A bolt of lightning discharges 9. 7 C in 8. 9 x 10^-5 s. What is the average current during the discharge?

The velocity vector is r'(t) = (4, -3 sin t, 3 cos t), the acceleration vector is r''(t) = (0, -3 cos t, -3 sin t), the curvature is κ = 3 / 14^(3/2), and the tangential and normal components of the acceleration are aT = 0 and aN = 3.

Space Curves: Arc lengthArc length formula is given by \(L = ∫a b |r'(t)|dt\)

, where r(t) is the vector function for the given curve.

Let's find the arc length of the given space curve:

r(t) = (2t, t^2 - 2, 5 - t^2) for 0 ≤ t ≤ 4.

The speed of r(t) is |r'(t)|.r'(t) = (2, 2t, -2t) and

||r'(t)|| = √(2^2 + (2t)^2 + (-2t)^2)

= 2√2t.So,

the arc length of the space curve is

L = ∫0 4 2√2t dt

= (4/3)√2 [t^(3/2)] from 0 to 4

= (4/3)√2 (4√2 - 0)= (16/3) * 2

= 32/3.

Therefore, the length of the given space curve with vector equation is 32/3. Vector Functions for the intersection of two surfaces

The equation for the given surface is \(F(x)=(2,x²-30).\)

Let's find the vector functions for the intersection of two surfaces.

To find the intersection, we equate the two given equations:2 = y = x².

We get y = x² = 2. So, x = ±√2.

The vector functions for the intersection of two surfaces are:

r1(t) = (t, 2, t^2 - 30)

for x = √2 and r2(t)

= (-t, 2, t^2 - 30)

for x = -√2.

Given TNB for a space curveLet's find the unit tangent vector to the space curve r(t) = (cos t, sin t, t).

The velocity vector is r'(t) = (-sin t, cos t, 1).

The speed of the curve is |r'(t)| = √(sin² t + cos² t + 1) = √2.

The unit tangent vector is T = r'(t) / |r'(t)| = (-sin t/√2, cos t/√2, 1/√2).

Now, let's find a unit normal vector to the space curve.The acceleration vector is r''(t) = (-cos t, -sin t, 0).

The magnitude of acceleration is |r''(t)| = 1.

The unit normal vector is N = r''(t) / |r''(t)| = (-cos t, -sin t, 0).The binormal vector is given by B = T × N.

Therefore, the unit tangent vector to the space curve r(t) = (cos t, sin t, t) is T = (-sin t/√2, cos t/√2, 1/√2),

the unit normal vector is N = (-cos t, -sin t, 0),

and the unit binormal vector is

B = (cos t/√2, -sin t/√2, 1/√2) × (-cos t, -sin t, 0)

= (sin t/√2, -cos t/√2, 1/√2).

Velocity, acceleration and curvature

Let's find the velocity vector, the acceleration vector, and the curvature of the space curve r(t) = (4t, 3 cos t, 3 sin t) for 0 ≤ t ≤ 27.

The velocity vector is r'(t) = (4, -3 sin t, 3 cos t).

The speed of the curve is |r'(t)| = √(16 + 9 sin² t + 9 cos² t) = 5.

The unit tangent vector is T = r'(t) / |r'(t)| = (4/5, -3 sin t/5, 3 cos t/5).

The acceleration vector is r''(t) = (0, -3 cos t, -3 sin t).

The magnitude of acceleration is |r''(t)| = 3.

The tangential component of acceleration is aT = T · r''(t) = 0.

The normal component of acceleration is aN = |r''(t)| · |N| = 3.

The unit normal vector is N = (-cos t, -sin t, 0).

The curvature is κ = |r''(t)| / |r'(t)|² = 3 / (25 + 9 sin² t + 9 cos² t)^(3/2) = 3 / (25 + 9)^(3/2) = 3 / 14^(3/2).

Therefore, the velocity vector is r'(t) = (4, -3 sin t, 3 cos t),

the acceleration vector is r''(t) = (0, -3 cos t, -3 sin t),

the curvature is κ = 3 / 14^(3/2), and the tangential and normal components of the acceleration are aT = 0 and aN = 3.

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Answer:

#A

Acceleration=a

\(\\ \tt\hookrightarrow a=\dfrac{v-u}{t}=\dfrac{8}{4}=2m/s^2\)

#B

\(\\ \tt\hookrightarrow a=\dfrac{0-8}{4}=\dfrac{-8}{4}=-2m/s^2\)

Answer(s):

Solution for Practice-A:

We know that:

Solution:

Hence, the acceleration is 2 m/s for practice A.

Solution for Practice B:

We know that:

Solution:

Hence, the acceleration is -2 m/s for practice B.

Hoped this helped!

Answer:

1.5 m

Explanation:

a = v/t

a = 2/1,5 = 4/3

x = 1/2 a t² + vt + x

x = 1/2 × 4/3 × 9/4 = 3/2 =1.5 m

Answer:

Explanation:

See attachment.

Decreasing the mass of the objects   No.  Force will change.

Increasing the temperature of the objects Yes,  No change in force (at most a very small change if the heat causes excessive expansion, reducing the distance, although 1/2 will be further apart)

Increasing the distance between the objects No.  Force will change.

Decreasing the distance between the objects  No.  Force will change.

F_net:-

Now

Apply Newton's second law

The momentum of the system before the collision 255 g⋅m/s.

In this case, the mass of the first cart is 250 grams, the velocity of the first cart is 0.42 m/s, the mass of the second cart is 500 grams, and the velocity of the second cart is 0.30 m/s.

The momentum of the first cart is:

momentum = 250 g × 0.42 m/s = 105 g⋅m/s

The momentum of the second cart is:

total momentum = 105 g⋅m/s + 150 g⋅m/s = 255 g⋅m/s

Therefore, the total momentum of the system before the collision is 255 g⋅m/s.

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The age of the universe in a flat universe, based on the given values, is approximately 3.454 × 10^16 seconds or approximately 1.094 billion years.

To calculate the age of the universe based on the observed recession velocity and assuming a flat universe, we can use the Hubble's Law equation:
v = H₀ × d
where:
v is the recession velocity of the galaxy,
H₀ is the Hubble constant, and
d is the distance to the galaxy.
The Hubble constant is the rate at which the universe is expanding and is typically expressed in units of km/s per megaparsec (km/s/Mpc).
Rearranging the equation, we can solve for time (t), which represents the age of the universe:
t = 1 / H₀
Given that the recession velocity (v) is 894 km/s and the distance (d) is 12 Mpc, we can substitute these values into the equation:
t = 1 / (894 km/s / 12 Mpc)
Converting the units to consistent values:
t = 1 / (894 km/s / 3.09 × 10^19 km/Mpc)
Evaluating the expression:
t = 1 / (2.897 × 10^−17 s^−1)

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Thermal insulation reduces unwanted heat loss and also reduces unwanted heat gain.

Insulation creates a barrier between the hot and the cold object by reducing heat transfer by either reflecting light radiation.

Insulating materials are bad conductors of electricity and heat. So, insulating reduces the heat loss via conduction.

Thermal energy is prevented to increase the temperature of building in summers and decrease in winters. The thermal energy transfer plays vital role in insulating a building.

Thus Thermal insulation reduces unwanted heat loss and also reduces unwanted heat gain.

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The speed  of a point on the rim is approximately 1.25 m/s.To determine the speed of a point on the rim of the thin disk, we need to use the formula for kinetic energy, which is KE = (1/2)mv^2, where m is the mass of the object, v is its velocity or speed, and KE is the amount of kinetic energy it possesses .

We also need to use the formula for the diameter of a circle, which is twice the radius. Since the disk has a diameter of 6.00 cm, its radius is half of that or 3.00 cm. From there, we can calculate the moment of inertia of the disk and use it to solve for the speed of a point on the rim. Once we plug in the given values and solve the equation, we find that the speed of a point on the rim is approximately 1.25 m/s.

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Answer:

C

Explanation:

It says is it a good idea the person so 1 person can say no and the other one can say yes so it is asks for a opinion

A question that asks for an opinion is as follows:

Thus, the correct option for this question is C.

An opinion may be defined as a type of viewpoint, judgment, or statement that is not conclusive, rather than facts, which are true statements. It may vary from person to person, topic to topic, and condition to condition.

The opinion of any individual belongs or relates to one particular person rather than to other people. For example, in this given scenario, some reply to the question with a yes answer. In a manner, it is definitely a good idea to try to establish human colonies on Mars. While some categorized themselves on no side.

Therefore,  the correct option for this question is C.

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1. The body must supply approximately 10.2 kJ of heat to warm 2.5 L of air from 0 °C to 37 °C.

To calculate the heat supplied, we can use the equation Q = mcΔT, where Q represents the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

Since we are given the volume of air and the temperature change, we need to determine the mass of air and the specific heat capacity.

The ideal gas law, PV = nRT, relates the pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T). Rearranging the equation to solve for the number of moles, we have n = PV/RT. Substituting the given values and using the molar mass of air, we can calculate the mass of air.

Next, we need to consider the specific heat capacity of air. The specific heat capacity of air at constant pressure (Cp) is approximately 1.0 kJ/(kg·K). Using the calculated mass, we can find the heat supplied by multiplying the mass by the specific heat capacity and the temperature change.

Therefore, around 10.2 kJ of heat is required for raising the temperature of 2.5 liters of air from 0 °C to 37 °C.

2. The air's volume increases by approximately 6.3% as it warms.

To calculate the volume increase, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature at constant pressure.

Mathematically, V₁/T₁ = V₂/T₂, where V₁ and T₁ represent the initial volume and temperature, and V₂ and T₂ represent the final volume and temperature.

Using the given initial volume, initial temperature, and the final temperature of 37 °C, we can solve for the final volume. The volume increase is then determined by subtracting the initial volume from the final volume and expressing it as a percentage of the initial volume.

Therefore, the volume of air expands by approximately 6.3% when it is heated.

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Answer:

speed of light: 299,792,458

what does light travel fasted through?: Light will have the fastest velocity when it travels through the air. Light will have the slowest velocity when it travels through gelatin. Why? Light slows down when passing through different transparent materials. The more it slows down, the more it bends when it hits a medium made of that material

The process of providing a pathway to drain excess charge into earth is called grounding. The pathway is usually a conductor such as wire that connects the electrical system to a grounding electrode or rod buried in the earth. This helps to prevent electrical shocks, fires, and equipment damage by redirecting excess voltage and current to the ground.

Grounding is typically achieved by connecting a conductor, such as a wire or metal rod, from an electrical or electronic system to the Earth's surface. Grounding helps to prevent the buildup of static electricity, protect against electrical shocks, and provide a safe discharge route for excess electrical charge.When an object is charged, it has an imbalance of electrons. This imbalance can create a potential difference between the object and the ground. If the potential difference is high enough, it can cause a spark or arc. Sparks and arcs can start fires or cause electrical shock.

Grounding provides a safe path for the excess charge to flow away from the object and into the ground. This prevents the potential difference from becoming high enough to cause a spark or arc.

Grounding is also used to improve the performance of electrical systems. For example, grounding can help to reduce noise and interference in electronic devices. It can also help to protect electrical systems from lightning strikes.

Grounding is an important safety measure that should be used in all electrical systems. It is a simple and effective way to protect people and equipment from electrical hazards.

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Answer:

through the vibration of particles

Explanation:

Energy is transferred in waves through the vibration of particles, but the particles themselves move in a perpendicular fashion to the horizontal movement of the wave.

Answer:

it is 4m

Explanation:

If a ball is tossed horizontal at a speed of 7.9 m/s, it will travel 4.8 meters (horizontally).

Teenagers, young adults, and others take various stimulant medications collectively referred to as "speed" to feel more focused and alert, as well as occasionally to get high. Additionally, some people take various forms or speed to suppress their appetite.

Relativistic speed is the rate at which relativity effects matter for the desired level of measurement precision of the phenomenon being examined. Relativistic effects are the differences between values calculated using models that take relativity into account and those that do not.

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The wavelength of a wave of the frequency is increased to 784 Hz will be 0.57 metre.

The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.

The given data in the problem is;

f₁ is the  frequency of  a sound wave in case 1 = 196 Hz

\(\lambda\)₁ is the wavelength for the  = 1.76 meters.

f₂ is the  frequency of  a sound wave in case 2 = 784 Hz

\(\lambda_2\) is the wavelength for case 2=?

The speed of the wave for the same medium is same which is given as;

\(\rm v = \lambda_1 f_1 \\\\ \rm v = 1.76 \times 196 \\\\ \rm v =344.96\ m/sec\)

For case 2;

\(\lambda_2 = \frac{v}{f_2} \\\\ \lambda_2 = \frac{344.96}{784} \\\\ \lambda_2=0.44\)

Hence the wavelength of a wave of the frequency is increased to 784 Hz will be 0.57 metre.

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Answer:

114.84

Explanation:

Impulse= F.ΔT

where F is the average force applied and ΔT is the change in time period

so,

Impusle= (522)x(0.22)

Impulse=114.84N-s

Answer: Assuming you meant 75 seconds and 1425 meters, the answer would be 19meters per second

Explanation: 1425/75

Answer:

In a neutralization reaction, hydronium and hydroxide ions react to form water.

Explanation:

Acids/Bases and how they interact:

A Bronsted-Lowry base is a substance that tends to bond with and "steal" a hydrogen ion, while an acid is a molecule containing a hydrogen ion that prefers to dissociate. Acids "give up" their hydrogen ions to water molecules in water, resulting in the formation of a hydronium ion. The pH of a given solution is determined by the amount of hydronium ions present.

A quick neutralization reaction takes place when a base is added to an acid because bases want to "take" the hydrogen. We have the ideal combination of bases that want to "take" the hydrogen ion and acids that want to "give up" the hydrogen ion, which allows them to neutralize one another. A conjugate base is created when hydrogen separates from an acid; having had its hydrogen torn from the complex, it may now receive a hydrogen (i.e., acts as a base). Once the base has a hydrogen, it behaves as a conjugate acid; it may then "lose" that hydrogen and behave as an acid.

Depending on which form the molecule favors, the acid's potency varies. The fact that hydrochloric acid (HCl) fully dissociates in aqueous solutions makes it a powerful acid:

HCl + H₂O -> Cl- + H₃O+

That is to say that the reaction equation strongly favours the right side.

Acetic acid, on the other hand, is a weak acid because only a small part of it dissociates:

CH₃COOH + H₂O <--> CH₃COO- + H₃O+

In contrast to the bulk of the chemical, which is shown on the left in the uncharged state, only a minor portion of acetic acid dissociates.

This brief explanation of acids and bases anthropomorphizes chemical substances as aware creatures with specific preferences for certain actions. These so-called "preferences" are, in reality, rough summaries of the relative stabilities of the compounds (acid vs. its conjugate base), mostly as a result of electrical processes.

Answer:

hydrogen and water other answer is wrong

Explanation:

Answer:

C

Explanation:

compound is a substance made from two or more different elements that have been chemically joined

Answer:

polarity completes the sentence

Answer:

a little to late

Explanation:

srry

It is likely that the can will sweat when the woman enjoys the drink in a room at 70°F and 38 percent relative humidity.

When a cold object, such as a can of chilled drink, is taken from a cold environment (in this case, the refrigerator at 40°F), and is placed in a warmer environment (the room at 70°F), the air around the can will cool and condensation will form on the surface of the can. This is because the colder air cannot hold as much moisture as the warmer air, and the excess moisture condenses on the colder surface of the can.

The relative humidity of the room (38%) indicates that the air is not particularly humid, which means that there is not a lot of moisture in the air to begin with. This could reduce the amount of condensation that forms on the can, but it is still likely that some amount of condensation will occur, especially if the can is very cold.

Therefore, it is likely that the can will ""sweat"" as the woman enjoys the drink.

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The movement of charges from one plate to the other in a capacitor is a fundamental process that underlies many electronic devices and applications.

When a capacitor is connected to a circuit, charges begin to flow from one plate to the other until both plates reach the same potential and the capacitor becomes fully charged.

This process involves the movement of electrons, which are negatively charged particles, from one plate to the other.

Initially, the capacitor is uncharged, and the plates have an equal number of positive and negative charges.

When a voltage is applied to the capacitor, electrons begin to flow from the negative plate to the positive plate, creating an electric field between the two plates. This electric field stores energy in the capacitor, which can be released later when the capacitor is discharged.

If the voltage across the capacitor is removed, the capacitor will retain its charge and will discharge slowly over time as the electrons flow back from the negative plate to the positive plate.

This discharge process can be used in various applications, such as in flash photography, where a capacitor is charged rapidly and then discharged quickly to produce a bright flash of light.

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The molar mass of a gas at 78 c and 560 torr if 206 ng occupies 0.206 ul is 41.64 g/mol

The molar mass of a gas can be calculated using the ideal gas law equation and the given values of temperature, pressure, mass, and volume.

To calculate the molar mass of a gas, we can use the formula:

Molar mass = (mass of gas) / (number of moles of gas)

First, we need to determine the number of moles of gas. We can use the ideal gas law equation:

\(PV = nRT\)

where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

We are given the temperature as 78 °C, which needs to be converted to Kelvin by adding 273.15:

T = 78 + 273.15 = 351.15 K

The pressure is given as 560 torr, and the volume is given as 0.206 µl.

Next, we can calculate the number of moles using the ideal gas law equation:

\(n = (PV) / (RT)\)

(0.5105 atm)(2.06×10⁻⁷ L) = n(0.0821 L-atm/mol-K)(318 K)

n = 4×10⁻⁹ mol

Molar mass = Mass/n = 2.06×10⁻⁷ g/4×10⁻⁹ mol

Molar mass = 41.64 g/mol

Now that we have the number of moles, we can calculate the molar mass by dividing the mass of the gas (given as 206 ng) by the number of moles.

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Equation of motion: To find the equation of motion and the oscillation frequency of a mass-spring system, we'll use Newton's second law of motion.

Force (F) = mass (m) × acceleration

F = ma

The force acting on a spring is given by Hooke's law:

F = -k x

where k is the spring constant and x is the displacement from the equilibrium position.

Thus, combining these two equations gives us the following equation of motion for a mass-spring system:

ma = -k x

Rearranging this, we get:

m(d²x/dt²) + k x = 0

This is the differential equation of motion of the mass-spring system.

Oscillation frequency:

The oscillation frequency can be calculated using the equation:

f = (1/2π) √(k/m)

where f is the frequency, k is the spring constant, and m is the mass.

Lagrange function:

The Lagrange function for a mass-spring system can be written as:

L = T - VL

is the difference between the kinetic energy (T) and potential energy (V) of the system.

The kinetic energy of the system is given by:

T = (1/2) mv²where m is the mass and v is the velocity.

The potential energy of the system is given by:

V = (1/2) kx²

where k is the spring constant and x is the displacement from the equilibrium position.

L = (1/2) mv² - (1/2) kx²

Equation of motion:

Using the Euler-Lagrange equation, the equation of motion for a mass-spring system can be derived.

It is given by:

d/dt (∂ L/∂v) - ∂L/∂x = 0

Substituting the values from the Lagrange function:

L = (1/2) mv² - (1/2) kx²∂L/∂v = m v ∂L /∂x = -k x.

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