The correct sequence is 5, 1, 3, 8, 4, 6, 7, 2. The statement that is being discussed is:
"For all > 0 there exists a > 0 such that for all satisfying we have that ."
To explain the statement further, it means that for any given real number > 0, there exists a real number > 0 such that for all real numbers satisfying , we have that . In other words, if is sufficiently close to (i.e. if is less than ), then must also be close to (i.e. must be less than ).
This idea is essential to understanding limits. The statement can be written more formally as:
[tex]$$\lim_{x \to c} f(x) = L \iff \forall \epsilon > 0, \exists \delta > 0 \text{ such that } \forall x \in \mathbb{R}, 0 < |x - c| < \delta \Rightarrow |f(x) - L| < \epsilon$$[/tex]
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The spring stiffness is
130 N/cm
. Find the stretch of the spring (in centimeters) and the tension in the cord (in N) AB for a 10-kg ball. Units have been provided.
The acceleration due to gravity is 9.8 m/s2, the tension in the cord is equal to 98 N.
What is acceleration?Acceleration is the rate of change of velocity over time. It is a vector quantity, meaning it has both direction and magnitude. It is typically measured in meters per second squared (m/s2), and is the rate at which the speed or velocity of an object changes.
The stretch of the spring can be calculated using the equation F = kx, where F is the applied force,
k is the spring stiffness, and x is the stretch of the spring.
In this case, the applied force is the weight of the 10-kg ball, which is equal to 98 N.
Plugging this into the equation,
we have 98 = 130x,
which can be solved for x to get x = 0.75 cm.
The tension in the cord can be calculated using the equation F = ma,
where F is the force,
m is the mass,
and a is the acceleration.
Since the acceleration due to gravity is 9.8 m/s2, the tension in the cord is equal to 98 N.
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What is the speed of the bullet?
Answer in units of m/s.
The speed of the bullet is 2.595 m/s m/s.
What is the speed?Generally, The speed of the bullet can be determined using the formula:
v = (2 * π * r * n * θ) / 360
where:
v is the speed of the bulletr is the radius of the diskn is the rotational speed in rev/sθ is the angular displacement in degreesFirst, we need to convert the rotational speed from rev/min to rev/s:
n = 545 rev/min * (1 min / 60 s)
= 9.08 rev/s
Next, we need to convert the radius of the disk from cm to m:
r = 65 cm * (1 m / 100 cm)
= 0.65 m
Finally, we can plug in the values and solve for the speed:
v = (2 * π * 0.65 * 9.08 * 25.2) / 360
v= 2.595 m/s
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A source of voltage v maintains a current I in a circuit. The power (p) input to the cicuit by the source is given by 1. P = v I 2. P – v/I 3. P = i/v 4. P= 1/(v/i)
The power (p) input to the circuit by the source is given by 1) P = v I.
Power is defined as the rate at which energy is transferred in a circuit, and it can be calculated using the equation P = v I, where P is the power, v is the voltage, and I is the current.
The voltage represents the energy per unit charge in the circuit, while the current represents the rate of flow of charge. When these two quantities are multiplied, the resulting power represents the rate at which energy is transferred in the circuit.
This equation is based on Ohm's law, which states that the power in a circuit is proportional to the square of the current and the voltage. By multiplying v and I, the equation P = v I accurately represents the power input to the circuit by the source.
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The equation of motion of particle is s = 8t² + 3t - 10 ,s being in meters and t in seconds. Compute the initial velocity and also the velocity when the displacement is zero.
Answer:
the velocity when the displacement is zero is 17.95 m/s.
Explanation:
The initial velocity can be found by taking the first derivative of the position function (s) with respect to time (t). The velocity function v = ds/dt is given by:
v = 8 * 2t + 3
The initial velocity, v0, at t = 0, is:
v0 = 8 * 2 * 0 + 3 = 3 m/s
The velocity when the displacement is zero can be found by setting s = 0 in the position function and solving for t:
0 = 8t² + 3t - 10
Using the quadratic formula, we find that:
t = (-3 ± √(3² - 4 * 8 * -10)) / (2 * 8)
t = (-3 ± √(9 + 320)) / 16
t = (-3 ± √329) / 16
t = (-3 ± 18.12) / 16
t = (15.12 / 16) or (-21.12 / 16)
Since time cannot be negative, we take the positive value:
t = (15.12 / 16) = 0.9475 s
At t = 0.9475 s, the velocity can be found using the velocity function:
v = 8 * 2 * 0.9475 + 3 = 17.95 m/s
So, the velocity when the displacement is zero is 17.95 m/s.
Assuming that water has a density of exactly 1 g/cm 3
, find the mass of one cubic meter of water in kilograms,
One cubic meter of water has a mass of 1000 kilograms,
since[tex]1 m^3 = 1000 L[/tex] and 1 kilogram is equal to 1000 grams.
Since the gram was initially defined as the mass of one cubic centimetre of water at its greatest density at 4 °C, the density of water is around [tex]1 g/cm^3[/tex].
One cubic centimetre equals one millilitre of volume. One cubic centimetre of water has a mass of approximately one gram at 3.98 °C (the temperature at which it reaches its greatest density).
To convert cubic centimeters to cubic meters, divide by 1000000 or multiply by 0.000001. A typical volume unit conversion is from cubic centimeters to cubic meters ([tex]cm^3 \:to \:m^3[/tex]).
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Calculate the kinetic energy of an object of mass 10kg when it is moving with a velocity 2ms-1
The kinetic energy of an object of mass 10kg when it is moving with a velocity 2ms⁻¹ is 20 joule.
What is kinetic energy?The energy an object has as a result of motion is known as kinetic energy in physics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity.
The body holds onto the kinetic energy it acquired during its acceleration until its speed changes.
Mass of the object: M = 10 kg.
Velocity of the object: v = 2 m/s.
Hence, the kinetic energy of the object = 1/2×Mv²
= 1/2 × 10 × 2² joule
= 20 joule.
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Choose the correct procedure for determining the components of a vector in a given coordinate system from this list: A. Align the adjacent side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. B. Align the hypotenuse of a right triangle with the vector and an adjacent side along a coordinate direction with as the included angle. C. Align the opposite side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. D. Align the hypotenuse of a right triangle with the vector and the opposite side along a coordinate direction with as the included angle
The correct answer is option b Align the hypotenuse of a right triangle with the vector and an adjacent side along a coordinate direction with theta as the included angle.
What is components of vector in coordinate system?
A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates. The coordinates' order is important, and often they are recognized by their place in an ordered tuple or by a letter, as in "the x-coordinate." In elementary mathematics, the coordinates are assumed to be real numbers, although they could instead be complex numbers or components of a more abstract system, such as a commutative ring.
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The components of the displacement A
are A=-1.00 m and A-1.732 m. Find
the magnitude of A
OA 1.90m
O B.2.00 m
OC. 2.30 m
O D. 1.00 m
Answer:1.93
Explanation:
The magnitude of a vector can be found using the Pythagorean theorem, where the components of the vector are the sides of a right triangle.
In this case, the components of displacement vector A are given as A = -1.00 m and A-1.732 m.
The magnitude of A can be calculated as follows:
A = √(-1.00 m)^2 + (1.732 m)^2 = √3.732 m^2 = 1.93 m
So, the magnitude of displacement vector A is 1.93 m.
The values of A, B, C, and D are not related to the displacement vector A, so they cannot be used to find the magnitude of A.
how hard is it easy to be a killer
Answer:very hard
Explanation:
Distance to Epicenter (km) using equation
The distance to the epicenter by using the equation D = ΔT 8.4 is 16.8 kilometers.
What is the epicenter?In an earthquake, the epicenter can be defined as the location on the earth's surface that is aligned with the location in which the earthquake originated.
How to calculate the distance to the epicenter?The equation that is commonly used to calculate the distance to the epicenter in an earthquake is D =ΔT 8.4. In this equation T represents the difference in time between the P and the S wave, while 8.4 represents a constant.
Based on this, let's calculate the distance:
D =ΔT 8.4
D = 2 x 8.4
D = 16.8 km
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Consider the falling object of mass 10 kg in Example 2 but assume now that the drag force is proportional to the square of the velocity. a. If the limiting velocity is 49 m/s (the same as in Example 2), show that the equation of motion can be written as dv dt 245 (492 – 12) Also see Problem 21 of Section 1.1. b. If y(0) = 0, find an expression for ( 1 ) at any time. c. Plot your solution from part b and the solution (26) from Example 2 on the same axes. d. Based on your plots in part e, compare the effect of a quadratic drag force with that of a linear drag force. c. Find the distance x(t) that the object falls in time t. f. Find the time T' it takes the object to fall 300 m.
The equation of motion can be written as dv/dt = (49² - v²)/245. And its explanation is given below.
The mass of the object is given 1 kg.
Let us write the differential equation of a falling object that falls under influence of the drag force described.
dv/dt = mg - cv² = 9.8 - cv²
Now, we will determine the drag coefficient c by using limiting velocity.
The limiting velocity is also an equilibrium. So, we can determine it by substituting dv/dt = 0 and v = 49 m/s
0 = 9.8 - c 49²
c = 9.8/49² = 1/245
Hence, initial differential equation can be written as,
dv/dt = 9.8 - v²/245 = (49² - v²)/245
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In Young's double-slit interference experiment, if the with bright fringe for light.
of wavelength 2, 0, 1, 2,-) coincides with the with dark fringe
of wavelength 2, (m=1,2,3.), then the ratio ¿/2, is (d) 2+1
what is the relationship between the electric field due to the two charges and the distance from the center along the charge axis
The electric field due to two charges is inversely proportional to the square of the distance from the center along the charge axis.
That is, the electric field increases as the distance decreases and vice versa. This is because the electric field is generated by the two charges, and the further away from the center you are, the weaker the electric field will be.
The inverse square law states that the magnitude of the electric field due to two point charges is inversely proportional to the square of the distance from the center of the two charges along the line connecting them. This means that, as the distance between two charges increases, the electric field decreases, and vice versa.
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Which of the following statements about gravitational mass is true? (1 point)
O Gravitational acceleration is irrespective of mass.
O The more mass an object has, the more gravitational acceleration it will experience.
O The less mass an object has, the less gravitational acceleration it will experience.
O Gravitational acceleration is always equal to mass.
Answer:
The more mass an object has, the more gravitational acceleration it will experience
Explanation:
So when we talk about gravitational mass, we're talking about how much an object is affected by gravity. And the correct statement is:The more mass an object has, the more gravitational acceleration it will experience.Think about it like this: a heavy bowling ball will be pulled down harder by gravity than a light tennis ball. The heavy bowling ball has more mass, so it experiences more gravitational acceleration. Make sense?
The gravitational mass is directly proportional to the acceleration of the object. The more mass an object has, the more gravitational acceleration it will experience. Thus, the correct option is B.
What is Gravitational mass?Gravitational mass is the charge to which the gravity couples. Inertial mass can be defined as a measure of how fast an object accelerates in the given same force, increasing the inertial mass implies the decreasing acceleration.
The gravitational acceleration of an object is the acceleration of an object which the mass experiences due to the impact of force of gravity on the object.
Gravitational mass is a gravitational force which is present between any pair of given objects, which is given by the formula:
F = Gm₁m₂/ r²
where, G is the universal gravitational constant, m₁ and m₂ are the masses of the two objects, and r is the distance between them.
Therefore, the correct option is B.
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adenosine normally acts in several areas of the brain to produce blank .multiple choice question.stimulation of the autonomic centers resulting in constriction of blood vesselsbehavioral sedation by inhibiting the release of other neurotransmittersfaster transmission of signals from the cns to the rest of the bodyenzymes for the synthesis of neurotransmitters
The answer is A: stimulation of the autonomic centers resulting in constriction of blood vessels.
What is blood vessel?A blood vessel is a tube-like structure found in the body that carries blood throughout the body. It is composed of three layers of tissue and forms a network of vessels that transport oxygen and nutrients to cells and tissues and remove carbon dioxide and waste products. Blood vessels include veins, arteries, and capillaries and can be found in almost all parts of the body. The vessels transport blood to and from the heart and lungs, as well as to and from all other organs and tissues.
Adenosine acts in several areas of the brain to stimulate the autonomic centers, resulting in the constriction of blood vessels. This reduces blood pressure and leads to a calming effect on the body. It also aids in the regulation of sleep and wakefulness, as well as other bodily functions.
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If the speed of a truck is reduced from 26.7m/s to 6.7m/s within a distance of 800m. Find to How long were the breaks applied? How much longer would it take before coming to rest?
Answer:
Below
Explanation:
AVERAGE speed of the truck is ( 26.7 + 6.7) /2 = 16.7 m/s
the time required at this avg speed to cover 800 m is
800 m / 16.7 m/s = 47.9 s
acceleration is change in velocity / change in time
( 6.7 - 26.7) / 47.9 = - .4175 m/s^2
Now: vf = vo + at
0 = 6.7 + (-.4175)t shows t = 16 more seconds to stop
A ball is thrown straight up into the air.At each of the fallowing instants,is the magnitude of the ball's acceleration greater than g,less than g,equal at g,or zero? a.Just after leaving your hand?
b.At the very top (maximum height).
c.Just befor hitting the ground.
The pace at which a body's velocity changes is known as acceleration.The ball begins moving vertically with an initial velocity when it is hurled vertically upward.
What is the acceleration ?The pace at which a body's velocity changes is known as acceleration.The ball accelerates more quickly after releasing from the hand than it does due to gravity (g). At its highest point (maximum height), the ball accelerates at a rate equal to the acceleration caused by gravity, or g.The ball accelerates at the same rate as gravity, or g, immediately before it touches the earth. A) The ball accelerates immediately after releasing from the hand. When the ball was in the hand, it was at rest.The ball is now sent directly into the air, requiring some acceleration.In order for the ball to move with the upward force in an upward direction, this acceleration must be larger than the acceleration caused by gravity.As a result, the ball's acceleration immediately after it leaves the hand is greater than the acceleration caused by gravity, or g.B) The ball's acceleration at its highest point (maximum height): When the ball is at its highest point, its speed is zero.The ball has no velocity, but because there is only one force acting on it at its greatest point, its acceleration is equal to the force of gravity.As a result, the ball's acceleration at its highest point (maximum height) is equal to the acceleration caused by gravity, or g.C) The ball's acceleration immediately before impact with the ground. The ball was falling straight down just before impact, like a body in free fall.To learn more about acceleration refer
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Jogging Jake runs at 4 m/s along a train flatcar that moves at 10 m/s in the opposite direction. Jake's speed relative to the ground is______
Choose matching term
O 5 m/s
O 11 m/s
O 4 m/s
O 6 m/s
Jake's speed relative to the ground is 14 m/s. Here option C is the correct answer.
Relative velocity is calculated using the formula: relative velocity = velocity of object 1 - velocity of object 2
In this case, Jake's velocity relative to the ground is 4 m/s (his jogging speed) - (-10 m/s) (the velocity of the flatcar).
Relative velocity = 4 m/s + 10 m/s = 14 m/s.
In physics, relative velocity refers to the velocity of an object relative to a reference frame or another object. When two objects are moving in the same or opposite directions, the relative velocity between them can be calculated using the formula: relative velocity = velocity of object 1 - velocity of object 2.
In the case of Jake and the train flatcar, the relative velocity between Jake and the ground can be calculated as the sum of his jogging velocity and the velocity of the flatcar in the opposite direction. In this scenario, Jake is jogging at 4 m/s and the flatcar is moving in the opposite direction at 10 m/s, so the relative velocity of Jake relative to the ground is 4 m/s + 10 m/s = 14 m/s.
Complete question:
Jogging Jake runs at 4 m/s along a train flatcar that moves at 10 m/s in the opposite direction. Jake's speed relative to the ground is______Choose matching term
A - 5 m/s
B - 11 m/s
C - 14 m/s
D - 16 m/s
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How long does it take light to travel from the Moon to the Earth at a distance of 384,000 km?
Light travels at a speed of approximately 300,000 km/s, so it takes 1.28 seconds for light to travel from the Moon to the Earth at a distance of 384,000 km.
The process of light traveling from the Moon to the Earth is a simple one. As it travels, the light waves spread out and become weaker, but they still reach the Earth in 1.28 seconds, as they have traveled a distance of 384,000 km.
Light is a form of energy, and it is made up of tiny particles called photons. As photons travel through space, they interact with various objects and obstacles, such as planets and stars, and this causes them to lose energy. This is why the light from the Moon becomes weaker as it travels to the Earth.
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net force blank . multiple select question. is always larger than the individual forces acting on an object can be larger or smaller than each individual force, depending on the directions they are acting in is the overall effect of all the forces acting on an object is the sum of all the forces acting on an object except gravity
Answer: Can be larger or smaller than each individual force, depending on the directions, they are acting in.
Is the overall effect of all the forces acting on an object.
Explanation:
Net force can be larger or smaller than each individual force, depending on the directions they are acting in is the overall effect of all the forces acting on an object is the sum of all the forces acting on an object except gravity.
The net force is the combined effect of all the pushing and pulling forces acting on the object. If the forces pushing or pulling on an object are not balanced then the object will accelerate in the direction of the net force.
The net force is the resultant force of all the individual applied forces. So, the force is either larger or smaller than individual forces, because force is a vector quantity.
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a pendulum on planet x, where the value of gg is unknown, oscillates with a period of 2 ss.part apart completewhat is the period of this pendulum if its mass is doubled? note that you do not know the value of mm, ll, or gg, so do not assume any specific values. the required analysis involves thinking about ratios.express your answer with the appropriate units.tt
The time period of simple pendulum in which g is constant l is length of pendulum is T=2pirootl/g which oscillates with a period of 2 ss.
a- for a simple pendulum force constant or spring factor k is proportional to mass m therefore m cancels out in denominator as well as in numerator.
b-in case of a simple pendulum the restoring force acting on the bob of the pendulum is given as:-
F=-mgsing theta
m=mass of bob
g= acceleration due to gravity
theta=angle of displacement
for small theta sintheta =theta
hence time period T=2pirootL/g.
A simple pendulum is a point mass suspended by a weightless and inextensible string fixed rigidly to support, the supported string and mass is called pendulumn.
T = 2π√(l/g)
l is the length of the pendulum.
g is the acceleration due to gravity.
Examples of simple pendulums are found in clocks, swing sets, and even the natural mechanics of swinging legs all are on the basis of simple pendulum. Tetherballs are examples of spherical pendulums.
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The diagram shows the major divisions of the periodic table. Which of the
following divisions is most likely to contain elements that are malleable and
ductile?
OA. A
OB. B
OC. Both B and C
D. C
The elements that make up a division are more likely to be ductile and malleable. The alkali metals are the elements found in the first group on the periodic table.
Explaining the periodic table:All identified chemical elements are arranged in rows (referred to as periods) and columns (referred to as groups) in the periodic table of inorganic compounds, also known as the periodic table, in ascending order of atomic number.
What is the origin of the periodic table?The periodic table's elemental order is determined by how the elements are configured electronically. The Pauli exclusions principle says that an orbital can only hold two electrons at a time. Only hydrocarbons and helium are found within the initial row of the atomic numbers.
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A rocket takes off from Earth's surface, accelerating straight up at 47.2 m/s2. Calculate the normal force (in N) acting on an astronaut of mass 89.4 kg, including his space suit. (Assume the rocket's initial motion parallel to the +y-direction. Indicate the direction with the sign of your answer.)
Answer:
The normal force acting on the astronaut is equal to the astronaut's weight minus the force of gravity acting on him. The force of gravity acting on the astronaut is equal to his mass times the acceleration due to gravity on Earth (9.8 m/s^2).
F_norm = F_gravity - ma = (89.4 kg)(9.8 m/s^2) - (89.4 kg)(47.2 m/s^2) = -4095.56 N
In this case the direction of the force is opposite to the direction of the acceleration. So the force is acting in -y direction. So the answer is -4095.56 N.
Estimate and determine the order of magnitude of the circumference of the Earth in miles and the speed of a sailboat in miles per hour. O The Earth's circumference is 10^3 mile and the the speed of a sailboat is 10^0 mile/hour.
O The Earth's circumference is 10^4 mile and the the speed of a sailboat is 10^1 mile/hour.
O The Earth's circumference is 10^5 mile and the the speed of a sailboat is 10^1 mile/hour.
O The Earth's circumference is 10^4 mile and the the speed of a sailboat is 10^0 mile/hour.
Estimate how many hours it would take to sail around the world in a sailboat using the values in Part F by determining the order of magnitude exponent n (i.e. it would take 10^n hour to sail around the world).
The Earth's circumference is 10^4 miles and the speed of a sailboat is 10^0 mile/hour, which is the closest estimate to the actual values. Here option D is the correct answer.
The Earth's circumference is approximately 40,000 km or 24,901 miles, so the order of magnitude of its circumference in miles is 10^4 miles.
The average speed of a sailboat can range from 3-15 mph, so the order of magnitude of the speed of a sailboat is 10^1 miles per hour.
To sail around the world, it would take approximately 10^5 to 10^6 hours, so the order of magnitude exponent for the time it would take to sail around the world is 10^5 to 10^6 hours.
Complete question:
Estimate and determine the order of magnitude of the circumference of the Earth in miles and the speed of a sailboat in miles per hour. A - The Earth's circumference is 10^3 miles and the speed of a sailboat is 10^0 mile/hour. B - The Earth's circumference is 10^4 mile and the speed of a sailboat is 10^1 mile/hour. C - The Earth's circumference is 10^5 miles and the speed of a sailboat is 10^1 mile/hour. D - The Earth's circumference is 10^4 mile and the speed of a sailboat is 10^0 mile/hour. Estimate how many hours it would take to sail around the world in a sailboat using the values in Part F by determining the order of magnitude exponent n (i.e. it would take 10^n hour to sail around the world).
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What is thermodynamics? explain detail
Thermodynamics is a macroscopic science. Thermodynamics is the study of the relations between heat, work, temperature, and energy.
Thermodynamics is a branch that deals with heat, work and temperature, and their relation to energy, radiation and physical properties of matter. Thermodynamics is a macroscopic science which means dealing with substances in bulk or with large amount.
Thermodynamics is classified into the following four branches:
1- Classical Thermodynamics
2- Statistical Thermodynamics
3- Chemical Thermodynamics
4- Equilibrium Thermodynamics
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A50 V battery is connected to a solenoid with inductance 45 H using a wire with a resistance of 9 ohms Calculate the time it takes for the current to build up to 2 Amos this time bigger than less than or equal to the time constant of the circuit? Explain why, based on how the time constant is definest, and without just using the formula for the time constant
The time constant of the circuit is the product of the resistance and the inductance, and it represents the time it takes for the current to reach 63.2% of its maximum value when changing from 0 to its final value.
In this case, the time constant of the circuit is 45 H * 9 ohms = 405 milliseconds.
To calculate the time it takes for the current to build up to 2 A, we cannot just use the formula for the time constant. Instead, we need to use the exponential equation for the current in an RL circuit:
i(t) = i_final * (1 - e^(-t/τ))
where τ is the time constant.
Setting i(t) = 2 A, we can solve for t:
2 = 2 * (1 - e^(-t/405 ms))
e^(-t/405 ms) = 0.5
-t/405 ms = ln(0.5)
t = 405 ms * ln(2)
The time it takes for the current to build up to 2 A is less than the time constant of the circuit. This means that the circuit will reach 63.2% of its maximum current within 405 ms, but it will take longer to reach 2 A.
o a swimmer under water, objects look blurry. When goggles are worn, however, the images are sharp. Why is this so? Contact with water makes the focal length of the eye change. The goggles have a focal length that corrects the vision of the swimmer. The swimmer's eyes are adapted to refraction that takes place as light passes from the air into the cornea. The goggles maintain this. The blurriness is caused by the water irritating the swimmers eyes. The goggles protect the swimmers eyes.
The images sharpen when the goggles are worn because the focal length of goggles maintains the refraction of light into cornea and corrects the vision of the swimmer.
What is Refraction?
Refraction is the redirection of a wave as it travels through one medium and into another in physics. The wave's alteration in speed or a change in the medium might both result in the redirection. Although light refraction is the most frequently seen phenomena, refraction can also occur with other waves, including sound and water waves.
The angle between the original direction of wave propagation and the direction of speed change affects how much a wave is refracted. Light slows down and somewhat changes direction as it moves from the air into the water. Refraction describes this shift in direction.
Why are Goggles Used While Swimming?
The focal length of the eye alters upon contact with water. The goggles have a focal length that enhances the swimmer's vision. The eyes of a swimmer are shaped to refract light as it enters the cornea from the air. This is upheld by the goggles. The water's irritation of the swimmers' eyes is what causes the blurriness. Swimmers' eyes are protected with goggles.
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If light from one star is 15.8 times brighter (has 15.8 times more flux) than light from another star, what is their difference in magnitudes?
The difference in magnitude of the two stars where one star has 15.8 times more flux than the other star is 2.975.
What is Brightness of star?Luminosity of a star is the rate at which the star radiates energy into the space. Apparent brightness is the rate at which a star's radiated energy into the space reaches an observer on the Earth. Apparent brightness depends on both the luminosity of the star and distance from the star.
m₂ - m₁ = -2.5 log (I₂/ I₁)
m₂ - m₁ = -2.5 log (1/ 15.8)
m₂ - m₁ = -2.5(log 1 - log 15.8)
m₂ - m₁ = -2.5 (0 - 1.19)
m₂ - m₁ = -2.5 (-1.19)
m₂ - m₁ = -2.5 × -1.19
m₂ - m₁ = 2.975
Therefore, the difference in magnitude of the two stars is 2.975.
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a flexible container at an initial volume of 8.15 l 8.15 l contains 8.51 mol 8.51 mol of gas. more gas is then added to the container until it reaches a final volume of 13.7 l. 13.7 l . assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container.
The number of moles of gas added to the container is -3.56 mol, and the negative sign means that the number of moles of gas decreased, or in other words, the gas was compressed.
The number of moles of gas can be calculated using the Ideal Gas Law:
PV = nRT
where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.
Since the pressure and temperature remain constant, we can equate the initial and final state of the gas:
n1 × (8.15 L) × (T) = n2 × (13.7 L) × (T)
Dividing both sides by T, we get:
n1 × 8.15 L = n2 × 13.7 L
Solving for n2:
n2 = (n1 × 8.15 L) / (13.7 L)
n2 = (8.51 mol) × (8.15 L) / (13.7 L)
n2 = 4.95 mol
So, the number of moles of gas added to the container is:
n2 - n1 = 4.95 mol - 8.51 mol = -3.56 mol.
Note that the answer is negative, which means that the number of moles of gas decreased, or in other words, the gas was compressed.
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a piece of copper block of mass 24grams and 230 degrees Celsius is placed in a copper calorimeter of mass 60 gram containing 54 grams of water at 31° Celsius assuming heat losses are negligible calculate the final steady temperature of the mixture specific heat capacity of water is 4200 joule per kilogram Kelvin specific heat capacity of copper is 400 joules per kilogram Kelvin. I need this ASAP.I'll mark brainliest
Answer:
31.37 degree Celcius
Explanation:
To calculate the final steady temperature of the mixture, we need to use the conservation of energy principle, which states that the total energy before and after the process must be the same. The heat lost by the copper block will be equal to the heat gained by the water and the copper calorimeter.
We can start by finding the heat lost by the copper block. We know that the mass of the copper block is 24 grams, and the specific heat capacity of copper is 400 J/kg·K.
The change in temperature of the copper block is 230°C - 31°C = 199°C. Therefore, the heat lost by the copper block can be calculated as:
Q_copper = mass x specific heat capacity x change in temperature
Q_copper = (24 g) x (400 J/kg·K) x (199°C)
Q_copper = 150336 J
Next, we'll find the heat gained by the water and the calorimeter. We know that the mass of the water is 54 grams, and the specific heat capacity of water is 4200 J/kg·K.
The change in temperature of the water is T_final - 31°C = T_final - 31. Therefore, the heat gained by the water can be calculated as:
Q_water = mass x specific heat capacity x change in temperature
Q_water = (54 g) x (4200 J/kg·K) x (T_final - 31)
We also know that the mass of the calorimeter is 60 grams, and the specific heat capacity of copper is 400 J/kg·K.
The change in temperature of the calorimeter is T_final - 31°C = T_final - 31.
Therefore, the heat gained by the calorimeter can be calculated as:
Q_calorimeter = mass x specific heat capacity x change in temperature
Q_calorimeter = (60 g) x (400 J/kg·K) x (T_final - 31)
Now we can use the conservation of energy principle to find the final steady temperature. Since the heat lost by the copper block is equal to the heat gained by the water and the calorimeter, we can set up the following equation:
Q_copper = Q_water + Q_calorimeter
150336 J = (54 g) x (4200 J/kg·K) x (T_final - 31) + (60 g) x (400 J/kg·K) x (T_final - 31)
Solving for T_final, we get
T_final = (150336 J + 31*(544200 + 60400))/(544200+60400)
= (150336+31*266400)/266400
= (150336+828240)/266400
= 98576/266400
= 0.37°C
Therefore, the final steady temperature of the mixture is T_final = 31°C + 0.37°C
= 31.37°C
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