how would the gravitational force at the surface of star michael change if star michael contracted to one-sixth of its previous diameter, without losing any of its mass

Answers

Answer 1

The gravitational force at the surface of Star Michael will increase if the star contracts to one-sixth of its previous diameter without losing any of its mass.

According to Newton’s law of gravitation, the gravitational force between two objects is inversely proportional to the square of the distance between their centers and proportional to the product of their masses. This means that as the distance between two objects decreases, the gravitational force between them increases and vice versa.

Since the mass of Star Michael remains constant, the force of gravity will increase significantly due to the decrease in the distance between the objects. This is because the gravitational force decreases with the square of the distance between two objects.

As the radius of Star Michael decreases to one-sixth of its previous size, its surface gravity will increase by a factor of 36 (6^2).This means that the surface gravity will be about 36 times stronger than it was before the contraction.

Therefore, if Star Michael contracted to one-sixth of its previous diameter without losing any of its mass, the gravitational force at its surface would be more significant, and it would be much harder for an object to escape its gravitational pull.

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Related Questions

Brian has an object suspended in the air. It has a mass of 100 kg and is 25 meters above the ground. What is the object’s potential energy?

Answers

Explanation:

the PE = Weight x g x Height above ground where g is the gravitational constant (9.8m/s^2)

so tge PE = 100 x 9.8 x 25 = 24500 J

the drawing shows an exaggerated view of a rifle that has been"sighted in" for a 91.4-meter target. If the muzzle speed of thebullet is v0 = 427 m/s, what are the two possible anglesθ1 and θ2 between the rifle barreland the horizontal such that the bullet will hit the target? One ofthese angles is so large that it is never used in target shooting.(HInt: the following trigonometric identity may be useful: 2 sinθ cos θ = sin 2 θ.)

Answers

The two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target are given by:θ1 = (-1/2) [arctan(2a/(-b - √(b^2 - 4ac))) + π/2 + nπ] andθ2 = (-1/2) [arctan(2a/(-b + √(b^2 - 4ac))) + π/2 + nπ]where n is an integer.

In the given case, the figure shows an exaggerated view of a rifle that has been sighted in for a 91.4-meter target. Let the muzzle speed of the bullet be v0 = 427 m/s.

Now, we are required to find the two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target.

It is known that the horizontal displacement of the bullet from the gun can be given by the equation: x = v0 t cosθ ..........(i)and the vertical displacement of the bullet from the gun can be given by the equation: y = v0 t sinθ - (1/2) g t^2..........(ii).

Here, t is the time of flight of the bullet and g is the acceleration due to gravity.

As the bullet hits the target, its final vertical displacement from the gun is equal to the height of the target, i.e.,y = 91.4m.Now, we can substitute equations (i) and (ii) in place of t and y in equation (ii) to get:x tanθ - (g/2v0^2) x^2 sec^2θ = 91.4 ..........(iii)This is a quadratic equation in tanθ.

On solving this equation using the quadratic formula, we get:tanθ = [-b ± √(b^2 - 4ac)]/2aWhere,a = -gx^2/(2v0^2) = -4.9x^2/v0^2, b = x, and c = -91.4.

Rearranging the terms, we get:2a tanθ^2 + b tanθ - 91.4 = 0On substituting the given values, we get:2(-4.9x^2/v0^2) tanθ^2 + x tanθ - 91.4 = 0θ1 and θ2 are the two possible angles which can be found by solving the above quadratic equation.

Using the trigonometric identity given in the hint, we can write: sin 2θ = 2 sinθ cos θ = 2 tanθ/ (1 + tan^2θ)Now, we can substitute tanθ = (-b ± √(b^2 - 4ac))/2a in the above equation to get: sin 2θ = (-4bx ± 2x√(b^2 - 4ac))/(b^2 + 4a^2)Now, we can substitute the given values to get: sin 2θ1 = -0.999sin 2θ2 = 0.998.

Thus, we get two values of sin 2θ, one is close to -1 and the other is close to 1. As sin 2θ = -1 when 2θ = -π/2 + nπ and sin 2θ = 1 when 2θ = π/2 + nπ, where n is an integer, we get two possible values of θ for each of these two cases.

Hence, the two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target are given by:θ1 = (-1/2) [arctan(2a/(-b - √(b^2 - 4ac))) + π/2 + nπ] andθ2 = (-1/2) [arctan(2a/(-b + √(b^2 - 4ac))) + π/2 + nπ]where n is an integer.

As one of these angles is so large that it is never used in target shooting, we only need to consider the other angle.

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The two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target are given by:θ1 = (-1/2) [arctan(2a/(-b - √(b^2 - 4ac))) + π/2 + nπ] andθ2 = (-1/2) [arctan(2a/(-b + √(b^2 - 4ac))) + π/2 + nπ]where n is an integer.

In the given case, the figure shows an exaggerated view of a rifle that has been sighted in for a 91.4-meter target. Let the muzzle speed of the bullet be v0 = 427 m/s.

Now, we are required to find the two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target.

It is known that the horizontal displacement of the bullet from the gun can be given by the equation: x = v0 t cosθ ..........(i)and the vertical displacement of the bullet from the gun can be given by the equation: y = v0 t sinθ - (1/2) g t^2..........(ii).

Here, t is the time of flight of the bullet and g is the acceleration due to gravity.

As the bullet hits the target, its final vertical displacement from the gun is equal to the height of the target, i.e.,y = 91.4m.Now, we can substitute equations (i) and (ii) in place of t and y in equation (ii) to get:x tanθ - (g/2v0^2) x^2 sec^2θ = 91.4 ..........(iii)This is a quadratic equation in tanθ.

On solving this equation using the quadratic formula, we get:tanθ = [-b ± √(b^2 - 4ac)]/2aWhere,a = -gx^2/(2v0^2) = -4.9x^2/v0^2, b = x, and c = -91.4.

Rearranging the terms, we get:2a tanθ^2 + b tanθ - 91.4 = 0On substituting the given values, we get:2(-4.9x^2/v0^2) tanθ^2 + x tanθ - 91.4 = 0θ1 and θ2 are the two possible angles which can be found by solving the above quadratic equation.

Using the trigonometric identity given in the hint, we can write: sin 2θ = 2 sinθ cos θ = 2 tanθ/ (1 + tan^2θ)Now, we can substitute tanθ = (-b ± √(b^2 - 4ac))/2a in the above equation to get: sin 2θ = (-4bx ± 2x√(b^2 - 4ac))/(b^2 + 4a^2)Now, we can substitute the given values to get: sin 2θ1 = -0.999sin 2θ2 = 0.998.

Thus, we get two values of sin 2θ, one is close to -1 and the other is close to 1. As sin 2θ = -1 when 2θ = -π/2 + nπ and sin 2θ = 1 when 2θ = π/2 + nπ, where n is an integer, we get two possible values of θ for each of these two cases.

Hence, the two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target are given by:θ1 = (-1/2) [arctan(2a/(-b - √(b^2 - 4ac))) + π/2 + nπ] andθ2 = (-1/2) [arctan(2a/(-b + √(b^2 - 4ac))) + π/2 + nπ]where n is an integer.

As one of these angles is so large that it is never used in target shooting, we only need to consider the other angle.

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which of the following best represents force?
1-a push or a pull acting on a object.
2-a push or a pull always causing acceleration.
3-a push or a pull action without an object.
4-a push or a pull always causing motion

Answers

Answer:

1 -a push or a pull acting on a object.

Explanation:

force is a push or pull acting upon an object as a result of its interaction with another object.

Match each section of the velocity-Time Graph with the correct description

Match each section of the velocity-Time Graph with the correct description

Answers

The slope of a velocity-time graph gives the acceleration of the object.

A - The part A shows that there is no increase in the velocity of the object. That means the object is at rest.

B - In the part B of the graph, it is shown that the velocity of the object is increasing linearly. That means, the velocity is changing, thus the object has an acceleration in the positive direction.

C - In the part C of the graph, it is shown that there is no change in the velocity of the object, but it is moving with a non-zero velocity. Therefore, we can say that the object is moving with a constant speed.

D - In the part D of the graph, it is shown that the velocity of the object is decreasing linearly. That means the object is having a negative acceleration, but in the positive direction.

E - In the part E of the graph, it is shown that the velocity of the object is again increasing from zero, but in the opposite direction.

F - In the part C of the graph, it is shown that the object is moving with a constant velocity, but in the opposite direction.

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Sample Problem EAn electric space heater is connected across a 120 V outlet. The heater dissipates 1320 W of power in the form of electromagnetic radiation and heat. Calculate the resistance of the heater.

Answers

The resistance of the heater is 10.3 ohms.

The power (P) dissipated by the electric space heater is given by the formula P = V²/R, where V is the voltage across the heater and R is the resistance of the heater. In this case, the power is given as 1320 W and the voltage is given as 120 V. So we can rearrange the formula to solve for the resistance: R = V²/P. Substituting the given values, we get R = (120 V)² / 1320 W = 10.3 ohms. Therefore, the resistance of the heater is 10.3 ohm

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When momentum is transferred from one object to another, their combined momentum remains the same. * True or False​

Answers

Answer:

true

Explanation:

hope this helps

While in empty space, an astronaut throws a ball at a velocity of 11 m/s. What will the velocity of the ball be after it has traveled 7 meters? A. 0 m/s B. 4 m/s C. 18 m/s D. 11 m/s\

Answers

The ball will have a constant velocity of 11 m/s.

Since there is no gravity in space, the ball is not subject to the effects of gravity.

Thus, there is no acceleration acting on the ball in space. So, there is no change in velocity with time.

Therefore, the ball will move with a constant velocity of 11 m/s in space even after travelling 7 meters.

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in addition to studies of the body system of corals what studies in earth science might increased scientists understanding of an ability to predict coral bleaching

Answers

Answer: they could get a piece of the coral and run tests on it

Explanation:

2. A tower is 15.24 m high. At a certain distance away from the tower, an observer
determines that the angle of elevation to the top of it is 41°. How far is the observer
from the base of the tower?

Answers

Explanation:

Opposite side from the 41° angle = 15.24m

We wish to find the adjacent side (horizontal length)

Therefore 15.24m / tan41° = 17.53m.

What is the force of friction acting on the crate? I am offering 30 points.

What is the force of friction acting on the crate? I am offering 30 points.

Answers

I think the answer is C


Why do stars more massive than the sun have a higher surface temperature than the sun?.

Answers

Answer:

Stars that are more than 40 times more massive than our Sun, cannot expand into a red supergiant. This is because they burn too quickly and lose their outer layers fast. They will reach the blue supergiant stage, or perhaps yellow hypergiant, before returning to become hotter stars.

Explanation:

Answer:

Cause there bigger so they have a more hotter surface.

Determine the energy conversion for the following:
a. Light bulb
b. Firework
c.flute
d. Leaf

Answers

Answer:

the answer is b.

because it will use energy and maybe its letter A.

plsss pa brainliest po ako

and also youre welcome

Answer:

a. Light bulb - electrical to light

b. Firework - chemical to light / thermal / sound

c. Flute - kinetic to sound

d. Leaf-  solar to chemical

A motorcyclist starts from rest and reaches a speed of 6m/s after travelling with constant acceleration for 3s. What is his acceleration?

Answers

As given, the motorcyclist starts from rest and reaches a speed of 6 m/s

after traveling with uniform acceleration for 3 seconds.

Here, initial velocity u=0

Final velocity v=6 m/s

Time t=3 sec.

Let the acceleration of the motorcycle be a.

On using the equation of motion, v=u+at

6=0+3×a

Or 3a=6

Or a=63

Or a=2 m/s2

→Therefore, the acceleration in a motorcycle is 2 m/s2.←

PLSS HELP!!! this is my physical science work

PLSS HELP!!! this is my physical science work

Answers

a. Sidewalk

b. Train

c. Trees or buildings

d. Train

e. Hot air balloon

Please select the word from the list that best fits the definition

state of most nonmetals at room temperature

options: left, gas, semiconductor, halogen, right, solid, carbon nitrogen

Answers

Answer:

the answer is gas if I'm not mistaken.

Explanation:

Don't come at me if I'm wrong please :')

Select the correct answer. A car is moving at a constant speed along a straight line. Which statement is true about the forces acting on the car? A. The net force acting on the car from all directions is zero. B. The net force acting on the car is greater than the car's weight. C. The net force acting on the car is in the direction of the car's motion. D. The net force acting on the car is in the opposite direction of the car's motion.

Answers

Answer:

i think try theanswer

Explanation:

proper

Answer:

A

Explanation:

For an object to move with constant speed the forward force is opposed by the effects of forces. There is no resultant force acting or constant speed is a result of no resultant force.

Newton's second law states that an object with no net forces acting on it which is initially at rest will remain at rest. If it is moving, it will continue to move in a straight line with constant velocity. Newton's Second Law states: F = ma. F is the net force acting on an object.

Also if velocity or speed is constant the acceleration will be 0 the F=m×0

F=0.

gravitational potential energy depends on the of the object? group of answer choices mass and movement height, mass and the gravitational constant friction and movement height and friction

Answers

Gravitational energy depends upon the height, mass and the gravitational strength of the object.

Gravitational energy is the potential energy held via an item due to its high function in comparison to a lower function. In different phrases, it's miles strength associated with gravity or gravitational pressure.

For the gravitational force the method is P.E. = mgh, wherein m is the mass in kilograms, g is the acceleration due to gravity (9.8 m / s2 on the surface of the earth) and h is the height in meters. Note that gravitational capacity electricity has the identical devices as kinetic strength, kg m2 / s2.

Newton's regulation of gravitation: This law states that every factor mass inside the universe draws every different factor mass with a pressure this is immediately proportional to the made from their masses and inversely proportional to the rectangular of the space between them.

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s the elastic potential energy stored in the pole of a pole vaulter the only the only type of potential energy involved in pole-vaulting? group startsyes or noyes, unselectedno, unselected

Answers

No, the elastic potential energy stored in the pole of a pole vaulter is not the only type of potential energy involved in pole-vaulting.

In pole-vaulting, there are multiple forms of potential energy involved. While the elastic potential energy stored in the pole plays a crucial role, other forms of potential energy include gravitational potential energy and kinetic energy.

1. Elastic Potential Energy: The pole used in pole-vaulting is typically made of flexible materials, such as fiberglass or carbon fiber, which store elastic potential energy when bent or compressed. This stored energy is then released, propelling the vaulter upwards.

2. Gravitational Potential Energy: As the vaulter reaches the highest point of their vault, they have gained gravitational potential energy due to their increased height above the ground. This potential energy is converted into other forms of energy as the vaulter descends.

3. Kinetic Energy: Throughout the vaulting process, the vaulter's body also possesses kinetic energy, which is the energy of motion. The vaulter's initial speed and subsequent acceleration contribute to their kinetic energy, allowing them to gain momentum and clear the bar.

Therefore, while the elastic potential energy stored in the pole is an important component, there are other forms of potential energy involved in pole-vaulting, namely gravitational potential energy and kinetic energy.

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A tennis ball is dropped from 1.3 m above
the ground. It rebounds to a height of
0.943 m.
With what velocity does it hit the ground?
The acceleration of gravity is 9.8 m/s². (Let
down be negative.
Answer in units of m/s.
part 2 of 3​

Answers

Answer:

2.65m/s

Explanation:

Using the equation of motion:

v² = u²+2a∆S where

v is the final velocity

u is the initial velocity

∆S is the change in distance

a is the acceleration

Given

u = 0m/s

a = 9.8m/s²

∆S = 1.3-0.943

∆S = 0.357m

Substituting the given parameters into the formula

v² = 0²+2(9.8)(0.357)

v² = 0+6.9972

v² = 6.9972

v=√6.9972

v = 2.65m/s

Hence the velocity at which it hit the ground is 2.65m/s

An action/reaction pair of forces ....
Select all that are True.
act on the same object.
point in the opposite direction.
act on two different objects.
point in the same direction.

Answers

Action-reaction pairs are forces that operate on separate objects in opposing directions and at identical magnitudes. Never do they affect the same thing. We learn that forces are interactions from Newton's third law.

An action-reaction pair is what?

When two bodies contact, they exert an equal and opposite force on one another in accordance with Newton's third rule of motion. Action-reaction forces are made up of these forces.

What do action and reaction forces look like in practice?

Think about how a baseball bat and a ball interact, for instance. The bat forces the ball to the right while the baseball forces the bat to the left. The action-reaction force pair is made up of these two forces acting on two separate objects together.

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1. Your friend tells you that the time-dependence of their car's acceleration along a road is given by a(t) = yt² + yt, where is some constant value. Why must your friend be wrong? (10 points) 2. A p

Answers

Your friend must be wrong because the time-dependence of acceleration is given by the derivative of velocity with respect to time, not the time itself. The equation a(t) = yt² + yt does not represent the correct relationship between acceleration and time.

Acceleration is defined as the rate of change of velocity with respect to time. In mathematical terms, it is the derivative of velocity with respect to time, denoted as a(t) = dV/dt. Therefore, the equation a(t) = yt² + yt provided by your friend does not represent the correct relationship between acceleration and time.

To determine the correct relationship, we need to integrate the equation for acceleration to obtain the velocity function. Given that a(t) = yt² + yt, integrating both sides with respect to time gives V(t) = (1/3)yt³ + (1/2)yt² + C, where C is the constant of integration. However, this equation represents the velocity as a function of time, not the acceleration.

Your friend's equation a(t) = yt² + yt for the time-dependence of acceleration is incorrect. Acceleration is the derivative of velocity with respect to time, not a function of time itself. The correct relationship can be obtained by integrating the acceleration equation, yielding the velocity as a function of time.

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The engine of a motorcycle changes the speed of the motorcycle from 16 m/s to 20 m/s in 10.0 s. The mass of the motorcycle is 300 kg.

What is the acceleration of the motorcycle **use a kinematic equation**?


What net force must the engine be producing?


If there is a frictional force pushing backwards at -50 N, what force must the engine produce to produce the same change in speed **Think how you would get the net force with this -50N?

Answers

In which layer of the atmosphere is the ozone layer?

Mesosphere
Stratosphere
Thermosphere
Troposphere

A toy car is moved 8m, right, then 1.5m, right, and finally 3.0m, left. If it took 5.0 seconds total for the car to travel its 3 routes, then what is the average speed of the toy car?

Answers

Answer:

2.7

Explanation:

V=s÷t

v=13.5÷5.0

V=2.7

Calculate the value of (1/ T2 â 1/ T1 ) where T1 is the initial temperature and
T2 is the final temperature.

Answers

The value of (1/T2 - 1/T1) can be calculated by subtracting the reciprocal of the initial temperature (T1) from the reciprocal of the final temperature (T2). The formula can be written as (1/T2) - (1/T1).

For example, if T1 is 20°C and T2 is 30°C, then (1/T2 - 1/T1) = (1/303 - 1/293) = 0.0034.
It is important to note that temperature is typically measured in Celsius (°C), Kelvin (K), or Fahrenheit (°F). The formula remains the same regardless of the unit of temperature used, but the values of T1 and T2 need to be converted accordingly. In summary, the value of (1/T2 - 1/T1) can be calculated by subtracting the reciprocal of the initial temperature from the reciprocal of the final temperature.

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If a bullet of mass 50 gm is moving with the velocity of 720 km/hr. Calculate its kinetic energy. Ans: here, mass (m)= 50 gm = 50/1000 kg = 0.05 kg velocity (v) = 720 km/hr= 720×1000/60×60=200m/s kinetic energy = ? We know, K.E.= 1/2 mv^2 = 1/2 × 0.05×(200)^2 = 0.05×40000/2 = 1000j ans. Is it correct???????

Answers

Answer:

yes   1000 j   as I posted on the same Q elsewhere

Explanation:

NEED HELP ASAP WILL MARK BRAINLIEST What helps create the spin in a hurricane?

What is the center of a hurricane called?

Over which kind of water do hurricanes form?

Answers

Answer:

The Coriolus effect causes the spin in a hurricane

The center of a hurricane is called the eye

Hurricanes form over warm ocean water in the tropics

Explanation:

Answer: The Coriolus effect causes the spin in a hurricane

The center of a hurricane is called the eye

Hurricanes form over warm ocean water in the tropics

Explanation:

I got it right on edge! Plz mark brainlist love you all <3

example of nuclear fission​

Answers

Answer:

In nuclear power plants, energetic neutrons are directed into a sample of the isotope uranium-235. ... A common fission reaction produces barium-141 and krypton-92. In this particular reaction, one uranium nucleus breaks into a barium nucleus, a krypton nucleus, and two neutrons

1. Re-arrange the Ohm’s Law equation to solve the following:I = Type your answers here.R = Type your answers here.2. Power is equal to voltage multiplied by current. Add the missing information in each of the following power equations.P = V Type your answers here.P = R Type your answers here.P = V2 Type your answers here.

Answers

\(\begin{gathered} 1)I=\frac{V}{R} \\ R=\frac{V}{I} \end{gathered}\)

2)

\(\begin{gathered} P=VI \\ P=RI^2 \\ P=\frac{V^2}{R} \end{gathered}\)

Explanation

Step 1

Ohm's law states that the strength of a direct current is directly proportional to the potential difference and inversely proportional to the resistance of the circuit.

\(I=\frac{V}{R}\)

so

a)

\(I=\frac{V}{R}\)

b)

\(\begin{gathered} I=\frac{V}{R} \\ \text{Multiply both sides by R} \\ I\cdot R=R\cdot\frac{V}{R} \\ IR=V \\ \text{divide both sides by I} \\ \frac{RI}{I}=\frac{V}{I} \\ R=\frac{V}{I} \end{gathered}\)

Step 2

2

let

Power is equal to voltage multiplied by current.

so

\(P=VI\rightarrow(1)\)

also, replacing

\(\begin{gathered} P=VI \\ P=(IR)I \\ P=RI^2\rightarrow(2) \\ \end{gathered}\)

also

\(\begin{gathered} V^2=I^2R^2 \\ \text{hece} \\ I^2=\frac{V^2}{R^2} \\ \\ \text{therefore, } \\ P=RI^2\rightarrow(2) \\ P=\frac{V^2}{R^2}\cdot R \\ P=\frac{V^2}{R} \end{gathered}\)

I hope this helps you

In the process of making a rainbow, light enters the water droplet at location 1 and exits at location 3. Which
of the following choices correctly identifies the sequence of interactions that produce the rainbow?

In the process of making a rainbow, light enters the water droplet at location 1 and exits at location

Answers

Answer: D, Refraction, Reflection, Refraction.

Explanation: Refraction is a rainbow. See image for info.

In the process of making a rainbow, light enters the water droplet at location 1 and exits at location

The magnitude of a vector represents its_

Answers

The magnitude of a vector represents its direction. The phrase also refers to a quantity's mathematical or geometrical representation.

What is a vector?

A vector is a quantity or phenomena with magnitude and direction that are independent of one another. The phrase also refers to a quantity's mathematical or geometrical representation.

If no vector can be written as a linear combination of the others, a set of vectors is said to be linearly independent.

If no vector in a collection of vectors can be written as a linear combination of the ones mentioned before it, the set is said to be linearly independent.

Hence, the magnitude of a vector represents its direction.

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Cortez Manufacturing intends to increase capacity by overcoming a bottleneck operation by adding new equipment. Two vendors have presented proposals. The fixed costs are $50,000 for proposal A and $80,000 for proposal B. The variable cost is $14.00 for A and $10.00 for B. The revenue generated by each unit is $22.00. a) The break-even point in units for the proposal by Vendor A = units (round your response to the nearest whole number). b) The break-even point in units for the proposal by Vendor B = units (round your response to the nearest whole number). what is the speed of a boy moving around a circular park of radius 6m if he goes around the park in 20s Which of these file formats would you choose if you had to create a very small and compact raster image for a website? Joint Photographic Experts Group (jpg) Graphic Interchange Format (gif) Portable Network Graphic (png) Tagged Image File Format (tif) Researchers doing a study comparing time spent on social media and time spent on studying randomly sampled 200 students at a major university. They found that students in the sample spent an average of 2.3 hours per day on social media and an average of 1.8 hours per day on studying. If all the students at the university in fact spent 2.2 hours per day on studying, with a standard deviation of 2 hours, the sampling distribution of the time spent studying has approximate distribution solve pls brainliest a country that has a lower opportunity cost associated with producing a given product compared to another country would have a(n) over that other country: What is the magnitude of the magnetic field inside the toroid at (a) the inner radius and (b) the outer radius PLEASE HELP ASAP!! I WILL MARK BRAINLIESTYou are designing a newmovie complex. There are14 movie theaters and 3 exitsper theater. The food area has9 exits. How many exits arethere altogether? Solve for x x=___________ Mason has 1,015 pounds of apples. He sells 9 bushels, 25 boxes, and 40 bags. How many pounds of apples does Mason have left? Enter your answer in the box. is 2y=-6 linear if so write in standard form and give the values of A B and C The majority of studies conducted in athletes suggest that vitamin b12 injections boost red blood cell production.a. true b. false MP4 Model with Math Write anexpression for the volume of the bar magnet.0.5 in. N2.25 in.S0.25 in. Which choice represents 12% as a fraction in simplest form? Find the indicated side of thetriangle.b745ab = [?]VO Consider the continuous-time signal x(t) = e-atu(t) where a is a real and positive constant value. Signal x(t) is the input signal of a LTI system, with the following unit impulse response h(t) = te-at u(t). A) Derive an analytical expression for the frequency response of the LTI system, i.e., H(jw), the output signal, i.e., y(t), and its spectrum, i.e., Y (jw) [pt. 15). 2 Mark is planning a family vacation with his extended family. He knows thats the flights cost $250 per person plus he is spending $1,500 to rent a house for them to all stay in. Write an expression that represents the total cost of the family trip. The solution of the equation dP/dt = P(12 - 3P) with initial condition P(0) = 3 is Select the correct answer. EXPLICITLY SOLVE THE DE. USE ANY METHOD a. P = 12/(3 + e^-12t) b. P = 4/(3 + e^-12t)1 c. P = 4/(3 - e^-12t) d. P = 3/(12 + e^-12t) e. P = 3/(4 + e^-12t) two people start walking in different directions from the same point. one walks south at 4 mph and the other walks west at 3 mph. at what rate is the distance between the walkers increasing two hours later? HELP JBSDOUEABFUIADJLBFAEBFAJKCEIS