Identical point charges (+50 x 10 power -6C) are placed at the corners of a square with sides of 2.0-m length. How much external energy is required to bring a fifth identical charge from infinity to the geometric center of the square?

Answers

Answer 1

Answer:

636.4 J

Explanation:

The potential energy between one of the charges at the corner of the square and the fifth identical charge is U = kq²/r where q = charge = +50 × 10⁻⁶ C  and r = distance from center of square. = √2 m (since the midpoint of the sides = 1 m, so the distance from the charge at the corner to the center is thus √(1² + 1²) = √2)

Since we have four charges, the additional potential energy to move the charge to the centre of the square is U' = 4U = 4kq²/r

U' = 4kq²/r

= 4 × 9 × 10⁹ Nm²/C² (+50 × 10⁻⁶ C)²/√2 m

= 900 Nm²/√2 m

= 636.4 J

Answer 2

The total external energy required is 636.4 J.

Electric potential energy:

According to the question, a square of side a = 2m has 4 identical charges on the corners with charge Q = 50×10⁻⁶C.

A fifth identical charge is brought at the geometric center of the square. The geometric center is at the center of the diagonal:

[tex]r=\frac{a}{\sqrt{2} }=\sqrt{2}\;m[/tex]

The potential energy is a state function which means that it depends on the initial and final position.

Now the energy required is equal to the change in potential energy

[tex]\Delta U=\frac{1}{4\pi\epsilon_o}\frac{4Q^2}{r}\\\\\Delta U=\frac{4\times9\times10^9\times(50\times10^{-6})^2}{\sqrt{2} } \\\\\Delta U=636.4\;J[/tex]

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Related Questions

A cord is wrapped around the outer surface of the 8-kg disk. If a force of F = (1⁄4u2) N, where u is in radians, is applied to the cord, determine the disk’s angular acceleration when it has turned 5 revol

Answers

A cord is wrapped around the outer surface of the 8-kg disk. If a force of F = (1⁄4θ²) N, where θ is in radians, is applied to the cord, determine the disk’s angular acceleration when it has turned 5 revolutions. The disc has an initial angular velocity [tex]\omega _o = 1 \ rad/s[/tex] and radius from the center of the disc = 300 mm

Answer:

the angular acceleration = 205.706 rad/sec²

Explanation:

GIVEN THAT:

The disc mass = 8 kg

Force = [tex]\dfrac{1}{4} \ \ \theta ^2* N[/tex]

We are told that the given θ is in radians; Therefore; the when it has turned 5 revolutions; we have the θ to be:

[tex]\theta = 5 rev * (\dfrac{2 \ \pi * rad}{1 rev}) \\ \\ \theta = 10 \ \pi \ rad[/tex]

Also;

the initial angular velocity [tex]\omega _o = 1 \ rad/s[/tex]

radius from the center of the disc = 300 mm = 0.3 m

Thus; the mass moment about the Inertia can be determined via the following expression;

[tex]I_o = \dfrac{1}{2}*m*r^2[/tex]

[tex]I_o = \dfrac{1}{2}*8*0.3^2[/tex]

[tex]I_o = 0.36 \ kg/m^3[/tex]

Now to calculate the angular acceleration; we equate the sum of the moments acting on the Inertia;

SO:

[tex]\sum M_o = I_o \alpha[/tex]

[tex]F*0.3 = 0.36* \alpha[/tex]

[tex]\dfrac{1}{2}* \theta^2 *0.3 = 0.36* \alpha[/tex]

[tex]\alpha = 0.20836 \ \theta^2 \ rad/sec^2[/tex]

[tex]\alpha = 0.20836 \ (10 \ \pi )^2 \ rad/sec^2[/tex]

[tex]\alpha = 205.706 \ rad/sec^2[/tex]

Hence; the angular acceleration = 205.706 rad/sec²

An injured monkey sits perched on a tree branch 9 m above the ground, while a wildlife veterinarian is kneeling down in the bushes 90.0 m away attempting to subdue the monkey with a tranquilizer gun. The vet knows that the moment the gun fires, the monkey will be frightened and fall down from the branch. At what angle up from the ground must the veterinarian aim the gun so that the tranquilizer dart will hit the falling monkey? Given the angle, what is minimum speed at which the tranquilizer dart must leave the gun to still hit the monkey?

Answers

Answer:

The hunter should aim directly at the perched monkey because the tranquilizer dart will fall away from the line sight at the same rate that the monkey falls from its perch.

Tan theta = 9 / 90 = .1      so theta = 5.71 deg

The time for the monkey to reach the ground is

t = (2 h / g)^1/2 = (18 / 9.8)^1/2 = 1.36 sec

So the horizontal speed of the dart must be at least

Vx = 90 m / 1.36 sec = 66.4 m/s

Vx = V cos theta

V = 66.4 m/s / cos 5.71 = 66.7 m/s

The angle of projection of the tranquilizer dart is 5.7⁰

The horizontal speed of the tranquilizer dart is 66.5 m/s

The given parameters;

vertical position of the monkey, y = 9 mhorizontal position of the veterinarian, x = 90

The angle of projection of the tranquilizer dart is calculated as;

[tex]tan(\theta) = \frac{y}{x} \\\\tan(\theta) = \frac{9}{90} \\\\tan(\theta) = 0.1\\\\\theta = tan^{-1}(0.1)\\\\\theta = 5.71 ^0[/tex]

The speed of the tranquilizer dart is calculated as;

X = v₀ₓt

where;

t is the time to reach maximum height

X is the horizontal displacement = 90 m

The time to reach maximum height is calculated as;

[tex]h = v_0_yt + \frac{1}{2} gt^2\\\\h = 0 + \frac{1}{2} gt^2\\\\h = \frac{1}{2} gt^2\\\\t = \sqrt{\frac{2h}{g} } \\\\t = \sqrt{\frac{2\times 9}{9.8} } \\\\t = 1.36 \ s[/tex]

The horizontal speed of the tranquilizer dart is calculated as;

[tex]X = v_0cos(\theta) \times t\\\\90 = v_0\times cos(5.71) \times 1.36\\\\90 = 1.353 v_0\\\\v_0= \frac{90}{1.353} \\\\v_0 = 66.5 \ m/s[/tex]

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A lonely child is swinging on a rusty old swing set, as seen in the image provided. If friction does 145 J of work slowing the swing, what is the maximum speed she can reach?

Answers

Answer:

2.331

Explanation:

It just the change of Energy from potential (PE) to kinetic (KE)

PE on A = PE on B + KE on B + friction works (Wf)

mg(ha) = mg(hb) + ½mv² + Wf

35 * 9.8 * 1.5 = 35 * 9.8 * 0.8 + ½ * 35 * v² + 145

514.5 = 274.4 + 17.5v² + 145

514.5 - 274.4 - 145 = 17.5v²

17v² = 95.1

v² = 5.434

v =√5.434 = 2.331 m/s

A water distiller which is used to purify water. The distiller boils water and then condenses most of the water vapour back to water. (a) The water distiller is filled with 5.0 kg of water at 20 °C The specific heat capacity of water = 4 200 J/Kg °C Calculate the energy needed to raise the temperature of the water to 100 °C ___________________________________________________________________

Answers

Answer:

Energy needed 1680kJ

Explanation:

The quantity of heat required to raise the temperature of water to 100 degrees is expressed as

[tex]Q= mc(T2-T1)[/tex]

Given data

mass of water = 5kg

initial temperature T1= 20 °C

final temperature T2= 100 °C

Specific heat capacity of water=  4 200 J/Kg °C

[tex]Q= 5* 4 200(100-20)\\Q= 21000(80)\\Q= 1680000\\Q= 1680kJ[/tex]

PLEASE HELP. Really important

Answers

Explanation:

2) C would need the least effort, because the longer the effort distance, the least the effort applied.

How much energy (in Joules) is released when 12.0 g of water cools from 20.0 °C to 11.0 °C? This is a grade 10 question from the Climate unit (from Canada)

Answers

Answer: - 452.088joule

Explanation:

Given the following :

Mass of water = 12g

Change in temperature(Dt) = (11 - 20)°C = - 9°C

Specific heats capacity of water(c) = 4.186j/g°C

Q = mcDt

Where Q = quantity of heat

Q = 12g × 4.186j/g°C × - 9°C

Q = - 452.088joule

40 POINTS!!! + BRAINLIEST!!!

In your own words, explain how a pendulum demonstrates the concepts of the conservation of energy. (1 or 2 sentences long)

Answers

Answer:

I think it is better if you read and shortly write my explanation

Explanation:

simple pendulum with no friction, mechanical energy is conserved. Total mechanical energy is a combination of kinetic energy and gravitational potential energy. As the pendulum swings back and forth, there is a constant exchange between kinetic energy and gravitational potential energy.

What is the wavelength of a 1.28 x 10^17 Hz wave?

Answers

Answer:

The wavelength of the wave is 2.34 nm.

Explanation:

It is required to find the wavelength of a [tex]1.28\times 10^{17}\ Hz[/tex] wave. A wave moves with a speed of light. Speed of a wave is given in terms of wavelength and frequency. So,

[tex]v=f\lambda[/tex]

[tex]\lambda=\dfrac{c}{f}\\\\\lambda=\dfrac{3\times 10^8}{1.28\times 10^{17}}\\\\\lambda=2.34\times 10^{-9}\ m\\\\\text{or}\\\\\lambda=2.34\ nm[/tex]

So, the wavelength of the wave is 2.34 nm.

The wavelength of the wave is 2.34 × 10⁻⁹ meters.

Given the data in the question;

Frequency; [tex]f = 1.28*10^{17}Hz[/tex]

Wavelength; [tex]\lambda =\ ?[/tex]

To determine the wavelength of the wave, we use the expression for the relations between wavelength, frequency and speed of light.

[tex]\lambda = \frac{c}{f}[/tex]

Where [tex]\lambda[/tex] is wavelength, f is frequency and c is speed of light ( [tex]3*10^8m/s[/tex] )

We substitute our values into the equation

[tex]\lambda = \frac{3*10^8m/s}{1.28*10^{17}Hz} \\\\\lambda = \frac{3*10^8m/s}{1.28*10^{17}s^{-1}} \\\\\lambda = 2.34 * 10^{-9}m[/tex]

Therefore, the wavelength of the wave is 2.34 × 10⁻⁹ meters.

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3.
If you are part of a center or network, you can use program-level data to
A. change the way you record and maintain information.
B. identify professional development needs.
C. improve the management systems to support child learning.
D. change the way you speak with families

Answers

Answer:

A

Explanation:

Answer: A

Explanation:

potential energy is frequintly converted into kenetic energey. kenetic energey

Answers

Answer:

When an object falls, its gravitational potential energy is changed to kinetic energy. ... Gravitational potential energy for a mass m at height h near the surface of the Earth is mgh more than the potential energy would be at height 0. (It's up to you where you choose height 0.)

Explanation:

Answer:

Qwertyujiknb vcdxrftyhbvcdxrft6y7uij

Explanation:

A) Is it possible for an object that, object with zero acceleration have velocity? If yes give an example if not give its proof.

Answers

Answer:

Yes, in case of uniform velocity

Explanation:

This is the case of uniform velocity. If a body covers equal displacement in equal intervals of time, then the velocity of a body is said to be ‘Uniform Velocity’. It meas that the velocity of a body remains constant during the motion and it does not change.

Since, acceleration is defined as the rate of change of velocity.

Therefore, if there is no change in velocity or in other words the change in velocity is zero, then the acceleration is also zero.

a = ΔV/t = 0/t

a = 0 m/s²

So, the acceleration of the body is 0 m/s², but it has a uniform velocity

Hence, it is possible for an object that, object with zero acceleration have velocity, which is the case case of uniform velocity.

Which of the following characterizes the particles in this diagram?

A. Two positive charges
B. One positive charge and one negative charge
C. Two negative charges
D. Two neutral charges

Answers

Answer:

B

Explanation:

One positive charger and one negative charger

Which of these would not improve accuracy? 

A)Taking a bigger sample size

B)Using a bigger range of the independent variable

C)Using measuring instruments that can read to a greater number of decimal places

D)Remove anomalies​

Answers

I think it’s D, mostly just because all the other ones seem like they couldn’t be the answer.
It’s not D, it’s B. Using a bigger range would mean there’s a greater expanse of answers, not a precise, accurate reading. Removing anamalies would make it more accurate- they’re results that don’t fit the pattern, so removing them would make the results even more results. Therefore, the answer is B. Hope this helps!

A closed-pipe resonator has a length of 1.73 m. The frequency of its second harmonic if the speed of sound is 343 m/s is: a)49,5 Hz b)99.13 Hz c)20.6 Hz d)72 Hz

Answers

Answer:

There is no answer, since a closed-pipe resonator can NOT have a second harmonic. However, if you were to plug the pipe length and the speed of sound into the closed-pipe equation anyway you would get 49.56 as your fundamental frequency, which means that 99.13 would be your "plug and play" 2nd harmonic.

Explanation:

A car is traveling in a race. The car went from the initial velocity of 35 m/s to the final velocity of 65 m/s in 5 seconds. What
is the acceleration?
-13 m/s
-6 m/s²
6mis?
13 m/s2

Answers

Acceleration = (change in speed) / (time for the change)

Change in speed = (speed after the change) - (speed before the change)

Change in speed = (65 m/s) - (35 m/s)  =  30 m/s

Acceleration = (30 m/s) / (5 s)

Acceleration = 6 m/s²

would iron and carbon form metallic bonds

Answers

Answer:

NO.

Explanation:

METALLIC BOND IS ONLY IN METALS.

Since iron is a metal and carbon a non- metal, they cannot form a metallic bond.

a vector points 12.0 units along the x-axis and 9.00 units along the y-axis. find the magnitude of the vector

Answers

Explanation:

R = [tex]\sqrt{(12.0)^{2} + (9.00)^{2}}[/tex] = 15 UNIDADES

The amplitude of a particle executing simple harmonic motion is 5cm, while its angular velocity is 10 rads -1 . Calculate the magnitude of the maximum acceleration of the particle.

Answers

Answer:

a_max = 50 cm/s^2

Explanation:

To find the magnitude of the maximum acceleration of the particle, you take into account the equation of motion in a simple harmonic motion:

[tex]x=Acos(\omega t)[/tex]

ω: angular velocity = 10 rad/s

A: amplitude = 5 cm

The acceleration is given by:

[tex]a=\omega^2 x[/tex]

and the maximum acceleration is obtained when the cosine function is maximum, that is, when cos(wt) = 1. Then, you have:

[tex]a_{max}=\omega^2 x_{max}=\omega^2A[/tex]

Then, you replace the values of w and A in order to calculate a_max:

[tex]a_{max}=(10rad/s)^2(5cm)=50\frac{cm}{s^2}[/tex]

hence, the maximum acceleration is 50 cm/s^2

Ethan pushes a wooden box across a carpeted floor. Then he pushes the same box across a smooth marble floor. Why does Ethan find it easier to push the box on the marble floor than on the carpeted floor?

A. The box experiences more friction on the marble floor.
B.The box experiences less friction on the marble floor.
C.The box experiences more applied force on the marble floor.
D.The box experiences less normal force on the marble floor.

Answers

Answer:

B.The box experiences less friction on the marble floor

Explanation:

Answer:

B. The Box experiences less friction on the marble floor

Explanation:

This is because the the carpet is not a flat surface and the marble is smooth

Assume that a machine puts out 8000 joules of work when the user puts in 10,000 joules of work. What is the efficiency of the machine?

Answers

Answer:

80 Percent

Explanation:

E=energy output/energy input×100

E=8000/10000×100

E=0.8×100

E=80 percent.

Mark brianliest if my answer suit your question

If the machine put, in 8000 J, and the user puts 10,000 J of work then the efficiency of the machine will be equal to 80%.

What is Work?

Work is a physics term used to describe the transfer of energy that takes place when an object changes above a distance because of an external force, at least some of which is given in the vector of the dislocation. The element of the force acting all along the path multiplied by the length of the path can be used to calculate work if the force is constant.

Mathematically, this idea is expressed as W = fd, where W is the effort and f is the force multiplied by d, the distance. Work is completed whenever the force is applied at an angle with about the displacement.

As per the data provided in the question,

Total input energy = 10,000 J

Total output energy = 8,000 J

Then, the efficiency (η) of the machine will be,

η = (output energy/input energy) × 100

η = 8000/10000 × 100

η = 80%.

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a motorcar is moving with a velocity of 108 km / h and it takes 4s to stop after the brakes are applied calculate the force exerted by the brakes on the motorcar if it's mass along with the passengers is 1000 kg​

Answers

Answer:

-7500 N

Explanation:

v₀ = 108 km/h = 30 m/s

v = 0 m/s

t = 4 s

a = Δv / Δt

a = (0 m/s − 30 m/s) / 4 s

a = -7.5 m/s²

F = ma

F = (1000 kg) (-7.5 m/s²)

F = -7500 N

Answer:-7500

Explanation v₀ = 108 km/h = 30 m/s

v = 0 m/s

t = 4 s

a = Δv / Δt

a = (0 m/s − 30 m/s) / 4 s

a = -7.5 m/s²

F = ma

F = (1000 kg) (-7.5 m/s²)

F = -7500 N

conditions for equilibriam

Answers

Statics is the study of forces in equilibrium. Two conditions must be met to achieve equilibrium, which is defined to be motion without linear or rotational acceleration. The first condition necessary to achieve equilibrium is that the net external force on the system must be zero, so thatnet F=0. net F = 0 .

what is a depletion layer​

Answers

Depletion region or depletion layer is a region in a P-N junction diode where no mobile charge carriers are present. Depletion layer acts like a barrier that opposes the flow of electrons from n-side and holes from p-side.

Explain how series circuits use current and voltage and Explain how parallel circuits use current and voltage

Answers

'''In a series circuit, the sum of the voltages consumed by each individual resistance is equal to the source voltage. Components connected in parallel are connected along multiple paths so that the current can split up; the same voltage is applied to each component.''

right auricale is bigger then left aurical, why?

Answers

Explanation:

Veins carry deoxygenated blood from different parts of the body to our heart. ... Since a larger volume of blood is collected in the right auricle than that of the left auricle, right auricle is larger than the left auricle.

what are two things that are infinite?

Answers

Answer:

Infinity = Never ending

Explanation:

The universe could be infinite, both in terms of space and time, but there is currently no way to test whether it goes on forever or is just very big. The part of the universe we are able to observe is finite, measuring about 46 billion light years in diameter.

The set of natural numbers is an infinite set. This kind of infinity is, by definition, called countable infinity. All sets that can be put into a bijective relation to the natural numbers are said to have this kind of infinity. This is also expressed by saying that the cardinal number of the set is aleph-naught (ℵ0).

Hope this helps. Mark as brainliest!

STARS ARE INFINITE , NUMBERS ARE INFINITE

Explanation:

a motorcar is moving with a velocity of 108 km / h and it takes 4s to stop after the brakes are applied calculate the force exerted by the brakes on the motorcar if it's mass along with the passengers is 1000 kg​

Answers

Answer: - 7500N

Explanation:

Given the following :

Initial Velocity of car = 108km/hr

Time taken to stop after applying brakes = 4s

Mass of passengers in car = 1000kg

Force exerted by the brakes on the car =?

After 4s, then final Velocity (V) = 0

Initial Velocity (u) of the car = 108km/hr

108km/hr = (108 × 1000)m ÷ (3600)s = 30m/s

Force exerted = mass(m) × acceleration(a)

Acceleration of car = Change in Velocity with time

a = (v - u) / t

a = (0 - 30) / 4

a = - 30/ 4

a = - 7.5m/s^2

Therefore,

Force exerted = mass(m) × acceleration(a)

Force exerted = 1000kg × (-7.5)m/s^2

Force exerted = - 7500N

Answer:

The force exerted by the brakes on the motor car is -7500 N.

Explanation:

Given :-

Mass of the motor car along with passengers (m)= 1000 kgInitial velocity (u) = 108 km/hTime taken (t) = 4 s

To find :-

The force exerted by the brakes on the motor car.

Solution :-

Since the car stops, the final velocity (v) will be 0 m/s.

• Initial velocity (u) = 108 km/h.

Converting initial velocity into m/s.

We know that,[tex] \sf{1\:km/h=\dfrac{5}{18}\:m/s}[/tex]

Then initial velocity,

= [108 × 5/18 ] m/s

= 30 m/s

Now find the force exerted by the brakes.

Formula used :

[tex]{\boxed{\sf{F=\dfrac{m(v-u)}{t}}}}[/tex]

   [put values]

[tex]:\implies \sf \: F= \dfrac{1000(0 - 30)}{ 4} \\ \\ : \implies \sf \: F \: = \dfrac{ - 30000}{4} \\ \\ : \implies \sf \: F \: = - 7500[/tex]

The force exerted by the brakes on the motor car = -7500 N.

•The negative sign of force(F) means that the force was applied in opposite direction of motion.

__________________

Benda setinggi 3 cm diletakkan pada jarak 10 cm di depan cermin cekung yang berjari-jari


kelengkungan 10 cm. Tentukan:


 Jarak bayangan


 Perbesaran bayangan


 Sifat bayangan

Answers

Answer:

a) Shadow distance

10 cm in front of the mirror.

b) Zoom in the shadow

The shadow formed is the same height as the object and is placed also at the centre of curvature of the mirror as shown in the attached image to this solution.

c) The nature of the shadow

The shadow formed is real, inverted, same size as the object and formed at the centre of curvature.

Explanation:

English Translation

Objects as high as 3 cm are placed at a distance of 10 cm in front of a concave mirror with 10 cm curvature. Determine:

a) Shadow distance

b) Zoom in the shadow

c) The nature of the shadow

Solution

The mirror equation is given as

(1/f) = (1/v) + (1/u)

f = focal length of the mirror = (radius of curvature)/2 = 10/2 = 5 cm

v = image distance = ?

u = object distance = 10 cm

We can then calculate the shadow' s distance from the mirror thus

(1/5) = (1/v) + (1/10)

(1/v) = 0.2 - 0.1 = 0.1

v = (1/0.1) = 10 cm

b) Zoom in the shadow

Since the object is placed at the centre of curvature, as shown in the attached image, the image is formed at a point of intersection of rays. The image formed is the same height as the object and is placed also at the centre of curvature of the mirror.

c) The nature of the shadow

Since the mirror is a concave mirror, the image is real and formed in front of the mirror. The image is also inverted and formed at the centre of curvature of the mirror.

Hope this Helps!!!

Just need the answer to D please

Answers

The boat has to pull with MORE force. Don't forget about the force of friction with the water, pulling the skier in the backwards direction. The force that accelerates him is the NET force ... boat force minus water resistance. So the boat force has to be greater than the net accelerating force.

a care starting from rest has an acceleration 0.3 m/s square, calculate the velocity and distance travelled by this car after 2 minutes?

Answers

Answer:

Final velocity (v) = 36 m/s

Distance traveled (s) = 2,160 m

Explanation:

Given:

Initial velocity (u) = 0

Acceleration (a) = 0.3 m/s

Time travel (t) = 2 minutes = 120 seconds

Find:

Final velocity (v) = ?

Distance traveled (s) = ?

Computation:

v = u + at

v = 0 + 0.3(120)

v = 0.3(120)

v = 36 m/s

Final velocity (v) = 36 m/s

Distance traveled (s) = ut + (1/2)at²

Distance traveled (s) = (0.5)(0.3 × 120 × 120)

Distance traveled (s) = 2,160 m

Other Questions
Can someone please write a short summary of early colonial governmental policies that are still in use today?Please and thank you Find the volume of a right circular cone that has a height of 8.1 in and a base with a diameter of 7.6 in. Round your answer to the nearest tenth of a cubic inch. Superman is jogging alongside the railroad tracks on the outskirts of Metropolis at 100 km/h. He overtakes the caboose of a 500-m-long freight train traveling at 50 km/h. At that moment he begins to accelerate at 10 m/s2. How far will the train have traveled before Superman passes the locomotive? A ride-sharing car moving along a straight section of road starts from rest, accelerating at 2.00 m/s2 until it reaches a speed of 28.0 m/s. Then the vehicle moves for 41.0 s at constant speed until the brakes are applied, stopping the vehicle in a uniform manner in an additional 5.00 s. (a) How long is the ride-sharing car in motion (in s)? (b) What is the average velocity of the ride-sharing car for the motion described? (Enter the magnitude in m/s.) A roof has the shape of an isosceles triangle with equal sides 8 cm long and base 12 m long. What is the measure of the angle of inclination of the roof to the nearest degree? 25 POINTS!!!!Which of the following statements are true? Select all that apply.A + B = B + AC - D = D - CB + 0 = BE - C = E + (-C)|A| = |E| HELP FAST 32 as a mixed radical What is the correct definition of the word militia?A. a shortage, something is in short supplyB. rights to ownership of land, sometimes a formal documentC. a group of armed citizens able to fight to protect their communityD. a period of poor economy, involving job losses, stock martket loss, and financial trouble el poema un dia de Alaide foppa y a quien va dirigido Which of these is the CORRECT description of Rome's relative location on this map?A)west of Rome B)south of Berlin C)41N, 13E D)41N, 13W Ist dein Freund ____ Hause? zum zu nach zur Need some help with a few consecutive integer word problems, tysm if you do :)The sum of three consecutive odd integers is -57. Find the integers.A. -19, -17, -15B. -19, -21, -23C. -21, -19, -17D. -21, -23, -25Three times the greater of two consecutive odd integers is 5 less than 4 times the smaller. Find the integers.A. 8, 9B. 7, 9C. 11, 13D. 3, 5Five times the smaller of two consecutive odd integers is 11 more than 4 times the greater. Find the integers.A. 13, 15B. -7, -5C. -7, -9D. 19, 21 Pls answer this correctly The number of pieces of popcorn in a large movie theatre popcorn bucket is normally distributed, with a mean of 1720 and a standard deviation of 20. Approximately what percentage of buckets contain between 1680 and 1760 pieces of popcorn? Approximately 68% Approximately 75% Approximately 95% 99.7% A manufacturer produces 1,000 basketballs each day, which it sells to customers for $30 each. All costs associated with production and sales total $10,000; however, if the manufacturer were to produce one additional basketball per day, total costs would increase to $10,100. From these amounts, we can tell that:________a. the firm has negative profit.b. marginal cost equals $100.c. marginal cost equals $150.d. marginal cost equals marginal revenue. which is a correct first step in solving the inequality-4(2x-1)>5-3x I need help in this ASAP!!!! Options first blank : Battle of Austerlitz, Peninsular War & battle of Waterloo, second blank: Spain, Sicily & Britain and third blank : Moscow, Sweden & Portugal . 1. At a leather shop, 50 leather jackets were sold in February. The shop keeper at the store wants to encourage the sales team to sell more leather jackets by giving all the sales team members a bonus if the number of leather jackets sold increases by 30% in March. How many leather jackets must the sales team sell in March to receive the bonus? Please HELP!!!!!!! PLEASE Evaluate the existentialist dictum that existence precedes essence. PLEASE HELP ME ASAP!! IVE BEEN TRYING TO SOLVE THESE FOR 2 HOURS NOW!! :(I WILL GIVE ALL 80 OF MY POINTS!! PLEASE AND THANK YOU SO MUCH!!!