Write a formula for a triangular wave with period 6, minimum value 0 and maximum value of 10

Answers

Answer 1

The equation for triangular wave with period 6 and amplitude 10 is -

[tex]$y=\frac{40}{6} |(x -\frac{6}{4})\;mod\;6)-\frac{6}{2}| - 10[/tex].

We have a triangular waveform.

We have to determine the equation representing this triangular waveform.

What is Waveform?

A waveform is a graphical representation of the shape of a wave that indicates its characteristics such as frequency and amplitude.

According to the question, we have -

Time Period = 6

Minimum value = 0

Maximum value = 10

Therefore -

Range → R ∈ [0, 10]

Amplitude = Max. value - Min. value = 10 - 0 = 10

The general equation for a triangle wave with amplitude 'a' and period 'p'  is given by →

[tex]$y=\frac{4a}{p} |(x -\frac{p}{4})\;mod\;p)-\frac{p}{2}| - a[/tex]

Now -

a = 10

p = 6

Substituting values -

[tex]$y=\frac{40}{6} |(x -\frac{6}{4})\;mod\;6)-\frac{6}{2}| - 10[/tex]

Hence, the equation for triangular wave with period 6 and amplitude 10 is -

[tex]$y=\frac{40}{6} |(x -\frac{6}{4})\;mod\;6)-\frac{6}{2}| - 10[/tex]

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Related Questions

How is the density of a fish controlled? how is the density of a submarine controlled?

Answers

The density of a fish is controlled by the expansion and contraction of its air sacs while the density of a submarine is controlled by ballast tanks. It was emphasized earlier that buoyant forces does not equal an objects weight but does equal the weight of displaced water.

What are mass, density, and volume ?

The three most fundamental characteristics of an object are mass, volume, and density. Volume indicates something's size, mass indicates how heavy it is, and density is calculated as mass divided by volume. Although you deal with mass and volume on a daily basis, the concept of density is less clear-cut and requires careful consideration.

Mass divided by density equals volume; and. Volume times density equals mass. A liquid's density is a gauge of how heavy it is relative to the amount being measured. The liquid that weighs heavier is more dense if you weigh two liquids with similar volumes or amounts.

The relationship between a substance's mass and the amount of space it occupies is known as its density (volume). The density of a substance is determined by the mass, size, and arrangement of its atoms.

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A physics student places an object 6.0 cm from a converging lens of focal length 9.0 cm. what is the magnitude of the magnification?

Answers

The magnitude of the magnification for converging lens is 3

Converging lens is convex lens whereas diverging lens is a concave lens.

Given:

distance of object from converging lens = 6.0 cm

focal length = 9.0 cm

To Find:

magnitude of the magnification

Solution: Magnification is the ability of a microscope to produce an image of an object at a scale larger (or even smaller) than its actual size.

Magnification (m) = h / h' Here, h is the height of the object and h' is the height of the object. Besides, it can also be related to the object distance and image distance. So, it can be written as: m = -v/u

Using the formula for magnitude of magnification

1/f = 1/d° + 1/di

M = - d1/d° = 3

Hence, magnitude of the magnification is 3

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A person who weighs 100 pounds steps onto a scale which indicates that they weigh 200 pounds. he/she gets off the scale, steps back on, and it still reads 200 pounds. that scale is considered:________

Answers

The scale is said to be reliable but not valid.

A person weighing 100 pounds is expected to return the same weight on mounting a scale, measuring 200 pounds means the scale is probably uncalibrated. However, when the person steps off and climbs back and the scale still shows 200 pounds this means the scale is reliable but not valid. The scale would have been rendered unreliable and invalid if it returns a different weight of the person. Hence, the scale is working but needs to be calibrated properly. It is also probable that the scale had been earlier set to 100 pounds which explains the reason for a doubled result.

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While passing a slower car on the highway, you accelerate uniformly from 17.5 m/s to 29.5 m/s in a time of 11.1 s. how far do you travel during this time?

Answers

When I accelerate uniformly from 17.5 m/s to 29.5 m/s in a time of 11.1 s, I travel 260.85 m

The formula for Uniformly varied rectilinear motion (UVRM) and procedure we will use to solve this exercise is:

x = [(vi + vf) /2] * t

Where:

x = distancevf = final velocityvi = initial velocityt = time

Information about the problem:

vi= 17.5 m/svf = 29.5 m/s t = 11.1 sx= ?

Applying the distance formula, we have:

x = [(vi + vf) /2] * t

x = [(17.5 m/s + 29.5 m/s ) /2] * 11.1 s

x = [(47 m/s ) /2] * 11.1 s

x = (23.5 m/s) * 11.1 s

x = 260.85 m

What is acceleration?

It is a physical quantity that indicates the variation of velocity as a function of time, it is expressed in units of distance per time squared e.g.: m/sec2 ; km/h2

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A doctor measures the temperature of a patient
to be 101°F. What is this temperature in kelvins?
(A) 38.3 K
73.8 K
311 K
(C)
214 K
(E) 346 K
(B)
(D)
-please help I’m too lazy to do the math

Answers

Answer: 311.483

Explanation:

(101°F − 32) × 5/9 + 273.15 = 311.483K

A road has a rise of 7m for every 120m of horizontal distance. what is the degree of the elavation?

Answers

The degree of the elevation is 3.3

What is the degree of elevation?Without altering the curve's shape, degree elevation raises the curve's degree. They offer two widely used methods to make two curves compatible, together with knot insertion.How do you measure elevation?"Rise over Run," which equals the rise (the change in vertical distance) divided by the run, is a simple formula for calculating the change in elevation as a decimal (the change in horizontal distance). Say, for illustration, that the rise is two and the run is six. Therefore, you would add 2 to 6 (or 2/6) to obtain.

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What strategies are likely to be most effective in teaching a young child to throw a ball?

Answers

The best strategy for teaching a toddler or pre-schooler to throw is to simply play lots of throwing games with them without providing instruction. This will enable children to learn the fundamentals of throwing as their muscle coordination gradually improves over time.

What do you mean by throwing?

Throw me a ball is an expression used to launch a ball through the air To abruptly place in a particular state or situation Please don't throw rubbish on the ground. He was thrown in jail to cause to tumble .The horse hurled its rider to put on or take off in a fast Let me throw on a coat.

Which three forms of throwing are there?

Overhand, underhand, and throws made with both hands are among the different kinds. Underhand throws are typically made below the shoulder, whereas overhand throws are typically made above.

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If a basketball player jumps and lands on the ground after 3.2 seconds with a final velocity of −5.5 m/s, what is the player’s initial velocity? Assume (a=−9.8 m/s2)


Show some work

Answers

The initial velocity of the player, given it landed on the ground after 3.2 s is 15.68 m/s

How to determine the time

We'll beging by obataining the time taken for the player to reach the maximum height. This can be obtannnned as follow:

Time for the entire trip (T) = 3.2 sTime to reach maximum height (t) = ?

T = 2t

3.2 = 2t

Divide both sides by 2

t = 3.2 / 2

t = 1.6 s

How to determine the initial velocity of the player

The initial velocity of the player can be obtained as follow:

Time to reach maximum height (t) = 1.6 sAcceleration due to gravity (g) = -9.8 m/s²Final velocity (v) = 0 (at maximum height)Initial velocity (u) = ?

v = u + gt

0 = u + (-9.8 × 1.6)

0 = u - 15.68

Collect like terms

u = 0 + 15.68

u = 15.68 m/s

Thus, we can conclude that the initial velocity of the player is 15.68 m/s

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If you have to change the composition of a substance to measure that property, it is a
physical property.

O True

O False

Answers

Answer:

False

Explanation:

Physical properties can be measured without changing the composition of the substance. Physical properties of matter include color, hardness, malleability, solubility, electrical conductivity, density, melting point, and boiling point.

However, the chemical properties have to be measured by changing the composition of the substance.

Have a lovely rest of your day! :)

False.







Is correct answer

Infrared radiation has wavelengths ranging from about 800 nm to 1 mm. What is the corresponding frequency of radiation of a wavelength of 970 nm?.

Answers

By using electromagnetic waves, the frequency of radiation is 3.09 x 10¹⁴ Hz.

We need to know about electromagnetic waves to solve this problem. Electromagnetic waves can propagate without media. The speed of electromagnetic in vacuum media is equal to the speed of light. Hence, the wavelength and frequency can be determined as

c = λ . f

where c is the speed of light (3 x 10⁸ m/s), λ is wavelength and f is frequency.

From the question above, we know that

λ = 970 nm = 970 x 10¯⁹ m

By substituting the given parameter, we can calculate the frequency of radiation

c = λ . f

f = c / λ

f = 3 x 10⁸ / 970 x 10¯⁹

f = 3.09 x 10¹⁴ Hz

Hence, the frequency of radiation is 3.09 x 10¹⁴ Hz.

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One of the fundamental general safety guidelines with respect to hot work is to keep the work area clear of combustibles for at least from the hot work area

Answers

One of the fundamental general safety guidelines is to keep the work area clear of combustibles for at least 35 feet from the hot work area.

Hot works or combustible works such as welding, heating or cutting should be done at a location which is far away form any combustible material.

Prior to start working in such a location make sure there are no hazardous or combustible material around such as fire, ignition source or electric spark.

All precautionary measures must be taken to confine heat, fire or spark so that they don not come into contact with nay combustible object.

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Find the vector v with the given magnitude and the same direction as u. magnitude direction v = 4 u = 1, 1

Answers

The vector v with the given magnitude and the same direction as u. magnitude direction v = 4 u =< 1, 1>

=4/[tex]\sqrt2{^{2} }[/tex] i + 4/[tex]\sqrt2{^{2} }[/tex] j

What is vector?

Vector, in physics, a quantity that has both magnitude and the direction. It is a typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity’s magnitude. Although vector has magnitude and direction, it does not have the position. That is, as long as its length is not changed, vector is not altered if it is displaced parallel to itself.

In contrast to vectors, ordinary quantities that have a magnitude but not a direction are called the scalars. For example, displacement, velocity, and acceleration are vector quantities, while the speed (the magnitude of velocity), time, and mass are scalars.

To qualify as a vector, a quantity having magnitude and direction must also obey certain rules of the combination.

Therefore,

A vector a with given magnitude in the direction of b, is given by:

(||a||.b)/||b||

||u||=[tex]\sqrt{1^{2}+1^{2} }= \sqrt{2^{2} }[/tex]

||v||=4

[4(1+1)]/[tex]\sqrt{2^{2} }[/tex]= 4/[tex]\sqrt2{^{2} }[/tex] i + 4/[tex]\sqrt2{^{2} }[/tex] j

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the energy flux associated with solar radiation incident on the outer surface of the earth's atmosphere has been accurately measured and is known to be 1368 w/m2 . the diameters of the sun and earth are 1.39 × 109 and 1.27 × 107 m, respectively, and the distance between the sun and the earth is 1.5 × 1011 m.

Answers

The emission power of sun is 3.868 * [tex]10^{26}[/tex] W

We know that,

Energy flux on earth = Emission power of sun / 4 π [tex]r^{2}[/tex]

where,

r = Distance between sun and earth

Given that,

Energy flux on earth = 1368 W / [tex]m^{2}[/tex]

Diameter of sun = 1.39 * [tex]10^{9}[/tex] m

Diameter of earth = 1.27 * [tex]10^{7}[/tex] m

r = 1.5 * [tex]10^{11}[/tex] m

Emission power of sun = 1368 * 4 * 3.14 * ( 1.5 * [tex]10^{11}[/tex] [tex])^{2}[/tex]

                                      = 1368 * 2.828 * [tex]10^{23}[/tex]

Emission power of sun = 3.868 * [tex]10^{26}[/tex] W

Energy flux is the rate of transfer of energy through a surface. The unit of total rate of energy transfer is W = J / s. The unit of specific rate of energy transfer is W / [tex]m^{2}[/tex] = J / [tex]m^{2}[/tex] s

Therefore, The emission power of sun is 3.868 * [tex]10^{26}[/tex] W

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An object that is dropped from a height H falls with a constant acceleration of g. The final
speed, v, just before it reaches the ground can be expressed as v = sqrt(2gh). By how much does the height need to change double the final velocity?

Answers

The height has to change by a factor of 1.

What is the height?

We can obtain the height from which the object falls using the equations of kinematics under gravity. We can see that the object was dropped from a height thus u = 0 m/s.

We can the write;

v= √2gh

h1 = v^2/2g

When the final velocity is doubled, we have;

2v= √2gh

h2 =4v^2/2g

h2 = 2v^2/g

The height changes by;

2v^2/g - v^2/2g = v^2/g

Thus the height has to change by a factor of 1.

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When bill butcher of port city brews discusses shelf space and the way that a merger could increase the leverage potential of large brewers, he is discussing which competitive force?

Answers

He is discussing Bargaining Power of Buyers competitive force.

What do you understand by  leverage?

The employment of various financial instruments or borrowed cash, or leverage, is an investing strategy that aims to improve an investment's potential return. The level of debt a company utilizes to finance its assets is another definition of leverage.

It offers a range of funding options so that the company can reach its desired earnings. Leverage is a crucial investing strategy because it enables businesses to establish a ceiling for the growth of their operations.

Leverage can be used, for instance, to support financially a new business. Purchasing fixed assets or borrowing money in the form of a loan from another business or person can serve as examples of leverage.

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A worker at the top of a 459-m-tall television transmitting tower accidentally drops a heavy tool. if air resistance is negligible, how fast (in m/s) is the tool going just before it hits the ground?

Answers

A worker at the top of a 459-m-tall television transmitting tower accidentally drops a heavy tool. If air resistance is negligible, how fast (in m/s) is the tool going just before it hits the ground?

The rule of conservation of energy (the heavy tool’s potential energy at a height of 551 meters above the ground becomes its kinetic energy at ground level) allows us to determine the speed of the object when it hits the ground:

Kinetic Energy Equals Potential Energy

PE=KE

Since mgh=1/2mv2, the mass can cancel out.

In the case where g=9.81m/s2, gh=1/2v2

V=√2gh

=√2*9.81m/s2*459

=3 m/s

It’s possible for an object to have both kinetic and potential energy at once. For instance, a falling object that has not yet hit the ground has both kinetic and potential energy because it is traveling downward and has the capacity to go still further.

The mechanical energy of an object is the total of its potential and kinetic energies.

A falling object loses potential energy while gaining kinetic energy. The difference between the increase in kinetic energy and the decrease in potential energy is exact.

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A car accelerates from 5.0 m/s to 21 m/s at a rate of 3.0 m/s2. how far does it travel while accelerating?

Answers

The car which accelerates from 5.0 m/s to 21 m/s at a rate of 3.0 m/s2 travels 69.33 m

The formula for Uniformly varied rectilinear motion (UVRM) and procedure we will use to solve this exercise is:

x = (vf²-vi²)/ (2a)

Where:

x = distancevf = final velocityvi = initial velocitya = acceleration

Information about the problem:

vi= 5.0 m/s vf = 21 m/sa = 3.0 m/s2x= ?

Applying the distance formula, we have:

x = (vf²-vi²)/ (2a)

x = [(21 m/s)²- (5.0 m/s)²]/ (2 * 3.0 m/s²)

x = (441 m²/s²- 25 m²/s²)/ 6 m/s²

x = 416 m²/s²/ 6 m/s²

x = 69.33 m

What is acceleration?

It is a physical quantity that indicates the variation of velocity as a function of time, it is expressed in units of distance per time squared e.g.: m/sec2 ; km/h2

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If you subtract vector 3.7 cm at 45° North of East from vector 4.5 cm at 57° West of North using a scale drawing, what is the resultant vector?

Answers

The resultant vector is 5.2 cm at a direction of 12⁰ west of north.

Resultant of the two vectors

The resultant of the two vectors is calculated as follows;

R = a² + b² - 2ab cos(θ)

where;

θ is the angle between the two vectors =  45° + (90 - 57) = 78⁰a is the first vectorb is the second vector

R² = (3.7)² + (4.5)² - (2 x 3.7 x 4.5) cos(78)

R² = 27.02

R = 5.2 cm

Direction of the vector

θ = 90 - 78⁰

θ = 12⁰

Thus, the resultant vector is 5.2 cm at a direction of 12⁰ west of north.

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John needs to measure the brightness of a light bulb using the metric system. in which unit does he express his measurement?
A. liter
B. meter
C. kilogram
D. candela

Answers

Option D: John will express his brightness unit in candela.

HOW IS THE BRIGHTNESS OF A LIGHT MEASURED?

Power, or the rate at which energy is utilized or produced over time, is measured in watts. Energy providers utilize watts to calculate the amount of electricity we use in Kilowatts per Hour (kWh), which is equivalent to 1,000 watts used for one hour.

A fundamental unit of measurement for the amount of visible light that a light source emits is called a lumen (lm), also known as luminous flux.

Simply put, to assess the power of a lamp inside a lighting fixture, look for the total number of Lumens.

SUCCESS FOR LUMINAIRE

In addition to the light itself, a number of other elements must be considered when estimating the amount of light that is emitted. Most lamps are housed in a light fixture that is composed of diffusers and reflectors, among other parts.

These variables, along with others like the shape and number of lights, will affect the luminaire’s brightness and light dispersion.

Luminaire efficacy considers these factors to give a more accurate estimation of the lumens generated by the entire luminaire once it is fully constructed.

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The hydrogen stored inside a large weather balloon has a mass of 135.5 g. what is the volume of the balloon (l) if the density of hydrogen gas is 0.089 g/l?

Answers

The volume of balloon will be 1522.5 cubic liter.

We have a hydrogen stored inside a large weather balloon of given mass and density.

We have to calculate the volume of balloon.

How is density and mass of body related ?

The density and mass of body are related as follows -

M = ρV

where -

ρ - Density of Object.

M - Mass of Object.

V - Volume of Object.

According to the question →

Using the formula discussed above -

M = ρV

V = M/ρ

V = 135.5/0.089

V = 1522.5 cubic liter.

Hence, the volume of balloon will be 1522.5 cubic liter.

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For an object being launched at ground level at a tilted non-zero initial velocity, is the velocity zero anywhere? are the horizontal or vertical components of the velocity zero at any point?

Answers

The correct answer No the velocity is not zero anywhere For an object being launched at ground level at a tilted non-zero initial velocity, and horizontal or vertical components of the velocity is zero at maximum height .

Because velocity is a vector (it has magnitude and direction), the overall velocity of an object can be calculated by adding the x and y components: v2 = vx2 + vy2. Meters are used to express horizontal and vertical distances (m). The horizontal velocity component (vx) describes the effect of velocity on horizontal displacement of the projectile.

The vertical velocity component (vy) describes the effect of velocity on vertical displacement of the projectile. The vertical component of a projectile's velocity is momentarily zero (vy = 0 m/s) when it reaches maximum height. The horizontal component of its velocity, however, is not zero.

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What did aristotle and ptolemy say about the relationship of earth to other celestial bodies?.

Answers

Aristotle and Ptolemy said that earth is in the center and all other planets move in a circular motion around Earth.

Aristotle from Classic Greece and Ptolemy from Roman Egypt agreed on three facts:

Earth and other celestial bodies are spherical in shape.Earth is in the center and all other celestial bodies revolve around it.The other planets orbit in a circular path.

This model of the solar system with Earth in the center is called as Geocentric model.

Therefore, Aristotle and Ptolemy said that earth is in the center and all other planets move in a circular motion around Earth.

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Newton did not discover gravity, for early humans discovered that whenever they fell. what newton did discover is that gravity _______.

Answers

What Newton discovered is that  gravity extends throughout the universe.

What is gravity?

The term gravity refers to the force that acts on a body in the universe. It is gravity that makes an object to fall when it is thrown up. The force of gravity acts on every object in the universe and it extends through the universe.

Humans have always known about gravity when they fall from a height and when they threw things up. However, human did not know that gravity extends throughout the universe.

Thus, what Newton discovered is that  gravity extends throughout the universe.

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The four phases of matter include all of the following except _____.
a. water
b. gas
c. liquid
d. plasma
e. solid

Answers

The correct answer is option A. Water is not a state/ phase of matter

What are the states of matter?

States are those phases that describe its physical attributes as well as how its constituent particles are arranged. Solid, liquid, gas, and plasma are the four main states of matter that can exist.

When something melts, it transitions from a solid to a liquid condition.

Water has a freezing point of 0°C.The melting point of flour is around 220 degrees Celsius, which is greater than that of salt and sugar. Sublimation is the process by which a solid transforms into a gaseous state, as in the case of camphor. Examples of changes in the states of matter include the melting of ice, the freezing of water, the burning of camphor, the melting of wax, and the production of precipitates.

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If, in the figure, you start from the Bakery, travel to the Cafe, and then to the Art Gallery in 1.50 hours. What is the average velocity?

Answers

The average velocity is 1 km/hr.

What is average velocity?

Velocity is the speed of a body in a given direction.

Velocity can also defined as the displacement of body with time.

The average velocity will be be the ratio of the total displacement with time.

Average velocity = displacement/time

Taking the right direction as positive and the direction to the left as negative:

displacement of the body = (4.0 - 2.5) km

displacement of the body = 1.5 km

Average velocity = 1.5 km/ 1/5 hours

Average velocity = 1 km/hr

In conclusion, the average velocity is obtained from the displacement and time taken.

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How many grams of solid magnesium nitrate (148.3 g/mol) should be added to 500 ml of 0.118 m of sodium nitrate in order to produce an aqueous 0.25 m solution of nitrate ions?

Answers

4.89g of solid magnesium nitrate (148.3 g/mol) should be added to 500 ml of 0.118 m of sodium nitrate in order to produce an aqueous 0.25 m solution of nitrate ions.

Solution and Explanation

From the given info, we know that there is already the presence of nitrate already mixed in the solution. then we have to find out how more is required to be added to it.

first, we find moles of NaNO3

0.500L x 0.118 M = 0.059 moles NaNO3

this means there are 0.059 moles of[tex]NO^{-} _{3}[/tex]

Here volume is not changing, so amount of moles needed to make this concentration = 0.25M x 0.5L = 0.125 moles

0.125 - 0.059 moles = 0.066 moles of [tex]NO^{-} _{3}[/tex] required to be added in the solution.

for every 1 mole of Mg[tex](NO^{-} _{3} )_ {2}[/tex], there are 2 moles of [tex]NO^{-} _{3}[/tex].

so, we will only need half of the total moles of magnesium nitrate.

converting moles to grams,

0.033 moles Mg[tex](NO^{-} _{3} )_ {2}[/tex] x 148.3 g/mol = 4.89g Mg[tex](NO^{-} _{3} )_ {2}[/tex]

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Water has a ph of 7. ph is defined as the negative log of the hydrogen ion concentration [h ]. explain why water is assigned a ph of 7.

Answers

Answer: Concentration of H+ =10^-7; log of 10^-7=7 so pH=7

Explanation:

Lamar walks 20 m to the west, and then 20 m to the east. it takes him 40 seconds to do this. what is his average velocity?

Answers

Lamar's average velocity is 1 m/s

We know that,

Average Velocity = Total distance travelled / Total time taken

Given that,

Distance travelled west = 20 m

Distance travelled East = 20 m

Total time taken = 40 s

Total distance travelled = 20 + 20 = 40 m

Average Velocity = 40 / 40 = 1 m/s

Average velocity is total rate of change of displacement.

Therefore, Lamar's average velocity is 1 m/s

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A liquid mixture of water and alcohol has density off 900 kg per metre cubic find the mass of alcohol in one litre of the mixture. .

Answers

The mass of alcohol in one litre of the mixture is 371g

Calculation and Explanation

Let us assume the alcohol to be ethyl alcohol (C2H5OH) with the temperature being 20°C.

Given we have assumed this, the density of water and ethyl alcohol becomes,

ρa=789.45g/L

ρw=998.23gL

and then it is given that the density of the solution is ρs=900gL

We know that,

ρ= m/v

⇒ m=ρv

⇒m=ρs Vs = 900g

Then we see that the sum of the mass of ethyl alcohol and water is the same as 900g

But we are interested in finding the values keeping the volume as 1L

hence, Va +Vw =1

⇒ Vw = 1-Va

Then we know that

900g=Va(789.45g/L)+(1−Va)(998.23g/L)

so solving the equation for ethyl alcohol, we have.

Va = 0.4705 L

then to get the mass of ethyl alcohol,

ma= ρaVa

ma= (789.45g/L) (0.4705L)

ma= 371g

Thus, the mass of alcohol (ethyl alcohol) as calculated is 371g.

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Sketch the vectors v1, v2, v3, v4 with tail p and head q, and com- pute their lengths. are any two of these vectors equivalent?

Answers

Two or more vectors are equivalent if they have same magnitude and direction.

Vectors are formed by joining tail with head and forming an arrow in the direction of head.

Lets find each of these vectors.

(i) v1= (position vector of Q)-(position vector of P)

 = (4i+4j)-(2i+4j)= 4i+4j-2i-4j=2i

v1= 2i

if a vector V= xi+yj

then the length of vi =2i

length of v1=2

(ii )v2= (position vector of Q)-(position vector of P)

(i=3j)-(-i+3j)= i+3j+i-3j=2i

v2= 2i

length of v2= 2

(iii)  v3= (2i+4j)-(-i+3j)= 2i+4j+i-3j

v3= 3i+j

length of v3= [tex]\sqrt{10}[/tex]

(iv) v4= (6i+3j)-(4i+j)= 6i+3j-4i-j

Length of v4= [tex]\sqrt{8}[/tex]

Two vectors are equivalent if they have same magnitude and direction.

Clearly vectors V1 and V2 have same magnitude and they have same direction as represented of their sketch.

Hence vectors V1 and V2 are equivalent.

How would you define magnitude?

Magnitude is a term used to describe size or distance. We can relate the magnitude of the movement to the size and movement speed of the object. The magnitude of a thing or an amount is its size.

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