Contact forces & friction. Please help!!! (20 points & brainliest!)

Contact Forces & Friction. Please Help!!! (20 Points & Brainliest!)

Answers

Answer 1

Let w denote the weight of the box, n the magnitude of the normal force (the sheet pushing up on the box), k the magnitude of the kinetic friction force, and µ the coefficient of kinetic friction.

The kinetic friction force doesn't kick in until the sheet is tilted at an angle θ₂. Since the box is sliding down at constant speed, it's in equilibrium and the forces acting on it sum to 0.

In the horizontal direction (literally left-and-right, parallel to the ground and not the sheet), we have only the horizontal components of the friction and normal forces to worry about, so that [tex]\mathbf n_x+\mathbf f_x=\mathbf0[/tex], which reduces to

f cos(θ₂) + n cos(90º + θ₂) = 0

(where we take the right to be positive and left to be negative)

Recall that cos(90º + x) = -sin(x) for all x, and that the friction force is proportional to the normal force by a factor of µ. This gives

µ n cos(θ₂) - n sin(θ₂) = 0

Solve for µ :

µ n cos(θ₂) = n sin(θ₂)

µ = sin(θ₂) / cos(θ₂)

µ = tan(θ₂)

Contact Forces & Friction. Please Help!!! (20 Points & Brainliest!)

Related Questions

A car is traveling down the highway cruise control at 50m/s (this means its is traveling with a constant velocity NOT accelerating). If it does this for 5 minutes (300s), how far does it travel?

Answers

Given parameters:

Speed of car = 50m/s

Time of travel = 5minutes (300s)

Unknown;

Distance of travel = ?

To solve this problem, we need to understand how speed relates with distance and time.

 Speed is a physical quantity. It is the distance traveled divided by time taken.

                Speed  = [tex]\frac{distance}{time}[/tex]

   So,

                Distance  =  speed x time

Input the parameters and solve for the distance;

               Distance  = 50m/s x 300s

               Distance  = 15000m

The distance covered during this time interval and speed is 15000m

A car travels 30 m in 5 seconds. After accelerating for 3 seconds, it travels 20 m in 2 seconds. The cars acceleration is ___m/s

Answers

divide them so 10m/s

Se lanza una piedra de 3.00 N verticalmente hacia arriba desde el suelo. Se observa que, cuando está 15.0 m sobre el suelo, viaja a 25.0 m/s hacia arriba. Use el teorema trabajo-energía para determinar a) su rapidez en el momento de ser lanzada. b) su altura máxima

Answers

Answer:

(a). The speed at the moment of being thrown is 30.41 m/s.

(b). The maximum height is 47.18 m.

Explanation:

Given that,

Weight of stone = 3.00 N

Height = 15 m

Speed = 25.0 m/s

(a). We need to calculate the speed at the moment of being thrown

Using work energy theorem

[tex]W=\dfrac{1}{2}m(v_{2}^2-v_{1}^2)[/tex]

[tex]-mg\times d=\dfrac{1}{2}m(v_{2}^2-v_{1}^2)[/tex]

Put the value into the formula

[tex]-9.8\times15=\dfrac{1}{2}\times(v_{2}^2-v_{1}^2)[/tex]

[tex]-2\times9.8\times15=25^2-v_{1}^2[/tex]

[tex]-v_{1}^2=-300-25^2[/tex]

[tex]v_{1}=\sqrt{925}[/tex]

[tex]v_{1}=30.41\ m/s[/tex]

(b). We need to calculate the maximum height

Using work energy theorem

[tex][tex]W=\dfrac{1}{2}mv_{2}^2-\dfrac{1}{2}mv_{1}^2[/tex]

[tex]mg\times d=\dfrac{1}{2}mv_{2}^2-\dfrac{1}{2}mv_{1}^2[/tex]

Here, [tex]\dfrac{1}{2}mv_{2}^2[/tex]=0

[tex]-(mg)\times d=\dfrac{1}{2}mv_{1}^2[/tex]

[tex]d=\dfrac{v_{1}^2}{2g}[/tex]

Put the value into the formula

[tex]d=\dfrac{30.41^2}{2\times9.8}[/tex]

[tex]d=47.18\ m[/tex]

Hence, (a). The speed at the moment of being thrown is 30.41 m/s.

(b). The maximum height is 47.18 m.

Which type of energy is stored in a battery?
O A. Nuclear energy
O B. Electrical energy
O C. Electromagnetic energy
O D. Chemical energy

Answers

Answer:

Chemical energy is in a battery

The type of energy is stored in a battery is Chemical energy (option d)

Batteries store chemical energy. When a battery is charged, a chemical reaction occurs inside it, converting the reactants into different products. This process stores energy in the form of chemical bonds within the battery's components.

When you use the battery to power a device, the reverse chemical reaction takes place, releasing the stored energy as electrical energy. This flow of electrons creates an electric current that powers the device connected to the battery.

The capacity of a battery to store and release energy depends on the type and quantity of chemicals used in its construction. Different types of batteries, such as alkaline, lithium-ion, or lead-acid batteries, have varying chemical compositions, affecting their energy storage capabilities and overall performance.

So, the correct option is (d).

To know more about energy here

https://brainly.com/question/1932868

#SPJ6

HI CAN ANYONE PLS ANSWER DIS PLS!!!!!!

Answers

Answer:

Volume of an object (L): blue 105.00, yellow 105.00, green 102.50, red 101.25

Density of an object (kg/L) Mass / Volume: blue 1, yellow 1, green 1.014, red .992

Sink or Float: blue sink, yellow sink, green float, red float

hope this helps

Anyone get this can you please help me, can you also please do it step by step

Answers

Answer:

7.69 hours

Explanation:

3 hr/ 1000mi x 130mi = 7.69 hours or 7.7 hours

A car is initially moving at 10.5 m/s and accelerates uniformly to reach a speed of 21.7 m/s in 4.34 s. How far did the car move during this acceleration?
A. 69.9m
B. 6.99m
C. 69.6m/s
D. 6.99m/s

Answers

Answer:

A. 69.9m

Explanation:

Given parameters:

Initial velocity = 10.5m/s

Final velocity  = 21.7m/s

Time  = 4.34s

Unknown:

Distance traveled = ?

Solution:

Let us first find the acceleration of the car;

  Acceleration  = [tex]\frac{v - u}{t}[/tex]

  v is final velocity

   u is initial velocity

   t is the time

     Acceleration  = [tex]\frac{21.7 - 10.5}{4.34}[/tex]   = 2.58m/s²

Distance traveled;

     V² = U² + 2aS

    21.7² = 10.5² + 2 x 2.58 x S

   360.64 = 2 x 2.58 x S

     S = 69.9m

7. A solid wax candle has a volume of 1,700 mL. The candle has a mass of 1.5 kg (1,500 g). What is the
density of the candle?

Answers

Answer:

The answer is 0.88 g/mL

Explanation:

The density of a substance can be found by using the formula

[tex]density = \frac{mass}{volume} \\[/tex]

From the question

mass = 1500 g

volume = 1700 mL

We have

[tex]density = \frac{1500}{1700} = \frac{15}{17} \\ = 0.88235294...[/tex]

We have the final answer as

0.88 g/mL

Hope this helps you

Answer:

0.88

Explanation:

density = mass/volume

density = 1500/1700

density = 0.88

If the radio waves that are sent from the speed gun have a frequency of 400,000,002 Hz and the radio waves reflected off an approaching car have a frequency of 400,000,109 Hz, what is the speed of the car? (Hz is the SI unit of frequency, equal to cycles per second).

Answers

Answer:

40.1 m/s or 144.36 km/h

Explanation:

The equation is (v=∆ f/f) x (c/2)

V is velocity

delta f is returned frequency minus intial frequency divided by the initial frequency

c is the speed of light in m/s divided by 2

v= (400,000,109 Hz - 400,000,002 Hz)/400,000,002Hz x (299,792,458 m/s)/2

An____ collision occurs when an arrow hits the target.

Answers

Answer:

I think it's An inelastic collision occurs when an arrow hits the target because when the arrow hits it, the target and the arrow do not bounce away from each other.

Explanation:

a dog walks 14 meters to the east and then 20 meters back to the west.

Answers

Answer:

who gets theses questions XD

Explanation:

Explain Kinetic and potential energy

Answers

Answer:

Energy implies as the object’s capability to perform work. It is something that cannot be created or destroyed but can only be transformed. An object loses its energy, when it performs work, whereas it gains energy when the work is performed on it. Energy is broadly classified as kinetic energy and potential energy. While kinetic energy is the energy which an object contains because of a particular motion.

On the other hand, potential energy is the stored energy, because of its state of rest. As both the two forms of energy are measured in joules, people get easily confused between these two. So, take a read of the article which will help you to understand the differences between kinetic and potential energy.

Explanation:

Hope this helps - Good luck ^w

Answer:

Energy stored in an object due to its position is Potential Energy. · Energy that a moving object has due to its motion is Kinetic Energy.

Explanation:

Explain experimental physics. ​

Answers

Answer:

This is a category of physics dealing with the observable phenomena, and experimental aspects by investigation, and scientific testing to measure the properties of matter, and energy.

Answer:

Experimental physics is the category of disciplines and sub-disciplines in the field of physics that are concerned with the observation of physical phenomena and experiments.

I hope you helped^_^

Follow me for more answers

A swimmer sets off headed west at 0.40 m/s directly towards the opposite shore of a swift river. The swimmer makes it to the opposite shore 30 meters downstream of their expected position. If the river is 7.5 meters wide, what is the velocity of the water relative to the shore?

Answers

Answer:

Explanation:

River is 7.5 m wide . Time taken by it cover this displacement

= displacement / velocity

=  7.5 / 0.4  

= 18.75 s

During this period , swimmer  will have a displacement of 30 m due to velocity of river water .

Displacement of 30 m downstream will be due to flow of river .

velocity of water flow = displacement / time

= 30 / 18.75

= 1.6 m /s

Which of these BEST explains how Earth's surface features are formed by moving tectonic plates? *
5 points
Earth's gravity acts as an opposing force, causing the crust to push upward, break into individual plates, and move along the surface.
The minerals in lithospheric plates are attracted to Earth's magnetic poles, which causes them to move along the surface.
The spinning of Earth's outer core causes the lithosphere to break into individual plates and collide with each other.
Earth's crust is separated into individual plates that float on top of molten material, convection currents in the mantle cause them to slowly move.

Answers

Answer: The spinning of Earth's outer core causes the lithosphere to break into individual plates and collide with each other.

Earth's surface forms because of this reason:

The spinning of Earth's outer core causes the lithosphere to break into individual plates and collide with each other.

It is required to design a zener shunt regulator to provide a regulated voltage of about 10 V. The available 10-V, 1-W zener of type 1N4740 is specified to have a 10-V drop at a test current of 25 mA. At this current, its r z is 7 . The raw supply, V S , available has a nominal value of 20 V but can vary by as much as ±25%. The regulator is required to supply a load current of 0 mA to 20 mA. Design for a minimum zener current of 5 mA.

Answers

Answer:

jgfsdghjjuk

Explanation:

khhnghjj

______________ rock forms beneath Earth's surface.

Answers

Answer:

Igneous rocks form beneath Earth's surface.

Explanation:

Igneous rocks form beneath the Earth's surface

The changes that are visible during a chemical reaction are signs that the nuclei in the reactants have been rearranged.
Please select the best answer from the choices provided
ОТ
OF

Answers

Answer:

the answer is F

Explanation: I put T on the question and got it wrong so it's F on edge ;)

What is the wavelength of a wave with a frequency of 466 Hz and a speed of
343 m/s?
A. 1.35 m
B. 0.74 m
C. 1.6 x 105 m
D. 6.25 x 10-6 m

Answers

Answer:

The answer is option B

Explanation:

The wavelength of a wave can be found by using the formula

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

where

c is the speed of the wave

f is the frequency

From the question

c = 343 m/s

f = 466 Hz

We have

[tex] \lambda = \frac{343}{466} \\ = 0.73605150...[/tex]

We have the final answer as

0.74 m

Hope this helps you

Answer: B: 0.74 m

Explanation:

Hope this helps / I did this question.

what does it mean mechanical advange is less than one?

Answers

Answer:

this happens when the input force is greater than the output force

HOPE IT HELPED YOU...


me·chan·i·cal ad·van·tage
noun
the ratio of the force produced by a machine to the force applied to it, used in assessing the performance of a machine.

1. How do you relate the law of inertia to the balanced and unbalanced force?​

Answers

??

Explanation:

I don't get you right

4. Prove that:
a.
The unit of pressure is a derived unit.​

Answers

Explanation:

The pascal (symbol: Pa) is the SI derived unit of pressure used to quantify internal pressure, stress, Young's modulus and ultimate tensile strength. It is defined as one newton per square metre. It is named after the French polymath Blaise Pascal

HURRRY PLEASSSSEEE
Energy required for cellular respiration can be processed from ____.
A) Carbohydrates
B) Fats/ Lipids
C) Proteins
D) All of the above

Answers

Answer:

fats / liquids or proteins one of them

Explanation:

..........

Answer:

D) All of the above

Explanation:

I googled it :)

A truck traveling at a velocity of 33m/s comes to a halt by decelerating at 11m/s^2. How far does the truck travel in the process of stopping. identify known variables such as V, V0, a, t, and delta x.

Answers

Answer:

The truck was moving 16.5 m/s during the time it took to stop, which was 3 seconds.

Initial velocity = 33 m/sFinal velocity = 0 m/sAverage velocity = (33 + 0) / 2  m/s = 16.5 m/s

Explanation:

First, how long does it take the truck to come to a complete stop?( 33 m/s ) / ( 11 m / s^2 ) = 3 secondsThen we can look at the average velocity between when the truck started decelerating and when it came to a complete stop. Because the deceleration is constant (always 11m/s^2) we can use this trick.

The time taken to stop the truck is 3 seconds. The final velocity is zero. Then, the distance travelled by the truck is 49.5  m.

What is acceleration ?

Acceleration is a physical quantity that, measures the rate of change in velocity. It is a vector quantity thus having both magnitude and direction. It can be defines as the ratio of change in velocity to the change in time.

Given initial velocity = 13.5 m/s

final velocity is zero since the bicycle is stopping.

then Δt = Δv/a

Δt = 33 m/s/ 11 m/s² = 3 seconds.

Hence, the truck will take 3 s to complete stop.

The distance covered within this time can be determined using the equation as follows:

s = u t + 1/2 at²

where u is the initial velocity

The acceleration a =  - 11 m/s² the minus sign is due to deceleration.

s =  (33m/s × 3 s) + (-11 m/s² ×3 s ×3 s) = 49.5 m.

Therefore, the truck will travel up to 49.5 m before stopping.

Find more on acceleration:

http://brainly.com/question/2303856

#SPJ2

A 4kg block and a 2kg block can move on horizontal frictionless surface. The blocks are accelerated by a +12-N force that pushes the large block against the smaller one.'

a) Determine the force that the 2kg block exerts on the 4kg block

b) Determine the force that the 4kg block exerts on the 2kg block.

Answers

Answer:

a) -4 N

b) +4 N

Explanation:

Draw a free body diagram for each block.

For the large block, there are 2 forces: 12 N pushing to the right, and F pushing to the left.

For the small block, there is 1 force, F pushing to the right.

There are also weight and normal forces in the vertical direction, but we can ignore those.

Sum of forces on the large block in the x direction:

∑F = ma

12 − F = 4a

Sum of forces on the small block in the x direction:

∑F = ma

F = 2a

2F = 4a

Substitute:

12 − F = 2F

12 = 3F

F = 4

The small block pushes on the large block 4 N to the left (-4 N).

The large block pushes on the small block 4 N to the right (+4 N).

A doctor takes an x-ray of your body this is an example of conduction, convection, radiation?

Answers

Answer:

Radiation

Explanation:

An x-ray emits radiation to see through the outer part of your body.

Hope this helps! <3

An X-ray is a type of radiation which is a type of electromagnetic radiation in the electromagnetic spectrum.

What is electromagnetic spectrum?

The  electromagnetic spectrum consists of electromagnetic radiation consists of waves made up of electromagnetic field which are capable of propogating through space and carry the radiant electromagnetic energy.

The radiation are composed of electromagnetic waves which are synchronized oscillations of electric and magnetic fields . They are created due to change which is periodic in electric as well as magnetic fields.

In vacuum ,all the electromagnetic waves travel at the same speed that is with the speed of air.There are 7 types of electromagnetic radiation in the electromagnetic spectrum.Gamma rays have the highest energy while radio waves have least energy.

Learn more about electromagnetic spectrum,here:

https://brainly.com/question/15576247

#SPJ2

An athlete starts running from rest such that he covers a distance of 5mm in 0.50s with a constant change in velocity per unit time . when will he reach the finish line, if he is running a race of 50m? ​

Answers

Answer:

50 s

Explanation:

Given:

Δx = 0.005 m

v₀ = 0 m/s

t = 0.50 s

Find: a

Δx = v₀ t + ½ at²

0.005 m = (0 m/s) (0.50 s) + ½ a (0.50 s)²

a = 0.04 m/s²

Given:

Δx = 50 m

v₀ = 0 m/s

a = 0.04 m/s²

Find: t

Δx = v₀ t + ½ at²

50 m = (0 m/s) t + ½ (0.04 m/s²) t²

t = 50 s

how much faster will a car be going if it accelerates at 1 m/s/s for a total of 60 seconds.

Answers

Answer:

Vf = 60 [m/s]

Explanation:

To solve this problem we must use the following equation of kinematics.

[tex]v_{f}= v_{i}+(a*t)[/tex]

where:

Vf = final velocity [m/s]

Vi = initial velocity = 0

a = acceleration = 1 [m/s^2]

t = time = 60 [m]

Now replacing:

Vf = 0 + (1*60)

Vf = 60 [m/s]

________are muscles connected to the skeleton.

1.) Smooth muscles
2.) Skeletal muscles
3.) Strong muscles
4.) Cardiac muscles

Answers

Answer: Skeletal Muscles

Explanation:

Skeletal muscles are attached to the skeleton by tough connective tissues called tendons


Q7 Describe two types of atomic change that produce electromagnetic
waves.

Answers

When a neutron or a proton in the nucleus changes a gamma ray is produced (gamma rays are electromagnetic waves)

When an electron drops from a higher energy level to a lower energy level an electromagnetic wave is give off.
Other Questions
Which of Congress's powers is implied through the necessary and proper clause? 1 Part AWhat can be inferred about Perseus in "Perseus and the Quest for Medusa's Head,"? He is excited to go on an adventure because the quest will be thrilling and take him to new lands. He knows his friends are rooting for him because they cheer for him and wish him well. He is confident that he will fulfill his promise and that he will impress the king. He realizes he has made a bad decision after he promises to bring the king the head of Medusa.Question 2Part BWhich evidence in the text best supports the answer to Part A? "His bold ways earned him the love of his fellows but also the anger of the king." "Swifter than an eagle, he flew through the sky, as the sandals carried him north over the sea, over cities and towns, over ranges of snowy mountains, and at last to the sea of ice." "Perseus was vexed by the kings request, which he knew was meant to shame him." "'And so I will,' said Perseus grimly, and he went away in anger, while his young friends laughed at him because of his foolish words."n the Newsela article "What Is Mythology?," which details best convey the central idea that myths are often closely tied to a culture's belief system?Select the two correct answers. 2 "Today, many Hindus incorporate this story into their religious practice during the Indian holiday of Diwali." "Many hero myths contain fantastical details." "Now it is possible to find written versions of many myths in books or online." "Some may even use the myth to govern how they live and behave."3 Which statement best describes the conflict Perseus has with the king? Perseus feels challenged to prove his worth to the king. Perseus tries to influence the king to be more kindly to everyone. He longs to have the king notice his courageousness and bravery. He fears the kings wrath when he is unable to fulfill his promise. whats the property for x 4y = 4x y sector.Raw materials and natural resources are obtained in theA secondaryB. primaryC tertiaryD. quatemaryPlease select the best answer from the choices provided TIMED QUIZ PLS HELP!!! 10 POINTSYou are using an email marketing service. They charge a setup fee of $250 plus $0.35 per email sent. How much will a 10,000 email mailing cost? 20 Points. I am currently writing a novel, and I need to have your honest opinion of the beginning. Not, this is a backstory of how the character Winter got into where she is currently in chapter one. Please give an honest opinion. Let me tell you a story, starting from the beginning."No no no no no no no!" Winter raced through he woods trying to find a safe place to hide. There was no place to hide. She was alone. She couldn't turn back, because behind her was a killer. A killer who had slaughtered her entire family, and is now after her. She is scared, hurt and desperately trying to get away. The killer was a demon, and she was human. There was absolutely no way she could outrun him, but she could try. Winter was a survivor. And she strives to survive any situation, even insane demonic ex's named Cain.So there she was, running for her life from the man who trapped her and promised her eternal suffering so long as she still existed. So she stops and hides in a hollowed out tree. She knows she is not safee, she never was safe to begin with. so she just sits there and waits. She's only human, so she can only run for so long. Her legs are tired, screaming at her in agony. And her heart is pounding right out of her chest."Winter~ Come on out my snowflake, I'm not going to hurt you, I just want to see you" She could hear his voice echoing, his voice alone sent shivers through her. The voice of a psycho that wanted to see her suffer. It terrified her and she constantly wondered why it was her he went after. "WINTER! I know you're hiding, i can't hear your footsteps anymore." He was close "Come. out. now." Her hear rate increased ten times over and she struggled to breathe, she was having a panic attack. She was crying, she let all the grief of what had just happened sink in. She let the fact of her impending doom sink in, and she cried. Then she saw him, he was right in front of her, she continued to cry softly, letting out pained whispered screams. He yanked her out by her arm and held her arms tight and just smiled at her. "Got you now little snowflake. It's time to bring out the sun so you can melt away." She stared in his eyes, shaking her head no, she couldn't speak, she couldn't move, and she was scared as hell. There was nothing she could do. So he dragged her back to her house, the same house that he turned to a slaughterhouse for her family. In the living room where her little brother lied mangled in the corner, he let her go. She immediately collapsed to her knees staring at the ground in fear, disbelief and pain. She couldn't get up and run because her legs were tired and practically useless as of now. She was useless. "Why so grim love? You did this to yourself. You and your little ways that got me to fall in love with you. A sheep and a ravenous demon. How'd that turn out for you?" Cain grinned. She didn't answer. she just kept quiet."Well then, you must know what time it is now don't you?" She did. He was going to send her to a hell. A world she knew nothing of, a world full of danger that she would be trapped in, for eternity. She did not move, she just waited for her fate to come.Now, I know you're wondering, 'Why would anyone wish anything like this upon another living being?' Well, let me give you a few simple answers. Cain was a psycho, in the worst way he could possibly be. Not only that, he was a sadistic freak that adored to see Winter in pain. Why Winter? Well I personally wonder the same thing myself. You see, Cain loved her, and at one point she loved him. At the time, she did not know he was a raging psychopath. She just loved him.He promised her love, love beyond anything that her world could offer. But as time passed, she realized how much of a monster he was. His true sadistic nature revealed itself, and she broke up with him. He would not take that. He loved her, and he was insane, so he promised her he would be back, and he would destroy everyone she ever loved. He was going to give her a fate worse than death, by sending her somewhere she could never escape, somewhere that is completely inhuman. He was sending her to a practical hell, and she had no idea as to where or what it was. And the only funny thing about this story is that she is me.And today I woke up in hell What kind of symbols are MOST likely to be found on a mask used in a ritual? those that relate to spiritual beliefs those that are common in all cultures those that are understood by few peoplethose that are aesthetically pleasing to the culture HELP ME PLEASE ASAP!!Who were the leaders of industry in late nineteenth-century America and what industries did they control? What types of business practices were they accused of? Simplify:1) (3x2y3)2 what.................. what was the cause proclamation of 1763 A conclusion in science states whether or not a hypothesis is corrector not? Find the difference between and 8/15 - -(2/3). Show all calculations in your final answer please!! :) People who buy stock in a company are known as 14x+1=8x+13please explain. Please help! Explain step by step pls :) (The question is on the image that i attached) How did Moctezuma treat Corts?a.He treated Corts as an invading enemy.b.He treated Corts as if he was their promised god, Quetzalcoatl.c.He treated Corts as a weak person who was not worth any attention.d.He treated Corts as a hero and champion of Moctezumas empire.Please select the best answer from the choices providedABCD If a 25 kg object is moving at a velocity of 5 m/s, the object has energy I NEED HELP WITH THIS DRAG-AND-DROP ASAP!!Drag the tiles to the correct boxes to complete the pairs.Item Original Price DiscountShirt $15 20%Pair of Pants $28 15%Pair of Shoes $35 40%Tie $12 15%Match the items with their prices after the discount.1 pair of shoes3 ties2 shirts1 pair of pants$30.60--->$21.00--->$24.00--->$23.80---> Sylvia buys a case of water that contains 24 bottles and sells x number of bottles to her co-workers. Sam buys a case of water than contains 36 bottles and sells three times as they bottles as Sylvia sold to his co-workers. How many bottles of water did Sylvia sell if they ended up with the same number of bottles of water left over?