If two identical sound waves arriving at the same point are in phase, the resulting wave, compared to the original waves, will have (A) an increase in speed (B) an incre…
If two identical sound waves arriving at the same point are in phase, the resulting wave, compared to the original waves, will have
(A) an increase in speed
(B) an increase in frequency
(C) a larger amplitude
(D) a longer period

Answers

Answer 1

If two identical sound waves arriving at the same point are in phase, the resulting wave, compared to the original waves, will have (C) a larger amplitude.

When two sound waves are in phase, their peaks and troughs align perfectly. This alignment causes constructive interference, which results in the combined wave having a larger amplitude.

The amplitude is a measure of the energy in the wave, so a larger amplitude means a louder sound or greater intensity.

The speed (A) and frequency (B) of the combined wave remain unchanged because these properties depend on the medium through which the sound waves travel and not on the interaction between the waves.

The period (D) of the combined wave also remains unchanged because it is the inverse of the frequency.

In summary, when two identical sound waves are in phase and arrive at the same point, they create a new wave with a larger amplitude due to constructive interference, while other properties like speed, frequency, and period remain the same.

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Answer 2

The correct option is (C) a larger amplitude.

When two identical sound waves are in phase, their peaks and troughs align, resulting in constructive interference. This means that the amplitude of the resulting wave will be the sum of the amplitudes of the original waves. Therefore, the resulting wave will have a larger amplitude compared to the original waves.

The amplitude of a sound wave is related to the loudness of the sound. So, when two identical sound waves arrive at the same point in phase, their amplitudes add up, resulting in a wave with a larger amplitude and thus a louder sound.

Neither the speed nor the frequency nor the period of the wave changes when the waves are in phase, as these properties are determined by the medium through which the wave is traveling and the source of the wave, and not by the interference of waves.

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Related Questions

What is the maximum velocity at which a 60-watt motor can lift an 8.5-kg mass upward?
(A) 0.72 m/s (B) 7.0 m/s (C) 18.2 m/s (D) 70 m/s

Answers

Pick choice-A .

Weight of a mass = (mass) x (gravity)

Earth gravity = (9.8 m/s )

Weight of a mass = (9.8 x mass) Newtons

Work = (force) x (distance)

Power = (work done) / (time to do the work)

Weight of this mass = (8.5 kg) x ( 9.8 m/s ) = 83.3 Newtons

Work to lift it 1 meter = (83.3 N) x (1 m) = 83.3 Joules

Power to lift it 1 meter/sec = 83.3 Joule/sec = 83.3 watt

Power to lift it ' v ' meters/sec = 83.3v watts

In this problem ...

83.3 v watts = 60 watts

v =  60/83.3 m/s

v =  0.72 m/s

Question: What is this? (look in image attached)

Question: What is this? (look in image attached)

Answers

Answer:

C. all of the above.

Explanation:

up at the top it says solar power bank.

in the boxes below it says LED flashlight and solar energy.

it is all of the above.

The density of water is 1000 kg m^3. What is the value expressed in gcm^-3 units? please help me..
(1) 1000 (2) 100 (3) 1 (4) 0.1 (5) 0.01​

Answers

The answer is 1 which is option 3

Here's the neat, cool way to convert units like this:

-- 1 kilogram  =  1,000 grams

-- 1 meter  =  100 centimeters

So . . . . .

(1000 kg/m³) x (1000 g/kg) x (1 m/100 cm)³ =

(1,000 kg/m³) x (1,000 g/kg) x (1 m³/1,000,000 cm³) =

(1,000 x 1,000 x 1 / 1,000,000) (kg-g-m³ / m³-kg-cm³)  =  1 g/cm³

a 70-kg astronaut floats at a distance of 10 m from a 50,000-kg spacecraft. what is the force of attraction between the astronaut and spacecraft?

Answers

The force of attraction between a 70 kg astronaut at a distance of 10m m from a 50000 kg spacecraft is 2.336×10¹⁶ N.

What is force?

Force is defined as the product of mass and the acceleration of a body.

To calculate the force of attraction between the astronaut and the spacecraft, we use the formula below.

Formula:

F = GmM/r²......... Equation 1

Where:

F = Force of attractionG = Universal constantm = Mass of the astronautM = Mass of the spacecraftr = Distance between the astraunaut and spacecraft

From the question,

Given:

m = 70 kgM = 50000 kgr = 10 mG = 6.673 x 10¹¹ Nm²/kg²

Substitute these values into equation 1

F = (70×50000×6.673 x 10¹¹)/(10²)F = 2.336×10¹⁶ N.

Hence, the force of attraction between the astronaut and the spacecraft is 2.336×10¹⁶ N.

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A 1.80-kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal force of 15.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The object is now released from rest from this stretched position, and it subsequently undergoes simple harmonic oscillations.
(a) Find the force constant of the spring.
N/m

(b) Find the frequency of the oscillations.
Hz

(c) Find the maximum speed of the object.
m/s

(d) Where does this maximum speed occur?
x = ±
m

(e) Find the maximum acceleration of the object.
m/s2

(f) Where does the maximum acceleration occur?
x = ±
m

(g) Find the total energy of the oscillating system.
J

(h) Find the speed of the object when its position is equal to one-third of the maximum value.
m/s

(i) Find the magnitude of the acceleration of the object when its position is equal to one-third of the maximum value.
m/s2

Answers

Answer:

Explanation:

(a) Force constant = force/displacement = 15/0.2

=75 N/m

(b) For SHM with spring, the angular frequency = sqrt ( force constant / mass )

= sqrt ( 75 / 1.8 )

= 6.455

Frequency = Angular frequency / 2pi

= 1.03Hz

(c) Maximum speed is when object's potential energy is at minimum.

1/2*mass*speed^2 = 1/2*force constant*displacement^2

speed^2 = 75*0.2^2/1.8 = 1.67

speed = sqrt (1.67)

= 1.29 m/s

(d) It occurs at x=0

(e) Maximum acceleration = Force / m = 15/1.8

= 8.33 m/s^2

(f) It occurs at x=0.2m

Answer:

Explanation:

given:

The mass of the object attached to the spring: m = 1.80 kg

The magnitude of the maximum horizontal force exerted: F = 15.0 N

The amplitude of the spring-object oscillation: A = 0.200 m

a. k=15/.2=75N/m

b. (2pi*frequency)^2 = k/m = 75/1.8 = 41.67

frequency = 1.03Hz

c. max speed^2 = amplitude^2*k/m = 0.2^2 * 41.67

max speed = 1.29 m/s

d. x=0m

e. max accel = F/m = 15/1.8 = 8.33 m/s^2

f. x=0.2m

e. energy = 1/2*k*A^2

= 1/2*75*0.2^2

= 1.5J

A paper airplane flies with a velocity of 1.5m/s North. If a cross-wind with a 3.7m/s East velocity also pushes the airplane, what will the total velocity of the airplane be?

Answers

The speed of the wind from the east with 3.7 m/s is pushing the paper airplane that flies with a velocity of 1.5 m/s north. Then the resultant velocity of the plane is 3.9 m/s.

What is resultant velocity ?

Velocity is a physical quantity measuring the distance travelled by an object per unit time. It is a vector quantity thus characterized by a magnitude and direction.

The velocity of an object moving north relative to wind towards east can be expressed as a resultant velocity or relative velocity of the former as:

v = √v1² + v2²

Given v1 = 1.5 m/s

v2 = 3.7 m/s

then v = √1.5² + 3.7² = 3.9 m/s

Therefore, the total velocity of the paper airplane is 3.9 m/s.

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Which is an example of a way that
machines make work easier?
A. They spread a small force over a small
distance.
B. They spread a small force over a larger
distance.
C. They make the force exert all at once.
D. They increase the time it takes to do a task.

Answers

Answer:

C Thy make the force exert all at once

Two rocks (call them S and T) are a distance of 50 km from one another. Rock S has 20 times the mass of rock T. Which rock will move faster if the only force involved is their mutual gravitational attraction

Answers

According to Newton's law of universal gravitation, the force of gravity between two objects is proportional to their masses and inversely proportional to the square of their distance.

In this scenario, the force of gravity between the two rocks will be stronger on the side of the rock with higher mass, and weaker on the side of the rock with lower mass. Therefore, rock T will be pulled towards rock S with a stronger force than rock S is pulled towards rock T. As a result, rock T will accelerate faster towards rock S, and move faster than rock S. The actual speed of each rock will depend on their initial velocities and the strength of the gravitational force between them.

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A box of mass 8.0 kg is lifted from the ground and placed on a shelf. The box gains 100J of potential energy. The box falls off the shelf. Air resistance can be ignored. At what speed does the box hit the ground?
A 3.5m/s
B 5.0m/s
C 25m/s
D 28m/s

HELP

Answers

Explanation:

\(pe = mgh \: \\ taking \: g \: as \: 10ms^{ - 2} \\ 100 = 8.0 \times 10 \times h \\ h = 1.25m \\ \\ using \: newtons \: third \: equation \\ v^{2} = u^{2} + 2gh \\ where \: v \: is \: final \: velocity \: and \: u \: is \: initial \: velocity \: = 0 \\ v^{2} = 0 + 2 \times 10 \times 1.25 \\ = 25 \\ v = 5.0ms^{2} \)

Why is the amount of energy transfer different depending on how high an air parcel travels?

Please give a simple explanation!

Answers

Answer:

When the parcel rises, its volume expands as it strives to maintain equilibrium with the lower pressure outside the air mass and pushes into the surrounding atmosphere. In this way, some of the thermal energy added to the air is used for expansion rather than warming.

A projectile is launched directly upward from the surface of the earth with an initial speed of 8. 8 km/s. Assuming air resistance is negligible, what is the maximum height of the projectile (in m)?.

Answers

Answer:

78m

Explanation:

A ball is launched from inside a cylindrical device that has been set on a frictionless incline and turned loose

What can be determined about where the ball will land ?

The ball will land back in the cylinder.
The ball will land behind the cylinder.
It depends on the mass of the ball.
The ball will land in front of the cylinder.
It cannot be determined.

Answers

The velocity of the ball in the forward direction is the same as the initial velocity with which it was launched.

A ball is launched from inside a cylindrical device that has been set on a frictionless incline and turned loose. What can be determined about where the ball will land?It can be determined that the ball will land in front of the cylinder.

This can be explained with the help of a few concepts of Physics. When an object moves on an incline without friction, then it can be divided into two components, which are: gravity and normal force.

Here, gravity is acting towards the center of the Earth, whereas the normal force is perpendicular to the incline. Let's suppose that the ball is launched with a certain velocity, which makes it move along the incline and get projected in the forward direction.

If we think of the motion of the ball from the observer's point of view who is standing on the incline, then the motion will appear to be parabolic. This is because the observer would see that the ball is moving forward with a constant velocity, but its vertical position keeps changing due to the effect of gravity.

However, from the observer's point of view who is standing in front of the cylinder, the motion of the ball will look like it is a projectile.

The velocity of the ball in the forward direction is the same as the initial velocity with which it was launched.

But, due to the effect of gravity, the vertical component of the velocity would change, which would result in a parabolic path of the ball. Therefore, the ball will land in front of the cylinder.

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The velocity of the ball in the forward direction is the same as the initial velocity with which it was launched. It can be determined that the ball will land in front of the cylinder. The correct option is The ball will land in front of the cylinder.

A ball is launched from inside a cylindrical device that has been set on a frictionless incline and turned loose. What can be determined about where the ball will land?It can be determined that the ball will land in front of the cylinder.

This can be explained with the help of a few concepts of Physics. When an object moves on an incline without friction, then it can be divided into two components, which are: gravity and normal force.

Here, gravity is acting towards the center of the Earth, whereas the normal force is perpendicular to the incline. Let's suppose that the ball is launched with a certain velocity, which makes it move along the incline and get projected in the forward direction.

If we think of the motion of the ball from the observer's point of view who is standing on the incline, then the motion will appear to be parabolic. This is because the observer would see that the ball is moving forward with a constant velocity, but its vertical position keeps changing due to the effect of gravity.

However, from the observer's point of view who is standing in front of the cylinder, the motion of the ball will look like it is a projectile.

The velocity of the ball in the forward direction is the same as the initial velocity with which it was launched.

But, due to the effect of gravity, the vertical component of the velocity would change, which would result in a parabolic path of the ball. Therefore, the ball will land in front of the cylinder.

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I need help with number 6 and 7 please and I’ll mark brainliest

I need help with number 6 and 7 please and Ill mark brainliest

Answers

Answer:

n.6 is T

Explanation:

because mass always stays the same where ever you are but weight changes depending on the gravity

a 50 kg box is pushed to the left using 500 N, the frictional force on the box is 100 N what is the acceleration on the box?

Answers

First thing's first, we need to find the Net Force of the system in order to solve for acceleration. Gravity and Normal Force cancel out, so we don't really have to worry about anything on the y-axis. However, looking at the x-axis, we see two forces: the Force of the push and Frictional Force.

This means that:

\(F_{net}\) = 500 - 100

\(F_{net}\) = 400 (N)

Recall that Force = Mass * Acceleration. Since we have the Force and Mass, we can easily solve for Accel:

F = ma

a = \(\frac{F}{m}\)

Plug the net force and mass into the equation:  

a = \(\frac{F}{m}\)

a = \(\frac{400}{50}\)

a = 8 (m/\(s^{2}\))

The box's acceleration is 8 m/\(s^{2}\)

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Which physical properties of the air in the balloon will change if you sit on a balloon without breaking it?

Responses

volume and density both increase
volume decreases, density increase
volume increase, density decreases
volume and density both decrease

Answers

Answer: volume increase and density decrease

Explanation:

when sitting on a ballon the volue will increase cause it will stretch

and the density is decreasing cause when pressure is applied to

the latex it gets bigger but the ballon gets thinner

A current-carrying conductor is kept at rightangles to the direction of a magnetic field. What happens to theforce acting on the wire if the strength of the magnetic fielddoubles?
A. The force is doubled.
B. The force is not charged.
C. The force is halved.
D. The force becomes one-fourth.

Answers

If the strength of the magnetic field doubles when a current-carrying conductor is kept at right angles to its direction, the force acting on the wire doubles.

The force experienced by a current-carrying conductor in a magnetic field is given by the formula F = BIL, where F is the force, B is the magnetic field strength, I is the current, and L is the length of the conductor in the magnetic field. In this scenario, if the strength of the magnetic field doubles while other factors remain constant, such as the current and the length of the conductor, the force will double as well. This is because the force is directly proportional to the magnetic field strength. Therefore, option A, "The force is doubled," is the correct answer.

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how is sound wave produced?​

Answers

Answer:

Sound is produced when an object vibrates, creating a pressure wave.

Explanation:

This pressure wave causes particles in the surrounding medium (air, water, or solid) to have vibrational motion. ... The human ear detects sound waves when vibrating air particles vibrate small parts within the ear.

Answer:

A sound wave is created by continuous vibration of an object. We hear sound when these waves created by vibrations reach our eardrum.

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The unit of work in terms of Newton and metre is _______

Answers

Answer:

Joule

Explanation:

the unit of work is Joule determined by the letter J.

Answer:

Joule

Explanation:

Joule is defined as the work done by a force of one newton causing a displacement of one meter. Sometimes, newton-metre (N-m) is also used for measuring work.

You drive a car 660 ft to the east, then 370ft to the north. (a) What is the magnitude of your displacement? (b) Using a sketch, estimate the direction of your displacement (c) Verify your estimate in part (b) with a numerical calculation of the direction

Answers

Answer:

a) 756.64 ft

b) 30 degrees

c) 29.27 degrees.

Explanation:

We can represent the situation as follows:

So, we can find the magnitude of the displacement (the green line) using the Pythagorean theorem. Then:

\(\sqrt[]{660^2+370^2}=\sqrt[]{435600+136900}=\sqrt[]{572500}=756.64\text{ ft}\)

Then, the angle of the displacement can be approximate finding the angle θ. So, using a protractor on the figure, we get that θ is approximately 30 degrees.

Now, we can find the direction using a trigonometric function as:

\(\tan \theta=\frac{370}{660}\)

Because 370 is the opposite side and 660 is the adjacent side. Therefore, the value of θ is:

\(\begin{gathered} \tan \theta=0.5606 \\ \theta=\tan ^{-1}(0.5606) \\ \theta=29.27\text{ degrees} \end{gathered}\)

So, the answers are:

a) 756.64 ft

b) 30 degrees

c) 29.27 degrees.

You drive a car 660 ft to the east, then 370ft to the north. (a) What is the magnitude of your displacement?

the density of a material is the mass per volume of 'one piece' of the material. the bulk density of the same material is...

Answers

While the density of a material refers to the mass per volume of one piece, the bulk density refers to the mass per unit volume of a larger sample or bulk quantity of the material.

The bulk density of a material refers to the mass per unit volume of a large quantity or a bulk sample of the material. It takes into account the overall volume occupied by multiple pieces or particles of the material.

Unlike the density of a single piece of the material, which considers the mass and volume of an individual unit, the bulk density considers the collective mass and volume of a larger sample that contains multiple pieces or particles.

It provides an average measure of the material's density when it is present in a larger quantity or in bulk form.

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If you don’t know the answer please please don’t answer, I have to do this for a test and it’s 100 points

If you dont know the answer please please dont answer, I have to do this for a test and its 100 points

Answers

Answer:

I believe that it's C

Explanation:

What patterns did you notice when comparing the interactions between the tape and van de Graaff generator to the tape and charged balloon?

Answers

The negatively charged van de Graff generator can make a flow of electrons through the tape and these both will repel each other. When the tape comes in contact with the balloon, the positive charges of balloon gets attracted and they stick together.

What is van de Graff generator?

Electrons are drawn from the earth by a Van de Graaff generator, transported via a belt, and then stored on the big sphere. These electrons are attracted to one another and try to distance themselves from one another by dispersing throughout the surface of the sphere.

Electrons can spread out widely on the earth, thus they will choose the shortest route possible to return to the ground. The electrons from the tape repel the electron from the tape, make the tape negatively charged.

This negatively charged tape when comes in contact with the balloon, it will polarize the balloon and its positive charges aligns with the tape's charge and gets stuck.

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The back of a loaded pickup truck is open.
A car rear-ends the pickup truck, causing its load to spill. Explain the event in terms of Newton's laws.

Answers

The load of the pickup truck spills due to an unbalanced force acting on it caused by the collision from the car.

Newton's first law states that an object at rest will remain at rest unless acted upon by an unbalanced force. In this scenario, the load of the pickup truck is at rest in the back of the truck, but when the car rear-ends the pickup truck, it applies an unbalanced force on the load, causing it to spill out of the truck.

Newton's second law states that the force applied on an object is equal to the mass of the object multiplied by its acceleration. In this scenario, the car applies a force on the load of the pickup truck, which is equal to the mass of the load multiplied by the acceleration of the car at the time of the collision. The force causes the load to spill out of the truck.

Newton's third law states that for every action, there is an equal and opposite reaction. In this scenario, when the car rear-ends the pickup truck, the car experiences an equal and opposite force, which is the reaction to the force it applies to the load of the pickup truck.

In summary, the load of the pickup truck spills due to an unbalanced force acting on it caused by the collision from the car. The force applied on the load of the pickup truck is equal to the mass of the load multiplied by the acceleration of the car at the time of the collision. And the car experiences an equal and opposite force, which is the reaction to the force it applies to the load of the pickup truck.

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If we apply a potential difference of 4. 50 v between the ends of a wire that is 2. 50 m in length and 0. 654 mm in radius, the resulting current through the wire is 17. 6 a. What is the resistivity of the wire material?.

Answers

According to the resistance, the resistivity of wire material is 1.37 x 10¯⁷ Ωm.

We need to know about the resistance of conductive material to solve this problem. Resistance can be defined as the ratio of the voltage applied to current flow It can be written as

R = V / I

where R is resistance, V is voltage and I is current.

The resistance of the material depends on its resistivity and follows this equation

R = ρ . L / A

where ρ is resistivity, L is the length of the material and A is the surface.

From the question above, we know that

V = 4.5 V

L = 2.5 m

r = 0.654 mm = 6.54 x 10¯⁴ m

I = 17.6 A

Find the surface area

A = π . r²

A = π . ( 6.54 x 10¯⁴ )²

A = 1.34 x 10¯⁶ m²

Find the resistivity of the wire

R = V / I

ρ . 2.5 / (1.34 x 10¯⁶)= 4.5 / 17.6

ρ = 1.37 x 10¯⁷ Ωm

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Molten (melted) iron and carbon monoxide are produced in a blast furnace by the reaction of iron(III) oxide and pure carbon. Fe2O3 + 3C ---> 2Fe + 3CO If 4 moles of Fe2O3 are used, how many moles of Carbon Monoxide (CO) can be produced?

Answers

Answer:

Explanation:

Fe₂O₃ + 3C ---> 2Fe + 3CO

1 mole                          3 moles

From the balanced equation above , we see that , 1 mole of Fe₂O₃ reacts with carbon to form 3 moles of CO .

So , 4 moles of  Fe₂O₃ will react with carbon to form 3 x 4  moles of CO .

moles of CO formed = 3 x 4 moles = 12 moles.

A pickup truck is being driven down the highway carrying eight 100 gallon fish tank full of water. A hole is punctured in each tank and the water flows out of the tanks and truck to the ground. If the driver maintains the same pressure on the gas pedal, and the road stays flat and level, what happens to the velocity of the truck and which conservation law applies?

Answers

Answer:

Explanation:

The velocity of the vehicle would increase because the the tanks (when filled with water) must have exerted a force which would reduce the velocity of the vehicle at a certain pressure on the gas pedal. Note that force equals mass multiplied by acceleration; as the mass decreases, so the force decreases. Thus, when the mass exerted by this tanks (on the vehicle) decrease as a result of the hole punctured in them, the force exerted by the tanks would also decrease causing an increase in velocity of the pick up truck when the same pressure is applied on the gas pedal throughout (before and after the puncture).

The conservation law that applied here is the law of conservation of energy which states that energy can neither be created nor destroyed but can be transformed from one form to another. This is because the energy the vehicle used in carrying the load (the tanks) was transformed to the energy that resulted in increasing  it's velocity (no new energy was formed as the pressure on the gas pedal remained the same).

Divide 6. 5×10^5kg / 3. 4×10^3m^3. Give the correct number of significant figures

Answers

Answer:

1.911665 x10^2

Explanation:

if u have a scientific calculator such as casio fx-991ES plus

just do shift mode 7 7

WHO HAS BIG BRAINS? not me... so please help?
What is isostasy dependent on a balance between?

A.)the downward push of the mantle and the upward push of the continents

B.)The downward push of the ocean floor and upward push of the continents

C.)The downward push of the continents and upward push of the mantle

D.)The downward push of the ocean floor and upward push of the mantle

Answers

Answer:

c

Explanation:

u only use 10% of your brain

Answer:

D

Explanation:

Isostatic equilibrium is the state of gravitational equilibrium between Earth 's crust and the mantle.

The more __________ energy being used, the ___________ the roller coaster will go. Question
A:Kinetic, slower
B:Potential, faster
C:Kinetic, faster
D:Potential, slower

Answers

Answer: b

Explanation:

Answer:

C.

The More Kinetic Energy being used, the Faster, the Roller Coaster will go.

Explanation:

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Television Advertising As Sales Manager for Montevideo Productions, Inc., you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of $2,900. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 11 contracts. This is down 5 contracts from the figure last year, when your company charged only $2,400. (a) Construct a linear demand equation giving the number of contracts a as a function of the hourly fee p Montevideo charges for development. 960) - (b) On average, Montevideo bills for 40 hours of production time on each contract. Give a formula for the total revenue obtained by charging $p per hour. R(D) - (c) The costs to Montevideo Productions are estimated as follows. Fixed costs: $140,000 per month Variable costs: $70,000 per contract Express Montevideo Productions' monthly cost as a function of the number of contracts. ca) - Express Montevideo Productions monthly cost as a function of the hourly production charge p. Cip) = (d) Express Montevideo Productions' monthly profit as a function of the hourly development fee p. Pp) - Find the price it should charge to maximize the profit (in dollars per hour). ps per hour

Answers

To find the hourly development fee (p) that maximizes the profit, you would need to analyze the profit function and determine the value of p that yields the maximum result.

The linear demand equation giving the number of contracts (a) as a function of the hourly fee (p) charged by Montevideo Productions can be represented as: a = m * p + b

Given that the demand is currently 11 contracts when the fee is $2,900 and it was 5 contracts higher at $2,400, we can find the values of m and b. Using the two data points:

(2900, 11) and (2400, 16)

m = (11 - 16) / (2900 - 2400) = -1/100

b = 16 - (2400 * (-1/100)) = 40

Therefore, the linear demand equation is:

a = (-1/100) * p + 40

(b) The formula for the total revenue (R) obtained by charging $p per hour and billing for 40 hours of production time on each contract is:

R = p * 40 * a

Substituting the demand equation, we get:

R = p * 40 * ((-1/100) * p + 40)

(c) The monthly cost (C) for Montevideo Productions can be expressed as a function of the number of contracts (a) as follows:

C = Fixed costs + (Variable costs per contract * a)

Given: Fixed costs = $140,000 per month

Variable costs per contract = $70,000

So, the monthly cost function is:

C(a) = $140,000 + ($70,000 * a)

(d) The monthly profit (P) for Montevideo Productions can be calculated by subtracting the monthly cost (C) from the total revenue (R):

P(p) = R - C(a)

Finally, to find the hourly development fee (p) that maximizes the profit, you would need to analyze the profit function and determine the value of p that yields the maximum result.

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