(1 point) find the total mass of the triangular region shown below. all lengths are in centimeters, and the density of the region is δ(x)=4 x grams/cm2.

Answers

Answer 1

The total mass of a triangular region with density δ(x) = 4x is found by integrating the density function over the region and multiplying by the area. For a triangular region defined by (0,0), (8,0), and (0,16), the total mass is approximately 170.67 grams.

To find the total mass of the triangular region, we need to integrate the density function over the region and then multiply by the area. The density function is given as δ(x) = 4x grams/cm², and the triangular region is defined by the vertices (0,0), (8,0), and (0,16) in the xy-plane.

To set up the integral, we need to express the density function as a function of x and y. The density varies only with x, so we can write δ(x, y) = δ(x) = 4x grams/cm².

The integral for the total mass M is given by:

M = ∬R δ(x, y) dA

where R is the triangular region, dA is the differential area element, and the integral is taken over the region R.

We can express the differential area element dA as dA = dx dy, since the region is defined in terms of x and y.

The limits of integration for x are from 0 to 8, and for y they are from 0 to (4/8)x, since the upper boundary is defined by the line y = (1/2)x.

Therefore, we have:

M = ∫₀^₈ ∫₀^(4/8 x) δ(x) dy dx

M = ∫₀^₈ ∫₀^(4/8 x) 4x dy dx

M = ∫₀^₈ 2x² dx

M = [2/3 x³] from 0 to 8

M = (2/3)(8³) - (2/3)(0³)

M = 170.67 grams (rounded to two decimal places)

Therefore, the total mass of the triangular region is approximately 170.67 grams.

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Related Questions

Atmospheric molecules do not fly off into outer space due toA) their chaotic speeds.B) their relatively low densities.C) Earth gravitation.D) cohesive forces.

Answers

Atmospheric molecules do not fly off into outer space due to **Earth's gravitation** and **cohesive forces**.

A) Chaotic speeds: Atmospheric molecules have varying speeds and directions due to their thermal energy, resulting in a chaotic motion. However, this alone does not prevent them from escaping into space.

B) Low densities: While atmospheric gases have relatively low densities compared to solid or liquid substances, it is not solely the low density that prevents them from escaping. Even gases with low densities can escape if not held by other forces.

C) Earth gravitation: Earth's gravitational force acts as a significant factor in keeping atmospheric molecules from flying off into space. Gravity pulls the molecules towards the Earth, providing the necessary centripetal force to maintain their presence in the atmosphere.

D) Cohesive forces: Cohesive forces, such as intermolecular attractions and Van der Waals forces, play a role in holding atmospheric molecules together. These forces help maintain the integrity of the atmosphere and prevent individual molecules from breaking free and escaping into space.

The combined effect of Earth's gravity and cohesive forces acts as a barrier, keeping atmospheric molecules bound to the planet and preventing their escape into outer space.

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consider the following statements and determine if true or false. false a spontaneous electrochemical reaction will always have a positive voltage false w

Answers

Yes this statement is true about electrical resistance.

What is electrical resistance ?

electrical resistance is a force that counteracts the flow of current.

Sol- when two lamps are connected in parallel to a battery, the total electrical resistance that the battery senses is more than the resistance of either . Beacuse In a parallel circuit each bulb is in its own circuit. As bulbs are added the resistance in the circuit decreases since each circuit is another pathway for electrons to move from one end of the circuit to the other.when two lamps are connected in series to a all the  battery the electricals resistance that the battery's senses is the more than the resistance of either lamp.

As each bulb is connected in parallel to the battery, each has the same potential difference across it as the all of  voltage across the battery of the  terminals. All other to the potential differences are zero, as all the wires have to the zero resistance.

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Let's assume that you are lost at sea on an old ship. It is possible to determine your longitude if you know your solar time and the time and longitude of another location. As an example, assume the last port you were in was near Greenwich, England (the Prime Meridian), and you set your pocket watch before departure. Assuming that it is solar noon at your location on the lost ship, what is your longitude if the time at the Prime Meridian is 12:30AM ? Use the format of 45 W or 37.5E (notice no space) We in California fall into into these lines of latitude: 32∘30′N to 42∘N and these lines of longitude: 114∘8′W to 124∘24′W. Lake Tahoe where the line that separates us from Nevada and then goes diagonally to the Colorado River, is located at 39∘N and 120∘W longitude. It is currently solar noon (subsolar point), what would be the solar time at 15∘W ? (time should be reported in this format) 7:17 am or 12:20pm (with the ":" and the "am" "pm" designation).

Answers

The longitude of the lost ship, assuming solar noon at the location and a time of 12:30 AM at the Prime Meridian, would be approximately 7.5 W.

To determine the longitude, we can use the concept of solar time and the time difference between the location of the lost ship and the Prime Meridian. Solar time is based on the position of the Sun in the sky, and it varies as we move across different longitudes.

Given that it is solar noon at the lost ship's location, it means the Sun is directly overhead at that moment. However, at the Prime Meridian (Greenwich, England), the time is 12:30 AM. The time difference between the two locations is 12 hours and 30 minutes.

Since each hour corresponds to 15 degrees of longitude (360 degrees divided by 24 hours), we can calculate the longitude by dividing the time difference by 1 hour per 15 degrees. In this case, the time difference of 12 hours and 30 minutes corresponds to 7.5 hours, which translates to 7.5 times 15 degrees, resulting in a longitude of 112.5 degrees west or 7.5 W.

As for the second part of the question, if Lake Tahoe is located at 120 degrees west longitude and it is currently solar noon, we can determine the solar time at 15 degrees west longitude. Each degree of longitude corresponds to 4 minutes of time (360 degrees divided by 24 hours), so the time difference between 120 degrees west and 15 degrees west is 105 degrees.

Multiplying 105 degrees by 4 minutes gives us a time difference of 420 minutes. Adding this to the solar noon time (12:00 PM), we get a solar time of 7:00 PM at 15 degrees west longitude. Therefore, the solar time at 15 degrees W would be 7:00 PM.

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what is the difference between atoms and particals? Help ​

Answers

An atom is the smallest unit of matter that forms a chemical element. An atom is made up of three kinds of subatomic particles: electrons, protons, and neutrons.A molecule is a combination of atoms bonded together through a covalent bond. Generally, we think of molecules as having no charge (although molecular ions do exist)

what is a microwave?

Answers

Answer:

an electromagnetic wave with a wavelength in the range 0.001–0.3 m, shorter than that of a normal radio wave but longer than those of infrared radiation. Microwaves are used in radar, in communications, and for heating in microwave ovens and in various industrial processes.

. The limit to the eye's acuity is actually related to diffraction by the pupil. (a) What is the angle between two just-resolvable points of light for a 2.8 mm-diameter pupil, assuming an average wavelength of 540 nm? 0 = ✔rads (b) Take your result to be the practical limit for the eye. What is the greatest possible distance a car can be from you if you can resolve its two headlights, given they are 1.1 m apart? r = km (c) What is the distance between two just-resolvable points held at an arm's length (1 m) from your eye? S= mm

Answers

Angle between two just-resolvable points of light:Angle between two just-resolvable points of light (θ) is given by the formula:

θ = 1.22 * (λ/D)

Here,λ is the average wavelength of light, which is 540 nm.D is the diameter of the pupil, which is 2.8 mm. 1 mm = 10^-3 m.2.8 mm = 2.8 × 10^-3 m.θ = 1.22 * (λ/D)θ = 1.22 * (540 × 10^-9/2.8 × 10^-3)θ = 2.357 × 10^-4 radians. (b)The greatest possible distance a car can be from you if you can resolve its two headlights, given they are 1.1 m apart is given by the formula:r = S * tanθ.

Here,θ is the angle between two just-resolvable points of light, which is 2.357 × 10^-4 radians.S = 1.1 m (distance between two headlights)r = S * tanθr = 1.1 * tan (2.357 × 10^-4)r = 2.576 × 10^-4 km (or 257.6 m) (approximately). (c)The distance between two just-resolvable points held at an arm's length (1 m) from your eye is given by the formula:S = r/ tanθHere,θ is the angle between two just-resolvable points of light, which is 2.357 × 10^-4 radians.r = 1 m (arm's length)S = r/ tanθS = 1/tan (2.357 × 10^-4)S = 4.23 mm.

Therefore, the required values are:Angle between two just-resolvable points of light (θ) = 2.357 × 10^-4 radians.The greatest possible distance a car can be from you if you can resolve its two headlights, given they are 1.1 m apart (r) = 2.576 × 10^-4 km (or 257.6 m) (approximately).The distance between two just-resolvable points held at an arm's length (1 m) from your eye (S) = 4.23 mm.

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What are the three stages of matter and how?​

Answers

Answer:

Solid, Liquid and Gas

Explanation:

They are the 3 states or stages of Matter

Carbon dioxide undergoes a phase change called sublimation, how does a single molecule of carbon dioxide change as a result of this process in terms of its energy and physical characteristics? a. There is a physical change from a gas to a liquid; energy is released into the environment reducing the molecular movement. b. There is a physical change from the solid state to a gas state where energy between the molecules increases. c. There is a chemical change between the carbona nd oxygen resulting int he formation of oxygen gas which has more energy d. There is a chemical change as the carbon dioxide is transferred from a liquid to a solid reducing the amount of energy

Answers

The correct answer is(b). There is a physical change from the solid state to a gas state where energy between the molecules increases.

What is the process of sublimation in carbon dioxide?

During sublimation, carbon dioxide transitions directly from the solid state (dry ice) to the gas state without passing through the liquid phase. In this process, individual molecules of carbon dioxide gain energy from the surroundings, leading to an increase in their kinetic energy and molecular movement.

As a result, the carbon dioxide molecules separate from each other and form a gas. This phase change is considered a physical change rather than a chemical change since the chemical composition of carbon dioxide remains the same throughout the process.

Therefore, the sublimation of carbon dioxide results in a physical change where the molecules transition from the solid state to the gas state, gaining energy and increasing their molecular movement.

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if you are driving 90 km/h along a straight road and you look to the side for 2.8 s , how far do you travel during this inattentive period?

Answers

During this interval of inattention, you go around 252 metres.

Determine the speed in metres per second.

Speed in km/h = 90 km/h

1 km/h = 1000/3600 m/s

Speed in m/s = 90 x 1000/3600 = 25 m/s

Determine the time in seconds.

Time = 2.8 s

Figure out the distance.

Distance = Speed x Time

Distance = 25 m/s x 2.8 s

Distance = 70 m

Do the conversion from feet to kilometres.

1 km = 1000 m

Distance in km = 70/1000 = 0.07 km

Determine the distance in metres.

1 km = 1000 m

Distance in m = 0.07 x 1000 = 70 m

Determine the total distance that was covered during the inattentive period.

Total Distance = Distance traveled before inattention + Distance traveled during inattention

Total Distance = 90 x 2.8 + 70

Total Distance = 252 m

Throughout this period of inattention, you move around 252 metres.

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yo pls help me I'm desperate lowkey

yo pls help me I'm desperate lowkey

Answers

The answer should be B
I think the awnser for this should be b

If the mass of the cement is 15000kg. calculate the density of this cement sample in kgm-3​

Answers

The density of this cement sample is equal to \(2727.27\;kg/m^3\)

Given the following data:

Mass of cement = 15000 kgLength = 1.1 mWidth = 2 mHeight = 2.5 m

To calculate the density of this cement sample​:

First of all, we would determine the volume of the rectangular block.

\(Volume = length \times width \times height\\\\Volume = 1.1 \times 2 \times 2.5\\\\Volume = 5.5 \;m^3\)

Now, can calculate the density of this cement sample:

Mathematically, the density of a substance is given by the formula;

\(Desnity =\frac{Mass}{Volume}\)

Substituting the values into the formula, we have;

\(Density=\frac{15000}{5.5} \\\\Density =2727.27\;kg/m^3\)

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Note: 1.1 m, 2 m, 2.5 m are the figures provided from a rectangular block of cement.

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Eren Jagear supremacy? kind of.. rip? Eren Jagear supremacy? kind of.. rip?Eren Jagear supremacy? kind

Answers

sis i love the eren season 1-2-3-4 but the eren season 5?....... i just :')

Answer:

Explanation:

Aaron yogurt supremacy

Raul is riding on a train that is moving at a speed of 20.0 meters per second. Kirstin is sitting across from him, and there is a distance of 1.8 meters between them. If Raul and Kirstin do not leave their seats, which of the following graphs shows the distance from Raul to Kirstin over the first 6 seconds of the trip?

Raul is riding on a train that is moving at a speed of 20.0 meters per second. Kirstin is sitting across

Answers

Answer:

C

Explanation: Study Island

Answer:

The Straight Line Graph

Explanation:

When you walk into a dark room and turn the light on, do the electrons travel all the way from the switch to the light?

Answers

Answer:

Yes

Explanation:

This is because for the light to come on, electric current has to flow through it which is due to electron motion. As the electrons move through the light, it turns electrical energy to light energy, so the light comes on.

For the following four scenarios, indicate whether star A is more luminous, star B is more luminous, or you can't tell.

Star A and B are the same size, but star A is red while star B is blue.

a.
Star A

b.
Star B

c.
Can't tell



QUESTION 3

Star A and B are the same color, but star A is larger than star B.

a.
Star A

b.
Star B

c.
Can't tell



QUESTION 4

Star A is larger than star B, and star A is blue while star B is red.

a.
Star A

b.
Star B

c.
Can't tell



QUESTION 5

Star A is larger than star B, and star A is red while star B is blue.

a.
Star A

b.
Star B

c.
Can't tell



QUESTION 6

If you could sample all of the stars in our Galaxy (which is simply a collection of stars, gas & dust which are all gravitationally bound to a common center of mass), which set (nearest or brightest) do you think would best represent the relative distribution of stars in that sample?

Answers

a. Star A

b. Can't tell

QUESTION 3) a. Can't tell

QUESTION 4) a. Star A

QUESTION 5) b. Star B

QUESTION 6 )The brightest set of stars would best represent the relative distribution in a sample of all stars in our Galaxy.

a) In scenario a, where Star A is red and Star B is blue, we can tell that Star A is more luminous. Generally, blue stars are hotter and more luminous than red stars. Therefore, Star B being blue implies it has a higher luminosity compared to Star A.

b) In scenario b, no information is provided about the colors or sizes of Star A and Star B. Without this information, we cannot determine which star is more luminous.

3) In scenario a, where Star A and Star B are the same color but Star A is larger than Star B, we cannot determine which star is more luminous based solely on their sizes and colors. Luminosity depends on factors such as surface temperature and stellar composition, which are not provided

4) In scenario a, where Star A is larger than Star B and Star A is blue while Star B is red, we can tell that Star A is more luminous. As mentioned before, blue stars are generally hotter and more luminous than red stars. Additionally, the larger size of Star A suggests it has a higher luminosity.

5) In scenario b, where Star A is larger than Star B and Star A is red while Star B is blue, we can tell that Star B is more luminous. Blue stars are hotter and more luminous than red stars, so Star B being blue implies it has a higher luminosity. Additionally, the larger size of Star A does not necessarily mean it is more luminous in this case.

The brightest set of stars would best represent the relative distribution in a sample of all stars in our Galaxy.

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A sample of oxygen gas occupies a volume of 200 mL at a pressure of 720 torr. What volume will the gas occupy at a pressure of 800 torr if temperature is held constant

Answers

We have that the gas will occupy at a pressure of 800 torr if temperature is held constant a Volume of

\(V_2=0.18L\)

From the Question we are told that

Initial Pressure \(P_1=720\)

final Volume  \(V_1=200mL\)

Initial Pressure \(P_2=800\)

final Volume  \(V_2=?\)

Generally the equation for Boyle's law  is mathematically given as

\(P_1V_1= P_2V_2\)

Therefore

\(V_2=\frac{ P_1V_1}{P_2}\\\\V_2=\frac{ 720*200}{800}\\\\V_2=180mL\)

\(V_2=0.18L\)

The gas will occupy at a pressure of 800 torr if temperature is held constant a Volume of

\(V_2=0.18L\)

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What is the molarity of a solution prepared by dissolving 200 g nacl in 1.50 l water?

Answers

The molarity of solution of NaCl is 2.28 M

What is the molarity of a solution?

The molarity of a solution is the amount in moles of a solute dissolved in a given volume of solvent in liters.

Molarity = moles/volume in L

The moles of a substance = mass/ molar mass

Molar mass of NaCl = 58.5 g/mol

Moles of NaCl = 200/58.5

Moles of NaCl = 3.42 moles

Molarity of solution = 3.42/1.5

molarity of solution = 2.28 M

Therefore, the molarity of the solution of NaCl is 2.28 M.

In conclusion, molarity is the ratio of moles of solute and volume of solvent.

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a 50 kg aardvark runs with a speed of 6 m/s. what is the kinetic energy of the aardvark

Answers

Answer:

900 J

Explanation:

0.5 x 50= 25 x 6^2= 900 J

A scientist studies what makes leaves fall off trees. Which of the following is
a testable question about this topic?
A. Should people be allowed to burn leaves?
B. Do stronger winds make more leaves fall?
C. Are trees an interesting topic to study?
D. Do leaves still look beautiful once they reach the ground?

Answers

The testable question about the topic being studied by the scientist is as follows: Do stronger winds make more leaves fall? (option B).

What is a scientific experiment?

An experiment is a test under controlled conditions made to either demonstrate a known truth, examine the validity of a hypothesis, or determine the efficacy or likelihood of something previously untried.

According to this question, a scientist studies what makes leaves fall off trees. Prior to the inception of the experiment, a scientific and testable question must be asked.

The testable question among the options given above is whether or not stronger wind can make leaves fall off a tree.

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A cyclist travels at 15 m/s during a sprint finish. What is this speed in km/h

Answers

Answer:

54 km/hr

Explanation:

m/s to km/hr => 18/5

15 m/s to km/hr => 15 x 18/5 =>3 x 18 => 54km/hr

the back wall of an auditorium is 25.0 m from the stage. part a if you are seated in the middle row, how much time elapses between a sound from the stage reaching your ear directly and the same sound reaching your ear after reflecting from the back wall? the speed of sound in the air is 343 m/s .

Answers

The difference of time between a sound from the stage reaching your ear directly and the same sound reaching your ear after reflecting from the back wall would be 0.036s.

What does a sound wave echoe mean?

An echo is a reflection of sound that comes to the audience with a delay after the direct sound in audio signal processing and acoustics. The delay is directly proportionate to the separation between the source and the listener of the reflecting surface. One the kind audio effect that involves significantly delaying a signal is an echo effect. In this instance, after some period of time, listeners hear the same signal repeated clearly. When there is a noticeable delay in the sound, listeners can differentiate individual echoes.

The person seated in the middle row:

The distance sound traveled to middle row => 25/2 = 12.5m

The total distance the sound traveled to full length of auditorium and to the middle row => 25+12.5 => 37.5m

t1 => d1/v => 12.5/343 => 0.036s

t2 => d2/v => 25/343 => 0.072s

t2-t1 => 0.036s

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large-scale winds are generated on earth primarily because of

Answers

Large-scale winds are generated on Earth primarily because of atmospheric pressure differences.

What is the main cause of winds on Earth?

The primary cause of large-scale winds on Earth is the uneven heating of the Earth's surface by solar radiation, which creates variations in atmospheric pressure.

The sun's energy heats the Earth's surface unevenly, with different regions receiving different amounts of heat. As a result, the air above these regions becomes warmer and expands, leading to a decrease in air pressure.

In contrast, areas with cooler temperatures have denser air, resulting in higher atmospheric pressure. The difference in pressure between these regions creates a pressure gradient, which drives the movement of air from high-pressure areas to low-pressure areas. This movement of air is what we perceive as wind.

The Earth's rotation also plays a significant role in shaping wind patterns. The Coriolis effect, caused by the planet's rotation, deflects moving air to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.

This deflection further influences the direction and patterns of large-scale winds, creating phenomena like trade winds, prevailing westerlies, and polar easterlies.

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how to find average velocity on a velocity time graph

Answers

To find the average velocity on a velocity-time graph, you need to calculate the slope of the line connecting two points on the graph. The average velocity represents the change in velocity divided by the change in time between those two points.

To calculate the average velocity, you can use the formula:

Average velocity = (change in velocity) / (change in time)

You can determine the change in velocity by finding the difference between the final velocity and the initial velocity. The change in time is the difference in the time coordinates of the two points.

Select two points on the velocity-time graph, typically denoted by (t₁, v₁) and (t₂, v₂), where t represents time and v represents velocity. Then, substitute the values into the formula mentioned above to calculate the average velocity.

It's important to note that the average velocity provides information about the overall change in velocity over a specific time interval, rather than instantaneous velocity at a particular moment.

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The organisms and environments that make up a community, called an Response area, are constantly changing. Sudden and violent events, such as Response area from the ocean and Response area, that often cause these changes are called Response area. Response area results when rainfall exceeds the holding capacity of a drainage system.

Answers

Answer:

ecosystem; hurricanes and tornadoes; catastrophic events.; Fooding; moving water; soil

Explanation:

After using the word bank to fill in the blanks in the passage, the passage reads;

"The organisms and environments that make up a community called an ecosystem are constantly changing. Sudden and violent events, such as hurricanes and tornadoes that often cause these changes are called catastrophic events. Fooding results when rainfall exceeds the holding capacity of a drainage system. The energy of the  fast-moving water and the layers of sediment carried by it  can uproot or bury plants, reshape the soil and destroy  roads and buildings."


PLZZZ HELLPP MEE

Which of the choices below shows a model of the atom Neon (Ne)?
B.
D.
Ne
Ne Ne
OB
ОС
OD

PLZZZ HELLPP MEE Which of the choices below shows a model of the atom Neon (Ne)?B.D.NeNe NeOBOD

Answers

Answer:

A is answer

Explanation:

this is helpful

why do we tilt umbrella in rain. Explain​

Answers

Answer:

Rain is falling vertically. A man running in the road keeps his umbrella tilted but a man standing on road keeps his umbrella vertical to protect himself from the rain but both of them keep their umbrella vertical to avoid the vertical sun-rays. ... Thus we can tilt the umbrella to avoid it.

Explanation:

XOXO

Kit

the transit method gives us the ________________________ of the exoplanet if we know the star's properties.
group of answer choices
A. mass
B. radius
C. composition
D. density

Answers

The transit method gives us the radius of the exoplanet if we know the star's properties. The correct answer is option B.

The transit method is one of the most commonly used techniques for detecting exoplanets. This method involves observing a star and looking for periodic dips in its brightness, which occur when an exoplanet passes in front of the star from our line of sight. By carefully measuring the shape and depth of these dips, astronomers can determine the size or radius of the exoplanet relative to the star. This is possible because the amount of light that is blocked by the planet during transit is directly related to the size of the planet relative to the size of the star.

However, to determine other properties such as the mass and density of the exoplanet, additional measurements are typically needed, such as radial velocity measurements or modeling the planet's atmospheric composition and structure.

Therefore option B is the correct answer.

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HELPPPPPPP!!!!!

why are cations drawn towards cathode and anions towards anode?​

Answers

Explanation:

Cations are positive and anions are negative, since opposite charged attract, the cations are drawn towards the cathode, which is the negatively charged electrode and anions are drawn towards the anode (positive electrode)

Answer:

because cations are negatively charged particles and their attracted towards a positive electrode that is anode while anions and positively charged particles and I attracted towards the negative electrode that is cathode

Explanation:

Josh pushes a table with a force of 80. N at an angle of 30°


to the table. If he pushes the table 5 meters, how much


work has he done? Joules

Answers

Josh pushes a table with a force of 80. N at an angle of 30° to the table. If he pushes the table 5 meters then Josh has done 346.41 Joules of work on the table.

To calculate the work done by Josh on the table, we can use the formula:

\(W = F \times d \times cos(\theta)\)

where W is the work done, F is the force applied, d is the distance moved, and theta is the angle between the force and the direction of motion.

Substituting the given values, we get:

\(W = 80 N \times 5 m \times cos(30^{\circ})\)

W = 346.41 J

Therefore, Josh has done 346.41 Joules of work on the table. To understand the concept of work, it is important to note that work is done when a force is applied to an object and it causes it to move.

In this case, Josh applies a force of 80 N at an angle of 30° to the table, causing it to move 5 meters. The work done is calculated by multiplying the force, distance, and cosine of the angle between them.

In summary, to calculate the work done by Josh on the table, we use the formula \(W = F \times d \times cos(\theta)\) , where W is the work done, F is the force applied, d is the distance moved, and theta is the angle between the force and the direction of motion.

By substituting the given values, we find that Josh has done 346.41 Joules of work on the table.

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An archer shoots an arrow with a mass of 45.0 grams from bow pulled
back 65.0 centimeters. It reaches 150.0 meters in height. Ignoring air
resistance, what force in Newtons did the archer need to pull in order to
achieve this height? Your answer should be reported to the appropriate
number of significant figures. *

Answers

Answer:

The force the archer need to pull in order to achieve the height is approximately 101.8 N

Explanation:

By energy conservation principle, puling an elastic bow with a force, for a given distance, performs work which is converted to the potential energy of the arrow at height

The given parameters are;

The mass of the arrow, m = 45.0 grams = 0.045 kg

The distance the elastic bow is pulled, d = 65.0 cm = 0.65 m

The height at which the arrow is reaches, h = 150.0 meters

Let 'F', represent the force the archer need to pull in order to achieve the height

Work done, W = Force × Distance moved in the direction of the force

Therefore;

The work done in pulling the arrow, W = F × d

By energy conservation, we have;

The work done in pulling the arrow, W = The potential energy gained by the arrow, P.E.

W = P.E.

The potential energy gained by the arrow, P.E. = m·g·h

Where;

m = The mass of the arrow

g = The acceleration due to gravity = 9.8 m/s²

h = The height the arrow reaches

∴ by plugging in the values, P.E. = 0.045 kg ×9.8 m/s² × 150 m = 66.15 J

W = F × d = F × 0.065 m

Also, W = P.E. = 66.15 J

∴ W = F × 0.065 m = 66.15 J

F × 0.065 m = 66.15 J

F = 66.15 J/(0.65 m) = 1323/13 N ≈ 101.8 N

The force the archer need to pull in order to achieve the height, F ≈ 101.8 N.

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