after a long time, the switch in the above circuit is opened, abruptly disconnecting the battery from the circuit. what is the current i through the vertical resistor immediately after the switch is opened? ( is in the direction of the arrow)

Answers

Answer 1

The current i through the vertical resistor immediately after the switch is opened is zero.

When the switch in the circuit is abruptly opened, the circuit becomes an open circuit, which means there is no complete path for current to flow.

In this scenario, the current through the vertical resistor, labeled as i, is determined by the current flow from the battery. However, since the switch is opened, the flow of current is abruptly stopped, resulting in no current passing through the vertical resistor.

When the switch is closed, allowing current to flow from the battery, the circuit reaches a steady state and the current i through the vertical resistor would be determined by the voltage provided by the battery and the resistance of the vertical resistor.

However, after the switch is opened, there is no voltage source connected to the circuit, and hence no current flows through the vertical resistor. Therefore, the current i through the vertical resistor immediately after the switch is opened is zero.

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Related Questions

A laser beam travels from a telescope on Earth to a Moon and then back to the Based on this information , how far is the Moon Earth? PLEASE HELP?

A. 384,000,000

B. 58.600, 000m;

C. 1, 536, 000, 000m

D. 117, 000, 000m

Answers

Answer is d hope this helps

i.the heater has power output of 3kw
What does the 'k' stand for in 'kW'?
How much energy (in joules) does the heater deliver in one second?
ii.
How much energy (in joules) does the heater deliver in 7 minutes?​

Answers

Answer:

2

cos

(

x

)

3

=

0

2

cos

(

x

)

-

3

=

0

5

3

y

+

5

2

=

5

5

3

y

+

5

2

=

5

x

4

0

Explanation:hopefully this helps you

applying newton's second law gives the equation ma = f

Answers

Newton's Second Law of Motion states that the net force acting on an object is directly proportional to its acceleration. The proportionality constant, which is the object's mass, gives the equation ma = f (force equals mass times acceleration). This means that if a force is applied to an object with a certain mass, it will accelerate proportionally to the magnitude of the force.

Applying Newton's Second Law of Motion allows us to determine the force required to move an object of a certain mass a certain distance. We can also use it to calculate the acceleration of an object given its mass and the force acting on it. The second law states that the acceleration of an object is proportional to the force applied to it and inversely proportional to its mass. If the mass of the object remains constant, the acceleration produced is directly proportional to the force applied.

The second law also tells us that if a net force is acting on an object, it will accelerate in the direction of that force. This law can be used to explain the motion of objects in both linear and rotational motion. For example, when a bat hits a ball, the force of the bat on the ball causes it to accelerate, and the ball moves in the direction of that force. In summary, applying Newton's Second Law of Motion is a powerful tool for understanding the motion of objects and how they respond to forces acting on them.

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8. A man takes one minute to lift 4 bags of sugar each of weight 50N
through a height of 1.5m. Calculate the power expanded
A. 1.25W
B. 5.00W
C. 75.00W
D. 300.00W
Lunite of measurements are​

Answers

Answer:

D

Explanation:

the formula is F=mgh

so now you can write it like

m= 4×50=200

200×1.5×10=30000

What is the difference between an Sa and an Sb galaxy? (Select all that apply.) An Sa galaxy has a larger nucleus. An Sb galaxy has more gas and dust, and more hot, bright stars. The spirals of an Sb galaxy are more tightly wound. An Sb galaxy has spiral arms spring from the ends of a bar, expanding out from the nucleus.

Answers

Sa and Sb galaxies differ in size, nucleus, spiral arms, and gas/dust. Sa has a larger nucleus, more gas/dust, and spiral arms. Hot and bright stars are formed in Sb galaxies.

The main differences between an Sa and an Sb galaxy are as follows:
1. An Sa galaxy has a larger nucleus compared to an Sb galaxy. This means that the central region of an Sa galaxy is more prominent.
2. An Sb galaxy has more gas and dust, as well as more hot, bright stars. This leads to an increased rate of star formation in Sb galaxies.
3. The spirals of an Sb galaxy are not necessarily more tightly wound than those of an Sa galaxy. However, the spiral arms of an Sb galaxy may appear more prominent due to the presence of more gas, dust, and bright stars.
4. An Sb galaxy may have spiral arms that spring from the ends of a bar, expanding out from the nucleus. This feature is not exclusive to Sb galaxies, but it is more commonly observed in them.

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The main difference between an Sa and an Sb galaxy is that an Sa galaxy has a larger nucleus, while an Sb galaxy has spiral arms that spring from the ends of a bar, expanding out from the nucleus.

1. An Sa galaxy has a larger nucleus: In an Sa galaxy, the nucleus, which is the central region of the galaxy, is relatively larger compared to other types of galaxies. This larger nucleus is a characteristic feature of Sa galaxies.

2. An Sb galaxy has spiral arms that spring from the ends of a bar: In an Sb galaxy, the spiral arms originate from a central bar structure rather than directly from the nucleus.

This bar structure extends across the nucleus, and the spiral arms emerge from its ends, expanding outward. This bar structure is a distinguishing feature of Sb galaxies.

The other statements mentioned in the options are not accurate differentiating factors between Sa and Sb galaxies:

- The presence of more gas and dust, as well as more hot, bright stars, is not specifically associated with Sb galaxies. Gas, dust, and star formation can vary in galaxies of different types and are not exclusive to Sb galaxies.

- The tightness of spiral arms is not a defining characteristic of Sb galaxies. The degree of tightness or openness of spiral arms can vary within the same galaxy type.

Therefore, the correct main answer is that an Sa galaxy has a larger nucleus, and an Sb galaxy has spiral arms that spring from the ends of a bar.

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Urgent Important!!

Many medications have a warning to avoid driving because.
A. they haven't been scientifically tested yet.
B. they have been proven to cause drowsiness.
C. they want to cover all their bases.

Answers

Answer:

B) they have been proven to cause drowsiness

Explanation:

B is the only answer that makes sense, as the other answers do not make sense.  All medications are scientifically tested before they can be used by someone.  Covering their bases would show negligence and is bad.

Hope this helps!

PS, this is biology or medical, not physics.

Read the passage. Then write a paragraph that explains why the two ecosystems have such different kinds of plants. Use the terms biotic factor, abiotic factor , and limiting factor in your explanation.

Read the passage. Then write a paragraph that explains why the two ecosystems have such different kinds

Answers

Answer:search this up but put quizzlet at the end it should be there

Explanation:

HELP ME I AM EXTREMELY DESPERATE!!!!!!

HELP ME I AM EXTREMELY DESPERATE!!!!!!

Answers

Answer: B is the correct answer because they are both showing a constant speed

Explanation:

Answer: C is the correct answer

Explanation:

A car drove 10m east and then turned around and drove back 5m west. What is the total distance traveled and the displacement

Answers

Answer:

15m

Explanation:

The social cognitive perspective of personality focuses on social factors such as your parents guardians and teachers and cognition what does cognition mean

Answers

The social cognitive perspective of personality focuses on social factors such as your parents guardians and teachers and cognition means how we as individuals process and store information.

What is Cognition?

This is referred to as the process in which information is stored and processed through the use of our senses, experience etc and is common to all individuals.

The social cognitive perspective of personality on the other hand focuses on social factors such as parents and also in which cognition is among and it is influenced by genetic and environmental factors which therefore makes it the most appropriate choice.

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A bat flies toward a wall, emitting a steady sound of frequency 1. 70 khz. This bat hears its own sound plus the sound reflected by the wall. How fast should the bat fly in order to hear a beat frequency of 8. 00 hz?.

Answers

The bat should fly about 0.8065 m/s in order to hear a beat frequency of 8 Hz.

The shift in a wave's frequency caused by an observer moving away from the wave source is known as the Doppler effect or Doppler shift. The equation for this is given by,

\(f=\frac{v \pm v_0}{v\mp v_s}f_s\)

where f is the observed frequency, v is the speed or velocity of the sound waves, v₀ is observer velocity ("+" if it's towards and "-" if it's away from the source), vs is source velocity("-" if it's towards and "+" if it's away from the observer), and fs is the actual frequency of the sound waves.

The velocity of sound waves in the air is 344 m/s, v₀ is zero for the incident, v is the source velocity towards the wall, and fs is 1700 Hz.

Then, the incident frequency is given by,

\(f_{incidence}=\frac{344-0}{344-v}\times f_s\)

The wall is stationary, therefore, f(incidence)=f(reflected). Then, the new frequency the bat hears is,

\(\begin{aligned}f_{new}&=\frac{344+v}{344}\times f_{reflected}\\&=\frac{344+v}{344}\times \frac{344-0}{344-v}\times f_s\\&=\frac{344+v}{344-v} \times f_s\end{aligned}\)

To hear a beat frequency of 8 Hz, the velocity of the bat should be,

\(\begin{aligned}f_{new}-f_s&=8\\\left(\frac{344+v}{344-v} \right)f_s-f_s&=8\\\frac{344+v}{344-v}-1&=\frac{8}{f_s}\\\frac{344+v-344+v}{344-v}&=\frac{8}{1700}\\2v&=0.0047(344-v)\\2v&=1.6168-0.0047v\\2.0047v&=1.6168\\v&=\mathrm{0.8065\;m/s}\end{aligned}\)

The answer is 0.8065 m/s.

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Given the specific heat of water is 4. 186 kJ/kg° C, steam is 2. 010kj/kg c and the L, is 2260 kJ/kg. What is the final temperature the steam reaches if 13553. 8 kJ of heat is released?

Answers

The final temperature that the steam reaches when 13553.8 kJ of heat is released is approximately 1126.8 °C.

To determine the final temperature that the steam reaches when 13553.8 kJ of heat is released, we can use the concept of heat transfer and the specific heat capacities of water and steam.

The formula for heat transfer is:

Q = m * c * ΔT

Where:

Q is the heat transferred (in kilojoules, kJ)

m is the mass of the substance (in kilograms, kg)

c is the specific heat capacity of the substance (in kilojoules per kilogram per degree Celsius, kJ/kg°C)

ΔT is the change in temperature (in degrees Celsius, °C)

We need to find the final temperature (ΔT) of the steam, so we rearrange the formula:

ΔT = Q / (m * c)

Given:

Q = 13553.8 kJ

c (specific heat of steam) = 2.010 kJ/kg°C

However, we don't have the mass (m) of the steam. To find it, we can use the heat of vaporization (L) and the equation:

Q = m * L

Given:

L (latent heat of vaporization) = 2260 kJ/kg

Let's solve for the mass (m) first:

m = Q / L

m = 13553.8 kJ / 2260 kJ/kg

m ≈ 6 kg (rounded to three decimal places)

Now we can substitute the values into the formula to find the final temperature:

ΔT = Q / (m * c)

ΔT = 13553.8 kJ / (6 kg * 2.010 kJ/kg°C)

ΔT ≈ 1126.8 °C (rounded to one decimal place)

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The position vector is given by vector r= 5t² I cap + 2 t³ j cap + 2 k cap. Find it's velocity and acceleration at t=2s.

Answers

Answer:

We have the position vector given in terms of time t. r(t) = t^3*i + t^2*j

To find the velocity vector we have to differentiate r(t) with respect to time.

r'(t) = 3t^2*i + 2t*j

The vector representing acceleration is the derivative of the position vector

r''(t) = 6t*i + 2*j

When time t = 2.

The velocity vector is 3*2^2*i + 2*2*j

=> 12*i + 4*j

The speed is the absolute value of the velocity vector or sqrt(12^2 + 4^2) = sqrt (144 + 16) = sqrt 160

The acceleration vector is 6*2*i + 2*j

=> 12*i + 2*j

The required acceleration at t=2 is 12*i + 2*j and the speed is sqrt 160.

Explanation:

Can I have thx and brainliest?

This is the written answers to find the velocity and acceleration of r
Will mark as BRAINLIEST.......The position vector is given by vector r= 5t I cap + 2 t j cap + 2 k cap.

Name the two types of vaporization and explain the difference between them. Give one example of each

Answers

Evaporation and Boiling are the two vaporizations.

Evaporation is the type of vaporization that occurs at temperatures below the boiling point, whereas boiling is the type of vaporization that occurs at temperatures above the boiling point. The other type of vaporization is boiling, which occurs when a liquid is heated to the point where its vapor pressure equals the external pressure surrounding the liquid. When the liquid is heated, bubbles form within the liquid.

Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?  

Answer:

sample respond: Vaporization is the process by which a liquid becomes a gas. The two types of vaporization are evaporation and boiling. Evaporation takes place at the surface of a liquid, such as a puddle drying up. Boiling takes place below the surface of a liquid and causes bubbling, like a pot of water on a hot stove. Explanation:

a red ball has a mass of 290 g. a constant force pushes the red ball horizontally and launches it at a speed of 20 m/s. the same force pushes a green ball through the same distance, launching it at 25 m/s. what is the mass of the green ball?

Answers

Using the theories of kinetic energy, we got that the  185.6g is the mass of the green ball if force pushes the red ball horizontally and launches it at a speed of 20 m/s, and the same force pushes a green ball through the same distance, launching it at 25 m/s.

Since force acting on both of the balls is constant, therefore work done by friction on both of the balls remains same, therefore we can conserve energy.

Since both of balls have velocity, therefore kinetic energy of both balls remains same

Using formula of kinetic energy, we got

=>[(1/2)×mass of red ball×(velocity of red ball)²]=[(1/2)×mass of green ball×(velocity of green ball)²]

=> [ (1/2)×290×(20)²]=[1/2×m×(25)²]

=>m=290×(20)²/(25)²

=>m=(290×400)/625

=>m=185.6g

Hence, if a red ball has a mass of 290 g. a constant force pushes the red ball horizontally and launches it at a speed of 20 m/s. the same force pushes a green ball through the same distance, launching it at 25 m/s, the mass of the green ball is 185.6g

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What are the three longest wavelengths for standing waves on a 264- cm -long string that is fixed at both ends

Answers

The three longest wavelengths for the standing waves on a 264-cm long string that is fixed at both ends are:

5.2 meters.2.6 meters.1.7meters.

Given data:

Length of the fixed string = 264cms = 2.64 meters

The wavelength for standing waves is given by:

λ = 2L/n

where,

λ is the wavelength L is the length of the string

For n = 1,

λ = 2×2.6/1

= 5.2 meters

For n = 2,

λ = 2×2.6/2

= 2.6 meters

For n = 3,

λ = 2×2.6/3

= 1.7 meters

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With what force does she hit the ball?

With what force does she hit the ball?

Answers

The force required to hit the ball by the tennis player is 500N.

How to calculate force?

The force required to change the direction or stop an object can be calculated by multiplying the mass of the object by its acceleration.

According to this question, a tennis player returns a 0.125kg tennis ball traveling at 40m/s back across the tennis court at 60m/s. The acceleration can be calculated as follows:

a = ∆V/t

a = (60 - 40)/0.005

a = 4,000m/s²

Force = 0.125kg × 4,000m/s²

Force = 500N

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Please Help Me!!!!!!​

Please Help Me!!!!!!

Answers

Answer: B

Explanation: It states they have the same mass so the eliminates the majority of the answers. Density = mass/volume so if sample A & B have the same mass but A is heavier that means A has more volume than sample B

Make the following conversion:


A) 60∘C into F

B)70∘C into K

C) 303∘K into C

D) 140∘F into C


If you don't know what I mean by C, F, K and ∘ it meaning is:

C- Celsius

F- Fahrenheit

K- kelvin
∘- degree sign

Answers

Answer:

Kelvin to Celsius: C = K - 273 (C = K - 273.15 if you want to

Which of the following is an example of a primary source?

Which of the following is an example of a primary source?

Answers

Answer:

An article written by a scientist .

Explanation:

Primary sources information are those that contain first  hand information probably from the place of the activities or by the original contact of the information (source ) .

So primary information is normally contained in artifact , journals , letter , dissertations manuscripts  , videos and audio recordings .

The fact that the article is written by the scientist means he is the one who has the original information hence he is the first person to access the information , meaning he is the original owner .

a 6 kg block is pushed 8m up a rough 37 degree inclined plane by a horizontal force of 75 n. the initial speed of the block is 2.2 m/s up the plane and a constant kinetic friction force of 25 n opposes the motion. calculate:

Answers

The final kinetic energy of the block is 308.98 J.

Let's solve the problem using the work-energy theorem.

Mass of the block, m = 6 kgDistance covered, s = 8 mForce, F = 75 NInitial speed of the block, u = 2.2 m/sAngle of inclination, θ = 37°Coefficient of kinetic friction, μk = 0.28

The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy

W = ΔKE

Initially, the block is at rest. Therefore, its initial kinetic energy is zero.

Ki = 0

We have to find the final kinetic energy of the block. Hence, Kf = ?

Work done on the block

W = Fscosθ

Work done by the applied force,

F = 75 Ns = 8 mθ = 37°

W = Fscosθ

W = 75 × 8 × cos 37°

W = 451.27 J

Work done by the frictional force

Ff = μkFn

The normal force

Fn = mg

Fn = 6 × 9.8

Fn = 58.8 N

Here,

Ff = μkFn

Ff = 0.28 × 58.8

Ff = 16.51 J

Work of friction:

W = Ff × s

W = 16.51 × 8

W = 132.1 J

The total work done on the block,

Wtotal = W + Wfriction

Wtotal = 451.27 + 132.1

Wtotal = 583.37 J

According to the work-energy theorem,

Wtotal = ΔKE

ΔKE = Wtotal

ΔKE = 583.37 J

Final kinetic energy of the block

Kf = KEFinal

Kf = ΔKE

Kf = 583.37 J

Kf = 308.98 J

Therefore, the final kinetic energy of the block is 308.98 J.

Complete question:

A 6 kg block is pushed 8m up a rough 37 degree inclined plane by a horizontal force of 75 N. The initial speed of the block is 2.2 m/s up the plane and a constant kinetic friction force of 25 N opposes the motion. Calculate the fianl kinetic energy of the block.

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students are experimenting with circuits in their physics class and they build the two working circuits pictured below. The battery in each circuit is identical and each bulb (resistor) they add provides the same amount of resistance.


They notice that every time they added bulb 3 (R3) to Circuit A, the brightness of all the bulbs dimmed but when they added bulb 3 (R3), nothing changed in the brightness of the bulb.  Which explanation of this observation is most complete?

Question options:

The brightness of the bulbs is all about the total amount of voltage at each resistor: less voltage = dimmer bulbs.  Circuit A is a series circuit, so the voltage of the battery is divided across all of the resistors.  Circuit B is a parallel circuit so the voltage across each resistor in parallel is the same as the battery. 

The brightness of the bulbs is all about the total amount of current in the circuit: less current = dimmer bulbs.  Circuit A is a series circuit, the more resistors you add, the less total current you get.  Circuit B is a parallel circuit so the more resistors you add, the more total current you get. 

The brightness of the bulbs is all about the total amount of resistance in the circuit: more resistance = dimmer bulbs.  Circuit A is a series circuit, so every time you add a resistor the total resistance increases.  Circuit B is a parallel circuit, so every time you add a resistor the total resistance decreases.

The brightness of the bulbs has to do with power which considers both the voltage and the current: less voltage x less current = dimmer bulbs.  In circuit A, the voltage is divided across the resistors and the current decreases as resistance increases.  In circuit B, the voltage is the same in each parallel section of the circuit and the current through that section of the circuit only depends on the resistor in that section.


students are experimenting with circuits in their physics class and they build the two working circuits

Answers

The complete observation about adding bulb 3 is the brightness of the bulbs has to do with power which considers both the voltage and the current: less voltage x less current = dimmer bulbs.  In circuit A, the voltage is divided across the resistors and the current decreases as resistance increases.  In circuit B, the voltage is the same in each parallel section of the circuit and the current through that section of the circuit only depends on the resistor in that section.

What is power of the circuit?

The power of the bulb or any resistor is equal to the product of voltage and  current flowing through it.

P = VI

Circuit A has bulbs in series while the circuit B has bulbs in parallel.

When bulb 3 added to circuit A,  the brightness of all the bulbs dimmed but when bulb 3 (R3) added to circuit B, nothing changed in the brightness of the bulb.

The brightness is depended on the power of the circuit. When both the voltage and current are less, the bulb will be dimmed. In circuit A, series resistors divide the voltage across them. In circuit B, voltage is equal for all the resistors.

Thus, the last option is correct.

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In typical game play situation, (with no overtime), when is a game over?
A. When both teams score
B. When there is a tie
C. When the time runs out
D. When the referee decides the game is over

Answers

C) When the time runs out (usually in sports such as soccer, but i don’t know what sport you’re referring to)

Answer:

C

Explanation:

Got it right on the test :)

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In typical game play situation, (with no overtime), when is a game over?A. When both teams scoreB. When

Ball P of mass of 0,16kg moving east at a speed of 10m.s collide head on with another ball Q of mass 0,2kg moving west at a speed of 15m.s. After the collision ball P moves west at a speed of 5m.s.

a. Calculate the velocity of the ball Q after the collision.

b. Calculate the magnitude of impulse of ball P during the collision

Answers

a) The momentum after collision of the ball Q is 12.8 m/s

b) The impulse on the ball P is 0.448 Ns.

What is the momentum?

We know that the momentum of the object can be obtained as the product of the mass and the velocity of the object. In this case, we can see that we have; Ball P of mass of 0,16kg moving east at a speed of 10m.s collide head on with another ball Q of mass 0,2kg moving west at a speed of 15m.s.

Given that;

Momentum before collision = Momentum after collision

(0.16 * 10) + (0.2 * 15) = (0.16 + 0.2) v

V = velocity after Collison

v = 1.6 + 3/0.36

v = 12.8 m/s

What is the impulse;

Impulse = Mv - Mu

Impulse = 0.16(12.8 - 10)

= 0.448 Ns

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As cars travel, oil and gasoline leaks onto the road surface. If a light rain falls, what does this do to the control of the car

Answers

When a light rain falls after oil and gasoline have leaked onto the road surface, it can cause the car to become less responsive and more difficult to control.

This is because the oil and gasoline act as a slippery layer on the road surface, which reduces the friction between the tires and the road. The rainwater can then mix with the oil and gasoline, making the layer even more slippery and reducing the vehicle's grip on the road.

To help mitigate this issue, drivers should be aware of their surroundings and the potential for slippery surfaces, and should adjust their speed and driving accordingly. Additionally, using tires with greater tread, or using more aggressive tires designed for wet and slippery conditions, can also help increase the vehicle's grip on the road.

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if a gun shoots a bullet straight up with an initial speed of 400 m/s, then how high will the bullet go? (8163 m) g

Answers

The height the bullet will reach is 8163 m. We use kinematic equations to find the result.

How to find the height of an object will reach?

In this case, the height the bullet will reach is determined by the initial speed, gravitational acceleration, and the time it is in the air. Using kinematic equations, the height of the bullet can be calculated as follows:

Initial vertical velocity, vi = 400 m/sGravitational acceleration, g = 9.81 m/sTime of flight, t = ?

Using the equation vf = vi + g × t, the final vertical velocity can be calculated as:

vf = 400 + 9.81 × t
vf = 0

Rearranging the equation and solving for t yields:

t = -400/9.81 = -40.7 s

The initial vertical velocity is equal and opposite to the final velocity, thus the time of flight is 40.7 s. To calculate the maximum height the bullet reaches, use the equation h = vi × t + 1/2 × g × t²:

h = 400 × (-40.7) + 1/2 × 9.81 × (-40.7)²
h = 8163 m

Therefore, the bullet will reach a maximum height of 8163 m.

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The _____ optical illusion contains a horizontal line terminating in inward- or outward-pointing arrowheads.

Answers

Answer:

Muller-Lyer optical illusion


Convert 5 x 105 into normal notation.

50,000

500,000

.00005

5,000,000

Answers

Answer:

5 * 10^5 = 5E5 = 500,000

Find the length of the curve for r(t)=⟨6t^3,−2t^3,−3t^3⟩ 1≤t≤2

Answers

The length of the curve for r(t) = ⟨\(6t^3, -2t^3, -3t^3\)⟩, 1 ≤ t ≤ 2 is approximately 20.26 units.

To find the length of the curve defined by the vector function r(t), we need to calculate the arc length integral over the given interval. The arc length integral formula is given by:

∫[a,b] √\((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 dt.\)

For the given vector function r(t) = ⟨\(6t^3, -2t^3, -3t^3\)⟩, we first need to find the derivatives of each component with respect to t:

dx/dt = \(18t^2\),

dy/dt = \(-6t^2\),

dz/dt = \(-9t^2\).

Now we substitute these derivatives into the arc length integral formula and integrate from t = 1 to t = 2:

∫[1,2] √(\((18t^2)^2 + (-6t^2)^2 + (-9t^2)^2\)) dt.

Simplifying the expression inside the square root:

√(\(324t^4 + 36t^4 + 81t^4\)) = √(\(441t^4\)) = \(21t^2\).\(6t^2\)

Integrating 21t^2 from 1 to 2:

∫[1,2] \(21t^2\) dt = [7\(t^3\)] from 1 to 2 = 7(\(2^3\)) - 7(1^3) = 56 - 7 = 49.

Therefore, the length of the curve for r(t) = ⟨\(6t^3, -2t^3, -3t^3\)⟩, 1 ≤ t ≤ 2 is approximately 49 units.

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What is the displacement of an object launched straight up into the air if it returns to its launch position?

Answers

Answer:

The displacement would be 0

Explanation:

The displacement is the shortest distance between two points, and the distance traveled is the actual distance. It would be zero because a ball thrown into the air would come down and the shortest distance is 0.

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