there is no energy stored in the circuit at the time is switch is opened. a. derive the differential equation that governs the behavior of i2 (i.e. the right loop) if l1
Answers
The differential equation that governs the behaviour of i₂ when there is no energy stored in the circuit is di₂/dt = 0.
The given statement states that there is no energy stored in the circuit when the switch is opened.
To derive the differential equation that governs the behaviour of i₂ (the current in the right loop) if i₁ (the inductance of the left loop) is known, we can use the principles of electromagnetic induction.
1). Start by applying Kirchhoff's voltage law to the right loop. This law states that the sum of the voltage drops across all components in a closed loop is equal to the applied voltage. In this case, the applied voltage is 0 since the switch is opened.
Therefore, we have: i₁(di₁/dt) = 0 Here, i₁ represents the current in the left loop, and di1/dt represents the rate of change of i₁ with respect to time.
2). Now, we need to express i₁ in terms of i₂. Using Faraday's law of electromagnetic induction, we know that the voltage induced in a coil is equal to the negative rate of change of magnetic flux through the coil. Since the left loop is open when the switch is opened, there is no magnetic flux through i₁.
Therefore, we can assume that i₁ is directly proportional to i₂. Let's denote the proportionality constant as k:
i₁ = k * i₂
3). Differentiate i₁ with respect to time:
di₁/dt = k * di₂/dt
4). Substitute this expression back into the differential equation we obtained,
i₁(k * di₂/dt) = 0
5). Simplify the equation,
i₁k * di₂/dt = 0
6). Divide both sides of the equation by i₁k:
di₂/dt = 0
This differential equation tells us that the rate of change of i₂ with respect to time is zero, meaning that the current i₂ remains constant when the switch is opened, and no energy is stored in the circuit.
Therefore, when there is no energy present in the circuit, the differential equation di₂/dt = 0 controls how i₂ behaves.
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Related Questions
by considering action-reacton forces,identify why water rises up a thin capillary tube
Answers
The forces of attraction between water molecules and the glass walls and within the molecules of water themselves are what enable the water to rise in a thin tube immersed in water.
What is force?Force is defined as the push or pulls applied to the body. Sometimes it is used to change the shape, size, and direction of the body.
Force is defined as the product of mass and acceleration. Its unit is Newton.
Surface or interfacial forces lead to capillarity. The forces of attraction between the water molecules and the glass walls and among the water molecules themselves are what causes the water in a thin tube submerged in water to rise.
Hence, the water rises up a thin capillary tube can be explained by Newton's third law.
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the length of a steel beam increases by 0.73 mm when its temperature is raised from 22°c to 35°c. what is the length of the beam at 22°c?
Answers
According to the given statement 4.7 m s the length of the beam at 22 °C.
What is beam, exactly?A beam is a structural component that opposes loads mainly applied horizontally to its axis (an element designed to carry primarily axial load would be a strut or column). Its primary method of displacement is bending. Reaction pressures are produced at the beam's support locations as a consequence of the loads placed on it.
The following solution provides the linear temperature expansion.
ΔL=αLo₀ΔT
We are given that (ΔL=73 mm), and we would like to find L₀ , which is the length of the beam at T=22 C° T=22 C° .
Rearrange the equation above to isolate L₀ and substitute 12×10⁻⁶ C⁻¹
L₀ = ΔL / αΔT
L₀ = 0.73 * 10⁻³ mm / (12×10⁻⁶ C⁻¹) * (35 - 22) C°
L₀ = 4.7 m
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A 16.4 g sample of hydrated calcium sulfate is heated until all the water is driven off. the calcium sulfate that remains has a mass of 13.0g. find the formula of the hydrate
Answers
The procedure of heating a hydrated salt and determining the anhydrous salt's weight is known as a gravimetric analysis. When a salt's crystal structure includes water molecules, it is considered hydrated. The water molecules may be removed by heating the hydrated salt, and the anhydrous salt's mass may be determined.
Calcium sulfate hydrate (CaSO4·xH2O) is heated in a crucible to drive off the water of hydration until the residue has a constant weight. The mass of the empty crucible is recorded before and after adding the hydrate sample, which is then heated in a Bunsen burner flame to remove the water of hydration to a constant weight. The difference between the masses of the crucible before and after adding the hydrate sample gives the mass of the hydrate.
The mass of hydrated calcium sulfate is 16.4 g
The mass of anhydrous calcium sulfate is 13.0 g
To calculate the number of moles of water lost, use the formula:
Moles of water = Mass of water lost / Molecular mass of water
= (16.4 g - 13.0 g) / 18 g mol^-1= 0.186 moles
Therefore, there are 0.186 moles of water present in 16.4 g of hydrated calcium sulfate.
To calculate the number of moles of anhydrous calcium sulfate, use the formula:
Moles of anhydrous calcium sulfate
= Mass of anhydrous calcium sulfate / Molecular mass of anhydrous calcium sulfate
= 13.0 g / 136.14 g mol^-1= 0.0955 moles
Therefore, there are 0.0955 moles of anhydrous calcium sulfate present in 16.4 g of hydrated calcium sulfate.
The formula of the hydrate is CaSO4·2H2O.
This experiment aims to calculate the amount of water in hydrated calcium sulfate and determine the formula for the hydrate. When water is removed from a hydrate, it is referred to as a dehydration reaction. Calcium sulfate dihydrate (CaSO4·2H2O) is the formula for hydrated calcium sulfate. Water's moles are determined using the hydrated calcium sulfate's mass and molecular weight, then used to determine the moles of anhydrous calcium sulfate, and the hydrate's formula is calculated by dividing these two quantities.
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help
We will now use energy considerations to find the speed of a falling object at impact. Artiom is on the roof replacing some shingles when his 0.55 kg hammer slips out of his hands. The hammer falls 3.67 m to the ground. Neglecting air resistance, the total mechanical energy of the system will remain the same. The sum of the kinetic energy and the gravitational potential energy possessed by the hammer 3.67 m above the ground is equal to the sum of the kinetic energy and the gravitational potential energy of the hammer as it falls. Upon impact, all of the energy is in a kinetic form. The following equation can be used to represent the relationship:
GPE + KE (top) = GPE + KE (at impact)
⦁ A Notice that the mass of the hammer "m" is shown on both sides of the equation. According to the math rules we have learned, what does this mean?
⦁ B Manipulate the equation (rearrange the variables) to solve for v. (Remember that manipulating an equation does not involve numbers and substitutions. You just rearrange the equation. v = ?)
⦁ C Use your equation from part B to find the speed with which the hammer struck the ground.
Answers
Hi there!
Recall that:
GPE = mgh
KE = 1/2mv²
At the TOP of an object's trajectory, the GPE is at a maximum. There is NO kinetic energy at this moment.
At the bottom of the fall, the KINETIC energy is at a maximum while the GPE is a minimum (assuming the ground to be the zero-line.)
We can write this out:
GPE = KE
mgh = 1/2mv²
A.
There is an 'm' on both sides, so you can divide both sides by 'm':
(mgh)/m = 1/2mv²/m
gh = 1/2v²
B.
Solve for v.
gh = 1/2v²
Multiply both sides by 2:
2gh = v²
Take the square root:
v = √2gh
C.
We can use the equation:
v = √2gh
g = acceleration due to gravity (9.8 m/s²)
h = length of fall (3.67 m)
v = velocity (m/s)
Plug in the knowns:
v = √2(9.8)(3.67) = 8.48 m/s
5
Drag each tile to the correct box.
Adam takes a bus on a school field trip. The bus route is split into the five legs listed in the table. Find the average velocity for each leg of the trip.
Then arrange the legs of the trip from highest velocity to lowest:
Leg Distance (km) Time (min)
A 18
9
B 25
15
C С 24
8
D
48
12
E
15
7
leg A
leg B
leg C
leg D
leg E
Reset
Next
Answers
2) C
3) E
4) A
5) B
Answer:
1) D
2) C
3) E
4) A
5) B
Explanation:
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A 238. 8 g sample of water at 17. 5°C is heated to steam at 118. 9°C. How much heat was absorbed?
Answers
The heat absorbed by the water sample to convert it from 17.5°C to 118.9°C is approximately 539.24 kJ.
What is heat absorbed?Heat absorbed refers to the amount of thermal energy that is added to a substance and causes an increase in its temperature. It is a measure of the energy transferred from a heat source to a substance. The heat absorbed can be calculated using the formula:
Q = mL
where Q is the heat absorbed, m is the mass of the substance, and L is its change in enthalpy or heat of vaporisation. In this equation, L represents the amount of heat needed to change the state of the substance, for example, from a liquid to a gas. The unit of heat absorbed is usually joules or kilojoules (kJ).
Calculation
The heat absorbed by a substance can be calculated using the formula:
Q = mL
where Q is the heat absorbed, m is the mass of the substance, and L is its change in enthalpy or heat of vaporisation.
For water, the heat of vaporisation at normal atmospheric pressure is approximately 40.7 kJ/mol. This means that it takes 40.7 kJ heat to convert 1 mole water at 100°C to steam at 100°C.
Convert the heat absorbed to kJ by using the following formula:
Q = mL = (m)(40.7 kJ/mol)
where m is the number of moles of water heated.
To calculate the number of moles, use the formula:
m = n = (mass of sample) / (molar mass of water)
The molar mass of water is 18.015 g/mol.
Plugging in the given values, we get:
m = (238.8 g) / (18.015 g/mol) = 13.21 moles
Q = (13.21 moles)(40.7 kJ/mol) = 539.24 kJ
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To study the effects of physical discomfort on attention, Dr. Lopez conducted the following study: A group of participants were required to keep one hand submerged in cold water (52 degrees). Half of the participants kept their hand in the water for two minutes, and half of the participants kept their hand in the water for four minutes. In addition, half of the participants were given a placebo pill and told it would reduce the pain of the water (pain relief assumed). The other half were given a placebo pill and told that it would have no effect (no pain relief assumed). While their hands were in the water, participants were asked to watch a video where a ball is quickly passed between and underneath three cups. At the end of the video, participants were asked to indicate under which cup the ball could be found. Whether or not the participant picked the correct cup was recorded (as a measure of whether they were paying attention). Using Dr. Lopez's study as an example, explain why an interaction is often described by saying "it depends".
Answers
Using Dr. Lopez's study on the effects of physical discomfort on attention as an example, we find that an interaction is often described by saying "it depends" because it reflects the complexity and variability of the relationship between different factors in a study.
When we say "it depends," we are acknowledging that the effect of one factor may vary depending on the level or presence of another factor. In this study, the interaction between the duration of hand immersion and the belief about pain relief may influence the participants' attention during the task.
For example, it is possible that participants who kept their hand in the water for four minutes and believed they had pain relief may exhibit higher attention levels compared to those who kept their hand in the water for two minutes with no pain relief belief.
On the other hand, participants who kept their hand in the water for two minutes with pain relief belief might perform similarly to those who kept their hand in the water for four minutes with no pain relief belief.
In this scenario, the interaction between the duration of hand immersion and the belief about pain relief impacts the participants' attention differently. The effect of one factor depends on the level or presence of the other factor, resulting in different outcomes.
Describing an interaction as "it depends" reminds us that the relationship between variables is not always straightforward or linear. It highlights the importance of considering multiple factors and their potential interactions to fully understand and interpret the findings of a study.
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how fast does light travel
Answers
A stationary source of light emits light at a speed of 300,000 km/sec.
Is there anything that moves more quickly than light?
No object can go more quickly than 300,000 kph (186,000 miles per second). Only massless particles, such as the photons that constitute light, are capable of traveling at that speed. Any material item cannot be accelerated to the speed of light since doing so would require a limitless supply of energy.
The exact distance that light travels in a vacuum at in a second is 299,792,458 meters (983,571,056 feet). This is roughly 186,282 miles per second, or "c," the symbol for light speed in mathematics.
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Which data set, a or b , is for the uniform line of charge and which set is for the uniformly charged sphere? select the correct answer and explanation
Answers
Data set A corresponds to the uniform line of charge and data set B corresponds to the uniformly charged sphere ar e correct . So, option A is the correct answer.
Data set A corresponds to the uniform line of charge because it shows a linear relationship between the electric field strength and the distance from the center of the object. This is characteristic of a uniform line of charge, where the electric field strength is directly proportional to the distance from the center of the line.
Data set B corresponds to the uniformly charged sphere because it shows a non-linear relationship between the electric field strength and the distance from the center of the object. This is characteristic of a uniformly charged sphere, where the electric field strength decreases as the distance from the center of the sphere increases.
Therefore, as per the above explanaions, option A is correct.
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The question is :
Which of the following options correctly identifies which data set corresponds to the uniform line of charge and which one corresponds to the uniformly charged sphere, and provides an explanation for the answer?
A) Data set A corresponds to the uniform line of charge because it shows a linear relationship between the electric field strength and the distance from the center of the object, while data set B corresponds to the uniformly charged sphere because it shows a non-linear relationship between the electric field strength and the distance from the center of the object.
B) Data set A corresponds to the uniformly charged sphere because it shows a non-linear relationship between the electric field strength and the distance from the center of the object, while data set B corresponds to the uniform line of charge because it shows a linear relationship between the electric field strength and the distance from the center of the object.
C) Both data sets correspond to the uniformly charged sphere because they both show a non-linear relationship between the electric field strength and the distance from the center of the object.
D) Both data sets correspond to the uniform line of charge because they both show a linear relationship between the electric field strength and the distance from the center of the object.
A radio station broadcasts at a frequency of 600 kHz. Knowing that radio waves have a speed of 300 000 000 m/s, what is the wavelength of
these waves?
Answers
Answer:
ccvtesgdujtdchgdrgggggggfrrrtyfaasdddfffghgdshh
How do you convert mcg to mg?
Answers
We can convert mcg to mg by using the unitary method.
To convert micrograms (mcg) to milligrams (mg), follow these steps:
Divide the number of micrograms by 1000: To convert from micrograms to milligrams, you need to divide the number of micrograms by 1000. This is because 1 milligram is equal to 1000 micrograms.
Multiply by 0.001: You can also multiply the number of micrograms by 0.001 to convert to milligrams.
Round the result to the desired number of decimal places: If desired, you can round the result to a specific number of decimal places, depending on the level of precision you need for your calculation.
For example, if you have 100 mcg, the conversion to milligrams would be:
100 mcg / 1000 = 0.1 mg
100 mcg * 0.001 = 0.1 mg
So, 100 micrograms is equivalent to 0.1 milligrams.
It's important to note that conversions between different units of measurement should be performed carefully to ensure that the correct units are used and that the calculations are done correctly. It's also important to use the correct number of significant figures when rounding results.
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It's physical science, but I don't know I should put for it HELP!!!
Answers
(A) The relationship between current and voltage when resistance is constant represents by graph 2. Option B is correct.
(B) Relationship between current and voltage is direct. Option B is correct.
What is resistance?Resistance is the electric component that regulates the flow of current through the conductors or circuits.
Here,
From ohm's low, we have
Voltage = Current × resistance
As resistance = constant
Voltage ∝ Current
The above expression implies that Voltage becomes directly proportional to the current. So as current increases voltage also increases simultaneously [Option B is correct]. And graph between current and voltage will be a straight line passing through the origin Option B is correct.
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The voltage or potential difference across an electric circuit is directly proportional to the current flowing through the circuit. Thus, the correct options for 1 and 2 are B and B, respectively.
What is the Ohm's law?Ohm's law is the description of the relationship between two variables which are current, voltage, and a constant called resistance. The amount of steady current which passes through a large number of materials is directly proportional to the potential difference, or the voltage across the materials or electric circuit.
It can be expressed as: V = IR
where, V is the potential difference across the circuit,
I is the electric current,
and R is the resistance
As voltage is directly proportional to the current. If the voltage is increasing, then the current will also increase and if the voltage decreases then the amount of current through the circuit also decreases.
Therefore, the correct options for 1 and 2 are B and B, respectively.
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Which of the following will increase as a material is heated and changes temperature?
the charge of the molecules
the mass of the molecules
the kinetic energy of the molecules
the potential energy of the molecules
Answers
As a material is heated and changes temperature, the kinetic energy of the molecules increases.
What is kinetic theory of gases?The kinetic theory of gases is a theory that can be used to deduce many of the gas's macroscopic features from a simplified molecular or particle description of the gas.
The most basic kinetic model is predicated on the following premises:
the gas is made up of a large number of identical molecules moving in random directions, separated by distances that are large in comparison to their size; the molecules collide perfectly elastically (with no energy loss) with each other and with the container walls, but otherwise do not interact; the transfer of kinetic energy between molecules is heat. The characteristics of gases can now be mathematically treated thanks to these simplifications.Learn more about kinetic theory of gases here:
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Which object has potential energy?(1 point)
Responses
unlit lightbulb
unlit lightbulb
rock on the ground
rock on the ground
stereo speaker
stereo speaker
can of gasoline
Answers
The object that has potential energy is the can of gasoline.
What is potential energy?Potential energy is described as the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
The forms of potential energy includes:
Elastic Potential Energy.Electrical (Electromagnetic) Potential Energy.Gravitational Potential Energy.Nuclear Potential Energy.Potential energy is described as the energy a system has due to position, shape, or configuration.
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Name the following ionic compounds: BeCl2
Answers
Answer:
Beryllium chloride
Explanation:
I hope this helps!
Can I get branliest?!
An object travels at a speed of 5m/s for 1 minute. What is the distance travelled by car.
Answers
Answer:
D = 300
Explanation:
Speed = 5 m/s
Time = 1 m = 60sec (now both variables have the unit of seconds)
NOTE: Equation: Distance (D) = Speed (S) X Time (T)
Now, fill in your variables:
D = S X T
D = 5 X 60
D = 300
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Examples of store-bought inhalants include:
A.
Glue
B.
Paint
C.
Gasoline
D.
All of the above.
Answers
Examples of store-bought inhalants include: Option D.All of the above. examples are glue, paint, gasoline.
Store-bought inhalants are any product or substance that may be inhaled to produce an intoxicating or otherwise desired effect.
They are readily available over-the-counter in a variety of common consumer products, including glue, paint, and gasoline.
Inhalants are a type of drug that can cause euphoria, hallucinations, and disorientation.
Inhaling solvents can cause intoxication, dizziness, and nausea, but it can also be fatal.
These products are dangerous and should not be inhaled.
A list of store-bought inhalants include:Model glue and plastic cementSpray paint and hairsprayGasoline and other fuel productsComputer keyboard cleaner and canned airPropane, butane, and other gas productsCleaning fluids and solventsLighter fluid and fire-starting productsWhipped cream cans and other pressurized food productsMarkers and correction fluidAir freshener and deodorizer sprayIf you suspect someone is inhaling inhalants, please get them help right away.
Therefore, Option D is correct answer.
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Power of convex lens is 10 Dioptre kept contact with concave lens of power -10 dioptre. Find combined focal length.
Answers
The combined focal length of a convex lens and a concave lens in contact, with powers of 10 Dioptre and -10 Dioptre respectively, is 0.05 m.
Given that power of the convex lens is 10 Dioptre is kept in contact with the concave lens of power -10 dioptre. We need to find the combined focal length. Firstly, let's recall the formula for calculating the power of a lens: P = 1/f where P is the power of the lens and f is the focal length of the lens. Now, let's calculate the focal lengths of the given convex and concave lenses: Focal length of convex lens = 1/10 = 0.1 m. The focal length of the concave lens = -1/-10 = 0.1 m (negative sign indicates that the lens is concave) To find the combined focal length, we use the formula: 1/f = 1/f1 + 1/f2 - d/f1f2 where f1 and f2 are the focal lengths of the two lenses and d is the distance between the lenses. Since the two lenses are in contact, d = 0. Plugging in the values, we get: 1/f = 1/0.1 + 1/0.1 = 20 Therefore, f = 1/20 = 0.05 m. Hence, the combined focal length is 0.05 m. Summary: The given problem is to calculate the combined focal length of a convex lens and a concave lens when in contact. The power of the convex lens is given as 10 Dioptre and that of the concave lens is -10 Dioptre. Using the formula for calculating the power of the lens, we get the focal lengths of both lenses. Then, we use the formula for combined focal length to get the final answer. The solution to this problem is f = 0.05 m.For more questions on focal length
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Thin lenses. Object O stands on the central axis of a thin symmetric lens. For this situation, each problem in the table (below) gives object distance p (centimeters), the type of lens (C stands for converging and D for diverging), and then the distance (centimeters, without proper sign) between a focal point and the lens. Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real or virtual, (d) inverted from object O or noninverted, and (e) on the same side of the lens as object O or on the opposite side.
Answers
The image distance i is - 8.6 cm and the lateral magnification m of the object, including signs is +0.39 .
How is it calculated ?For a diverging (D) lens we know that the focal length value should be negative ( f=–14cm).
1. The image distance :
i = \(\frac{pf}{p-f}\)
∴ i = [22 × (-14)] / [22 -(-14) ]
∴ i = -8.6 cm
2. The magnification :
m = - i / p
∴ m = - (-8.6 / 22)
∴ m = +0.39
3.The image distance being a negative number indicates that the image is virtual (V).
4.A positive magnification value indicates that the image is not reversed (NI).
5.The image is on the same side of the object as the object.
6. This problem's ray diagram is similar to the one depicted in Figure. The lens is diverging, creating a virtual image with the same orientation as the object and on the same side.
What is ray diagram ?Ray diagrams are a visual representation of light propagation in physics. They can help us understand and visualize a variety of scenarios, such as light reflecting off a mirror or changing direction while passing through a lens.A ray diagram is a simplified representation of light that is used to analyze its journey as it moves from one place to another.Can learn more about ray diagram from https://brainly.com/question/14483129
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(i) An object has moved through a distance. Can it have
zero displacement? Justify your answer with an
example.
(ii) Define acceleration using your own
words.
Answers
Yes, an object can have zero displacement even if it has moved through a distance.
Displacement is a vector quantity that represents the change in position from the initial point to the final point.Yes, an object can have zero displacement even if it has moved through a distance. It takes into account the direction of motion as well as the magnitude.To illustrate this, consider a scenario where an object moves in a circular path and returns to its initial position. In this case, the object has covered a certain distance along the circumference of the circle. However, since it ends up at the same position it started, the displacement is zero because there is no change in its position relative to the initial point.
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How much heat is required to warm 230 g of water from 12°C to 90°C?
(Specific Heat of Water = 4.184)
Answers
John, who has a mass of 65kg stands at rest on the ice. He catches a 10kg ball that is thrown to him at 5m/s.
A. Find John's momentum.
B. Find the momentum of the ball.
C. Find the total momentum of the system.
Answers
A. Since John has a mass of 65 kg and stands at rest on the ice, John's momentum is 0 Kgm/s.
B. The momentum of the ball is 50 Kgm/s.
C. The total momentum of the system is 50 Kgm/s.
Given the following data:
Mass of John = 65 kgVelocity of John = 0 m/s (since he is at rest).Mass of ball = 10 kgVelocity of ball = 5 m/sA. To find John's momentum:
Mathematically, momentum is given by the formula;
\(Momentum = Mass\) × \(Velocity\)
Substituting the given parameters into the formula, we have;
\(Momentum = 65\) × \(0\)
John's momentum = 0 Kgm/s.
b. To find the momentum of the ball:
\(Momentum = Mass\) × \(Velocity\)
Substituting the given parameters into the formula, we have;
\(Momentum = 10\) × \(5\)
Ball's momentum = 50 Kgm/s.
c. To find the total momentum of the system:
\(Total\; momentum = John's \;momentum + Ball's \;momentum\)
Substituting the values into the formula, we have;
\(Total\; momentum = 0 + 50\)
Total momentum = 50 Kgm/s.
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You are a lifeguard and spot a drowning child 30 meters along the shore and 60 meters from the shore to the child. You run along the shore and for a while and then jump into the water and swim from there directly to child. You can run at a rate of 5 meters per second and swim at a rate of 1 meter per second. How far along the shore should you run before jumping into the water in order to save the child? Round your answer to three decimal places.
Answers
Answer:
The lifeguard should run approximately 17.752 meters along the shore, before, jumping in the water
Explanation:
The given parameters are;
The rate at which the lifeguard runs = 5 m/s
The rate at which the lifeguard swims = 1 m/s
The horizontal distance of the child from the lifeguard = 30 meters along the shore
The vertical distance of the child from the lifeguard = 60 meters along the shore
Let x represent the distance the lifeguard runs
We have;
The distance the lifeguard swims = √((30 - x)² + 60²)
Time = Distance/Speed
The time the lifeguard runs = x/5
The time the lifeguard swims = √((30 - x)² + 60²)/1
The total time = √((30 - x)² + 60²) + x/5
The minimum time is given by finding the derivative and equating the result to zero, as follows;
Using an online application, we have;
d(√((30 - x)² + 60²) + x/5)/dx = 1/5 - (30 - x)/(√((30 - x)² + 60²)) = 0
Which gives;
1/5 - (30 - x)/(√(x² - 60·x + 4500) = 0
(30 - x)/(√(x² - 60·x + 4500)) = 1/5
5×(30 - x) = √(x² - 60·x + 4500)
We square both sides to get;
(5×(30 - x))² = (x² - 60·x + 4500)
(5×(30 - x))² - (x² - 60·x + 4500) = 0
25·x² - 1500·x + 22500 - x² + 60·x - 4500 = 0
24·x² - 1440·x + 18000 = 0
Dividing n=by 24 gives;
24/24·x² - 1440/24·x + 18000/24 = 0
x² - 60·x + 750 = 0
By the quadratic formula, we have;
x = (60 ± √((-60)² - 4×1×750))/(2 × 1) =
Using an online application, we have;
x = (60 ± 10·√6)/(2)
x = 30 + 5·√6 or x = 30 - 5·√6
x ≈ 42.25 m and x ≈ 17.752 m
At x = 42.25
Time = √((30 - 42.247)² + 60²) + 42.247/5 ≈ 69.69 seconds
At x = 17.75
Time = √((30 - 17.752)² + 60²) + 17.752/5 ≈ 64.79 seconds
Therefore, the route with the shortest time is when the lifeguard runs approximately 17.752 meters (rounded to three decimal places) along the shore, before, diving in the water
A tea kettle is used to boil liquid water. When the water is boiling, a whistling sound comes from the kettle. Which provides the best explanation for the sound?
A. The liquid particles are sliding past each other slowly as the temperature increases
B. The gas particles are being pushed below the water at the bottom of the kettle.
C. The gas particles spreading out in all directions are being pushed quickly through a small opening.
D. The liquid particles are moving very quickly to the center of the kettle and pushing any gas particles out of the way.
Answers
Answer:
C would be the correct answer
Answer:
It has to have a whistle device on the spout. When boiling occurs, water vapour displaces air above the water which has to escape through the whistle hence activating the required vibrations. Thereafter, the continuing supply of steam does the same job until the cook involves turns off the heat. The whistle is not made to exacting scientific standards and there is no doubt a range of pressures above which it will work it. It would be interesting to know how you observed the water boiling without using a transparent kettle.
Explanation:
hope it helps
A 745 kg race car experiences an applied force from the engine of 38900 N and a frictional force of 34000 N. How long does it take to go from rest to 21 m/s ?
Answers
The time taken for the car to go from rest to 21 m/s is 3.2 seconds.
What is the acceleration of the car?The acceleration of the car is determined by applying Newton's second law of motion as shown below.
Mathematically, the formula for Newton's second law of motion is given as;
F (net) = ma
where;
m is the mass of the cara is the acceleration of the carThe net force acting on the car is calculated as follows;
F (net) = F - Ff
where;
F is the applied forceFf is the force of frictionF (net) = 38,900 N - 34,000 N
F (net) = 4,900 N
The acceleration of the car is calculated as follows;
a = F (net) / m
a = ( 4,900 N ) / ( 745 kg )
a = 6.58 m/s²
The time of motion of the car is calculated as follows;
v = u + at
v = 0 + at
v = at
t = v / a
t = ( 21 m/s ) / ( 6.58 m/s² )
t = 3.2 s
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which type of magnetic material cannot be used to make permanent magnets: a ferromagnetic substance, an antiferromagnetic substance, or a ferrimagnetic substance?
Answers
Antiferromagnetic materials are magnetic materials that cannot be used to create permanent magnets.
Explain about the Antiferromagnetic materials?In the case of anti-ferromagnetism, materials that exhibit magnetic ordering below a certain temperature exhibit magnetic magnetism.
Antiferromagnetic substances have magnetic moments that are antiparallel to the applied magnetic field, while ferromagnetic substances have magnetic moments that are parallel to the applied magnetic field. This causes antiferromagnetic materials to have zero total magnetism and positive magnetism for ferromagnetic materials.
Two magnetic characteristics of materials are ferrimagnetism and anti ferromagnetism. Ferrimagnetic materials are strongly drawn to a magnetic field in contrast to antiferromagnetic materials. Other magnetic properties of matter include para magnetism, ferromagnetism, and diamagnetism.
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Two birds have the same mass but one has bigger feet. How would pressure that they produce on the ground be different ?
Answers
Answer:
the pressure per square inch is greater from the smaller feet.
Explanation:
different weight distribution
which best describes elements that are shiny, malleable, ductile, and good conductors of heat and electricity?
Answers
Answer:
Explanation:
They are called metals. Metals that are shiny, malleable, ductile and solid are great conductors of electricity EXCEPT mercury because mercury is the only metal that is a liquid at room temperature. Metals that can be hammered or rolled into sheets are ductile and the metal that are drawn into wires are malleable.
At what velocity will a 300.W motor pull a mass if it applies a force of 13.9N?
4170m/s
286m/s
21.6m/s
0.0463m/s
Answers
To answer this question, we need to use the formula that relates force, mass, and acceleration: F=ma. We can rearrange this formula to solve for acceleration: a=F/m.
In this case, we are given that the force applied by the motor is 13.9N, and we need to find the velocity at which it will pull a mass. We are not given the mass directly, but we can calculate it using the power of the motor (300W) and the velocity we are trying to find.
Power is defined as the rate at which work is done, or P=W/t, where W is the work done and t is the time it takes to do that work. In this case, we can assume that the work done is moving the mass a certain distance, and we can use the velocity to calculate the time it takes to do that work. So, we have:
P=Fv
where P=300W, F=13.9N, and v is the velocity we want to find. Rearranging this equation gives:
v=P/F
Now we can substitute in the values for P and F to get:
v=300/13.9
v≈21.6 m/s
So, at a velocity of 21.6 m/s, a 300.W motor applying a force of 13.9N can pull a mass.
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if you have any questions, let me know
Answers
Answer:
The red car would experience the greatest acceleration.
Explanation:
Newton says that Force equals mass times acceleration or F = ma
We get a = F/m
If we want the greatest acceleration or a, mass or m must be the lowest.