden, the others may still be lurking somewhere in the yard thus there is only one person left in the garden and that is you.
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Which restricted basin has the coolest temperatures?
Hudson Bay is the restricted basin that has the coolest temperatures
Hudson Bay is a restricted basin which remains frozen or is dominated by ice over the summer solstice and through- out much of the high-sun season. This basin experiences a harsh continental climate.
The average annual temperature in almost the entire bay is around 0 °C (32 °F) or below. In the extreme northeast, winter temperatures average as low as −29 °C or −20.2 °F. The region of this basin has very low year-round average temperatures.
This basin starts freezing up by early November, and the northern part of the basin is typically entirely iced over by the end of the month.
correct answer is Hudson bay
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What minimum volume must the slab have for a 75.0 kgkg woman to be able to stand on it without getting her feet wet
V = 0.9375 m3 is minimum volume .
What is density ?We use the word "density" to indicate how much space (or "volume") an object or substance occupies in relation to the amount of matter contained therein (its mass). Density can also be defined as the quantity of mass per unit of volume. A dense object is one that is both hefty and small.Given,
1000 kg/m3 = density of water
920 kg/m3 = density of ice
BF = Woman Weight + Slab Weight
Pvg = 75 + Pvg
V = 75 kg / (1000 - 920)
V = 75 / 80
V = 0.9375 m3
Therefore, V = 0.9375 m3 is minimum volume .
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Ungrounded alternating-current systems from 50v to 1,000v or less that are not required to be grounded in accordance with article 250.20(b) shall have___________.
Ungrounded alternating-current systems from 50v to 1,000v or less that are not required to be grounded in accordance with article 250.20(b) shall have ground detectors installed.
What is current system analysis?The current systems is known to be a kind of techniques that are often used to examine the current systems and know the extent of support given to the set of business activities.
A ground detector is known to be a tool that is often use to be able to know or detect conductor insulation that are said to be resistance to ground.
Note that the ground detection is also a sensing equipment that is linked as close as possible to where the system gets its supply and as such, Ungrounded alternating-current systems from 50v to 1,000v or less that are not required to be grounded in accordance with article 250.20(b) shall have ground detectors installed.
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Why is it that astronomers rely upon the 21-centimeter line associated with the spin flip in hydrogen and not the more familiar hydrogen Balmer lines to gather information from the far side of the galactic plane
Hydrogen, the element that is by far the most prevalent in the universe, exhibits radio emissions with a wavelength of 21 centimetres.
This makes it practical for using radio waves to explore space objects. An object in space emits radio waves that are more noticeable the more hydrogen it has.
What is a Galactic plane ?The majority of a disk-shaped galaxy's mass is located on the galactic plane. The galactic poles are shown by directions that are perpendicular to the galactic plane.
The Galaxy is divided in half by the planetary plane (top and bottom). The celestial equator is at an angle of 63 degrees with the galactic plane, whereas the ecliptic is at an angle of 60 degrees.The poles of all three coordinate systems each point in a different sky direction.Learn more about Galactic plane here:
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irius, the brightest star in the sky, is 2.6 parsecs (8.6 light-years) from Earth, giving it a parallax of 0.379 arcseconds. Another bright star, Regulus , has a parallax of 0.042 arcseconds. What is its distance in parsecs
The actual distance of Regulus from Earth is 23.81 parsecs.
Given:
Parallax of Regulus, p = 0.042 arc seconds
Calculation:
When an observer changes their position, an apparent change in the object's position takes place. This change can be calculated using the angle ( or semi-angle) made by the observer and object i.e. the angle made between the two lines of observation from the object to the observer.
Thus from the relation of parallax of a celestial body we get:
S = 1/ tan p ≈ 1 / p
where S is the actual distance between the object and the observer
p is the parallax angle observed
Here for Regulus, we get:
S = 1 / p
= 1 / (0.042) [ 1 parsecs = 1 arcseconds ]
= 23.81 parsecs
We know that,
1 parsecs = 3.26 light-years = 206,000 AU
Converting the actual distance into light years we get:
23.81 parsecs = 23.81 × (3.26 light yrs) = 77.658 light-years
Therefore, the actual distance of Regulus from Earth is 23.81 parsecs which is 77.658 in light years.
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