How many carbon atoms placed end to end would equal the width of a human hair

Answers

Answer 1

The carbon atoms placed end to end would equal the width of a human hair are 1 million.

What is carbon?

The carbon is an element in the periodic table. It has atomic number 6 and the atomic mass 12 units.

Molecules anyway can shift in size from 0.1-0.5nm (nanometres) across so it would take a component of around 100,000 particles in width so that us might be able to see it with the unaided eye. Assuming that there's around 100,000 molecules in the width of one piece of hair, envision the number of there are in objects around you.

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Related Questions

The fatty layer contains many nerves and blood vessels. True or False

Answers

Answer:

False , The fatty layer do not contains many nerves and blood vessels. The fatty layer is related to skin layers.

Explanation:

The fatty layer is the most under a layer of skin. It made up of a system of collagen and fat cells. It helps maintain the body's temperature and shields the body from harm by serving as a shock absorber.

The dermis is the central layer of the skin. The dermis is maintained collectively by a protein termed collagen. This layer gives skin elasticity and power. The dermis also holds shock and feel receptors.

What does the table suggest about the acceleration of the marble and why?

Answers

The table suggests that the acceleration of the marble increases steadily over time due to the increasing force being applied to it. This is because acceleration is directly proportional to the force applied, according to Newton's second law of motion (F = ma).

Newton's second law is a quantitative description of the changes that a force can produce on the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it.

Newton's second law is often stated as F=ma, which means the force (F) acting on an object is equal to the mass (m) of an object times its acceleration (a). This means the more mass an object has, the more force you need to accelerate it. And the greater the force, the greater the object's acceleration.

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Is 35 miles per hour a vector or a scalar?
1. vector
2. scalar

Answers

Answer:

scalar

is the correct answers

Answer:

Scalar

Explanation:

Mph, cubic feet,pounds, and hours are scalar terms

A body has an initial velocity of 12 m s^-1 and is brought to rest over a distance of 45 m. What is the acceleration of the body?

Answers

Answer:

-1.46 m/s^2

Explanation:

Write down what is given first:

v0 = 12 m/s

vf = 0 m/s

d = 45 m

We are trying to find acceleration, so we will use the equation vf^2 = v0^2 + 2ad

Plug in the values we have:

0^2 = 12^2 + (2 x 45 x a)

a = - 1.46 m/s^2

Note that this acceleration is negative because the body is slowing down, so the acceleration with be negative, because the change in velocity is negative.

According to the given statement - 1.46 m/s²  is the acceleration of the body.

What is a acceleration explain?

Acceleration is the rate of change in a moving asteroid's speed and direction over time. When something moves faster or slower, it is considered to be accelerating.

How is acceleration determined?

Use the formula a = v / t to determine acceleration, where v stands for the change in velocity and t for the time it took for the change to take place. Use the formula v = vf - vi to determine v, where vf stands for final velocity and vi for starting velocity.

Briefing:

Write down what is given first:

v0 = 12 m/s

vf = 0 m/s

d = 45 m

We are trying to find acceleration, so we will use the equation

vf² = v0² + 2ad

Plug in the values we have:

0² = 12² + (2 x 45 x a)

a = - 1.46 m/s²

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A 0.76 kg ball moves in a circle that is 0.8 m in radius at a speed of 4.3 m/s. Calculate
the centripetal acceleration of the ball.

Answers

Answer:

The centripetal acceleration of the ball can be calculated using the formula:

a = v^2 / r

where

v = 4.3 m/s (speed of the ball)

r = 0.8 m (radius of the circle)

Plugging in the values:

a = (4.3 m/s)^2 / 0.8 m

a = 23.035 m/s^2

Therefore, the centripetal acceleration of the ball is 23.035 m/s^2.

Answer:

\(\huge\boxed{\sf a_c \approx 23.1 \ m/s^2}\)

Explanation:

Given data:

Mass = m = 0.76 kg

Radius = r = 0.8 m

Speed = v = 4.3 m/s

Required:

Centripetal acceleration = \(a_c\) = ?

Formula:

\(\displaystyle a_c=\frac{v^2}{r}\)

Solution:

Put the given data in the above formula.

\(\displaystyle a_c=\frac{(4.3)^2}{0.8} \\\\\displaystyle a_c=\frac{18.49}{0.8} \\\\a_c \approx 23.1 \ m/s^2\\\\\rule[225]{225}{2}\)

Do two magnets create magnetic force fields that allow them to interact without touching? Did the investigation answer the question? Explain whether the investigation gave enough evidence to support the idea that invisible magnetic force fields exist.

Answers

Answer:

Magnetic forces are non contact forces; they pull or push on objects without touching them. Magnets are only attracted to a few 'magnetic' metals and not all matter.

Answer:

the person above me is correct i think respectlfully he

not correct

Explanation:

lots of time spent wondering

how can i solve density​

Answers

Answer:

p=m÷v

Explanation:

that is the formula for it. now, using your numbers p=density,m=mass and v= volume. you just divide it.

after you measurement would be in cm/3

Answer:

You can simply find density by using formula

\(d = \frac{m}{v} \)

where m represents mass of an object and v represents volume of an object.

hope it helps..

The unit we use to measure speed is

Answers

Answer:

However, to mention a few, there are other units of speed such as meters per second, feet per second, light-years per millennium, and knots. Feet per second, but specially meters per second are usually used to measure speed of animals, humans, and free fall objects. Knots is used to measure the speed of ship and/or boats.

Explanation:

Match each compound name with the correct chemical formula. Drag the items on the left to the correct location on the right. can someone help me with the last 3 please

Match each compound name with the correct chemical formula. Drag the items on the left to the correct

Answers

Each compound name with chemical formula:

Silicon tetrafluoride - SiF₄

Potassium sulfite - K₂SO₃

Diphosphorous trisulfide - P₂S₃

Siver(II) fluoride - AgF₂

Magnesium perchlorate - Mg(ClO₄)₂

What is chemical formula?

A compound's constituent elements and their relative proportions are listed in a chemical formula. No subscript is used when there is only one atom of a particular type. A subscript is added to the symbol for the atom when there are two or more of a particular type of atom present.

A chemical formula lists the constituent elements of a compound along with how many atoms of each are present in the compound's smallest unit, whether it be a molecule or a formula unit. We can name simple compounds given their chemical formulas by using the names of the elements and a few simple rules.

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As the train went up the hill,(blank)
A)Gravitational potential energy...kinetic energy
B) Kinetic energy...Gravitational potential energy
was converted into
A)Gravitational potential energy...kinetic energy
B) Kinetic energy ... gravitational potential energy

As the train went down the hill,(blank)

A)Gravitational potential energy...kinetic energy
B) Kinetic energy... gravitational potential energy

was converted back into
A)kinetic energy ..
gravitational potential energy

B)gravitational potential energy... kinetic energy

As the train went up the hill,(blank)A)Gravitational potential energy...kinetic energyB) Kinetic energy...Gravitational

Answers

Answer:

1. B- kinetic to gravitational potential energy

2. A-gravitational to kinetic energy

Explanation:

When the train goes up the hill, the kinetic energy decreases (the speed decreased) due to the pull of gravity.

When the train goes down the hill, the speed increases (kinetic energy increases) and since the object is coming downwards the gravitational potential energy decreases

As the train went up the hill, Kinetic energy was converted into Gravitational potential energy, and As the train went down the hill, Gravitational potential energy was converted back into Kinetic energy. The correct option for both is B.

What is the conversion of energy?

The conversion of energy refers to the process of changing energy from one form to another. Energy can be converted from one form to another, but it cannot be created or destroyed. This is known as the law of conservation of energy. Therefore, the total amount of energy in a closed system remains constant, even though it can be converted from one form to another.

Energy can be converted between different forms, such as mechanical, thermal, electrical, chemical, and nuclear energy. For example, when a car moves, the energy from the fuel is converted into mechanical energy to make the car move. When a light bulb is turned on, electrical energy is converted into light and heat energy. When food is digested, chemical energy is converted into mechanical and thermal energy.

The efficiency of energy conversion is an important factor in many processes, and the goal is often to maximize the amount of useful energy that can be obtained from a given amount of energy input. Energy conversion is an important concept in physics, engineering, and many other fields, as it helps us understand and analyze various physical processes and phenomena.

Here in the Question,

As the train went up the hill, Kinetic energy was converted into Gravitational potential energy. Because As the train goes up the hill, it gains height, and its potential energy increases. At the same time, its speed decreases due to the work done by gravity against the train's motion, causing a decrease in kinetic energy. Therefore, the kinetic energy of the train is converted into gravitational potential energy.

As the train went down the hill, Gravitational potential energy was converted back into Kinetic energy. Because As the train goes down the hill, its height decreases, and its potential energy decreases. At the same time, its speed increases due to the work done by gravity in the direction of the train's motion, causing an increase in kinetic energy. Therefore, the potential energy of the train is converted back into kinetic energy.

Therefore the correct answer to both questions is option B.

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The ratio of the potential difference across a conductor to the current in the conductor is called
A) conductivity
B) resistance
C) charge
D) power

Answers

Answer:

The ratio of the potential difference across a metallic conductor to the current in the conductor is known as.

B. Resistance.

Explanation:

According to ohms law   " the current  passing through a conductor is directly proportional to the potential difference between the ends provided the temperature of the wire remains constant".

What is resistance ?

Resistance is a measure of the opposition to current flow in an electrical circuit

what is a resistor ?

a resistor is a n electric conductor which forms resistance to free flow of electric current, the resistance is measured in Ω

The ratio of the potential difference across the conductor to the current is called resistance

What is Resistance?

It is defined as the ratio of the potential difference across the conductor to the current. The resistance is measured in Ω.

\(R = \dfrac VI\)

Where,

\(R\) - resistance

\(V\)- voltage (Potential difference)

\(I\) - current

Therefore, the ratio of the potential difference across the conductor to the current is called resistance.

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What are fossil fuels made from?
A. Radioactive Material
B. Harmful Poisons
C. Organic Material
D. Non-Organic Material

Answers

Answer:

organic material

Explanation:

An insulator________the loss of heat energy.

A.)speeds up
B.)slows down

which one is it?

Answers

Answer:

A) speed up

is the correct option

Answer:

slows down

Explanation:

As the temperature difference decreases the rate of transfer slows (hope this helps)

what is latent inhibition? the time it takes to move from a broad idea to a specific idea that can be implemented

Answers

An individual's capacity to notice and learn about a stimulus is diminished if they have previously been exposed to it in a neutral or irrelevant environment. This phenomenon is known as latent inhibition.

With the use of traditional training procedures, latent inhibition is frequently examined. In a typical experiment, an individual or an animal is repeatedly exposed to an unimportant stimulus with no noticeable results. In following trials, the neutral stimulus is coupled with a physiologically important stimulus (such as food or an electric shock).

The goal is to determine how the subject's capacity to build an association between the neutral stimulus and the important stimulus is affected by the subject's prior exposure to the neutral stimulus. According to the phenomena of latent inhibition, prior exposure to a stimulus without any discernible effects results in a reduction in attention or learning when the stimulus is subsequently encountered in a pertinent context.

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The mass is given as 14.6 g to 15.2 g. The volume is given as 2.4 to 2.8 m? State the density using center value with error method. a. 5.8 +/-0.6 g/m3 b. 5.77 +/-0.56 g/m3 c. 5.4 +/-0.2 g/m3
d. 5.52 +/-0.21 g/m3

Answers

The final correct answer is option b. 5.77 +/- 0.56 g/m^3.

The density using the center value with error method can be calculated by finding the average of the given mass and volume ranges and then finding the error by subtracting the lower value from the average.

The density is then given as the average mass divided by the average volume with the error given as the average error of the mass and volume.

The average mass is (14.6 g + 15.2 g) / 2 = 14.9 g and the average volume is (2.4 m^3 + 2.8 m^3) / 2 = 2.6 m^3. The error for the mass is (15.2 g - 14.6 g) / 2 = 0.3 g and the error for the volume is (2.8 m^3 - 2.4 m^3) / 2 = 0.2 m^3.

The density is then given as 14.9 g / 2.6 m^3 = 5.73 g/m^3 and the error is (0.3 g + 0.2 m^3) / 2 = 0.25 g/m^3. Therefore, the density using the center value with error method is 5.73 +/- 0.25 g/m^3.

Hence, The correct answer is option b. 5.77 +/- 0.56 g/m^3.

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A baseball with a mass of 0. 15 kilograms collides with a bat at a speed of 40 meters/second. The duration of the collision is 8. 0 x 103 seconds. The

ball moves off with a speed of 50 meters/second in the opposite direction. What is the value of the force?

Answers

The value of force is 1.7 × 10⁻³ N, with the direction opposite to that of the bat's motion.

When an object collides with another object, they exchange energy. For example, a baseball and bat collision or a car collision. When two objects collide, the force of the collision has to be equal on both sides of the collision according to Newton's Third Law. So, to find the value of force, we will apply the equation:

F = ΔP / ΔT

where F is the force, ΔP is the change in momentum, and ΔT is the time of collision. The equation represents the impulse momentum theorem.

Now, let's apply the given values to the above equation.

Final momentum (p2) = mass × final velocity (v2)

p2 = 0.15 kg × (-50 m/s)

p2 = -7.5 kg.m/s

Initial momentum (p1) = mass × initial velocity (v1)

p1 = 0.15 kg × (40 m/s)

p1 = 6 kg.m/s

Change in momentum (ΔP) = p2 - p1

ΔP = -7.5 kg.m/s - 6 kg.m/s

ΔP = -13.5 kg.m/s

Time of collision (ΔT) = 8.0 × 10³ s

Now, putting the values of ΔP and ΔT in the equation of impulse momentum theorem, we get:

F = ΔP / ΔT

F = -13.5 kg.m/s ÷ 8.0 × 10³ s

F = -1.7 × 10⁻³ N

Thus, the value of force is 1.7 × 10⁻³ N, with the direction opposite to that of the bat's motion.

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John compressed a spring 27 cm from its resting position. If the
spring's constant of proportionality is 32 N/m, what is the
spring potential energy? (Keep 3 significant figures)

Answers

When spring constant k is 32 N/m and the spring stretch from the equilibrium position is 27 cm is 1.1664 Joules.

Ability of an object or material to regain its normal shape after being stretched or compressed is called elasticity. For example, A rubber gets its shape  stretch because of its elastic property.

It can also be defined as the ability of a body to resist a distorting influence and to return to its original shape when the force is removed.

Given spring constant k is 32 N/m and the spring stretch from the equilibrium position is 27 cm

27 cm = 0.27m

we can find the spring's potential energy from the equation:

PE = 0.5 * spring constant * ( extension)^2

= 0.5 *32 *(0.27)^2

= 1.1664 Joules

Potential energy is 1.1664 Joules.

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You take a spectrum of a star and its absorption lines are broadened due to the star's rotation. You measure (delta frequency) / frequency = (delta wavelength) / wavelength 0.001. How fast is the star rotating? A. 30 km/s B. 300 km/s C. 3,000 km/s D. 30,000 km/s E. 300,000 km/s

Answers

The rotational velocity of the star is E. 300,000 km/s.option E.

The broadening of absorption lines of a star's spectrum can be used to determine its rate of rotation. The amount of broadening is determined by measuring the change in frequency or wavelength of the spectral lines, which can be expressed as (delta frequency) / frequency = (delta wavelength) / wavelength.

The equation for calculating the rotational velocity of the star is:

V = (delta wavelength / wavelength) * c / (2 * sin i)

Where V is the rotational velocity of the star, delta wavelength is the measured broadening of the spectral line, wavelength is the rest wavelength of the spectral line, c is the speed of light, and i is the inclination angle of the star's rotation axis with respect to our line of sight.

Substituting the given values, we get:

V = (0.001) * c / (2 * sin i)

V = (0.001) * 3 x 10^8 m/s / (2 * sin i)

We can convert this velocity to km/s by dividing by 1000:

V = (0.001) * 3 x 10^8 / (2 * sin i) km/s

Since we don't have the value of i, we cannot calculate the exact value of V. However, we can determine the order of magnitude of the velocity by assuming i = 90°, which gives us:

V = (0.001) * 3 x 10^8 / (2 * sin 90°) km/s

V = 1.5 x 10^5 km/s.

option E.
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An airplane pilot wishes to fly due west. a wind of 88.0 km/h is blowing toward the south.
a. if the airspeed of the plane (its speed in still air) is 420.0 km/h, in which direction should the pilot head?
b.what is the speed of the plane over the ground?

Answers

The typical speed of commercial aircraft is approximately 460-575 mph, or 740-930 km/h, according to Flight Deck Friend.

How do you calculate an airplane's speed?

The amount of time needed to cover a particular distance on the ground is referred to as ground speed. For instance, when flying at cruising altitude, airplanes may have a ground speed of 300-600 knots (555-1,110 kmph). However, depending on the wind, the plane's speed over the ground may alter.

Calculation:

The aircraft must travel south at a component speed that is opposite of and equal to 80 km/h. The plane's overall speed can only be the same after that. There will be a speed of 320 kilometers per hour.

The typical speed of a commercial airplane is between 460 and 575 mph (740 to 930 km/h).

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PHYSICS.
……………………………………………….

PHYSICS. .

Answers

Answer:

Work, W = F * d, and

Work = change in kinetic energy, so W=deltaKE.

Hence,

deltaKE=F * d

(1/2)*m*v^2 =F * d

d=[(1/2)*m*v^2]/F

d=[(1/2)*0.6*20^2]/5

d=24 m.

Explanation:

Work = change in kinetic energy, so W=deltaKE.

Name the form of energy each example represents.
1. Wind
2. Bow and Arrow
3. Fire
4. Microwave
5. Talking
6. Lightning
7. Fuel
8. Fusion of atoms

Answers

3) chemical energy

Explanation:

fire fire concert of something where they recall chemical chemical chemical chemical

What must happen for electricity to be useful in your home?

Answers

Answer:

current must flow and chemical energy must take place

a projectile is launched horizontally, from the top of a 30 m high building with an initial velocity of 30 m/s. the speed of the projectile just before it strikes the ground is:

Answers

The speed of the projectile just before it strikes the ground is  29.4 m/s.

Since the projectile is launched horizontally, it will only experience acceleration due to gravity acting vertically downwards. The horizontal velocity of the projectile will remain constant throughout its flight.

We can use the following kinematic equation to find the speed of the projectile just before it strikes the ground:

\(v^2 = u^2 + 2as\)

where:

v is the final velocity (which we want to find)

u is the initial velocity in the horizontal direction, which is 30 m/s

a is the acceleration due to gravity, which is approximately 9.81 m/s²

s is the vertical displacement of the projectile, which is equal to the initial height of the building, 30 m.

Since the projectile is launched horizontally, the initial vertical velocity is zero.

Substituting these values into the equation, we get:

v² = (30 m/s)² + 2(-9.81 m/s²)(30 m)

v² = 900 m/s² - 1765.4 m^2/s²

v² = -865.4 m²/s² (note that the result is negative because the velocity is in the opposite direction to the acceleration)

Taking the square root of both sides of the equation (ignoring the negative solution since speed is always positive), we get:

v = 29.4 m/s (rounded to one decimal place)

Therefore, the speed of the projectile just before it strikes the ground is approximately 29.4 m/s.

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the closest approach distance between mars and earth is about 56 million km. assume you can travel in a spaceship at 58,000 km/h, which is the speed achieved by the new horizons space probe that went to pluto and is the fastest speed so far of any space vehicle launched from earth. how long would it take to get to mars at the time of closest approach? note: for simplicity, this assumes that mars doesn't move relative to earth during the entire trip (which is of course not true, so this estimate is way too optimistic). pick the closest answer.

Answers

To travel 56 million km distance between Earth and Mars at the time of closest approach,Assuming a constant speed of 58,000 km/h, it would take approximately 97 hours, or 4.04 days.

We can use the formula:

time = distance / speed

where distance is the distance between Earth and Mars during closest approach, and speed is the speed of the spaceship.

substituting in the given values, we get:

time = 56,000,000 km / 58,000 km/h

time = 965.5 hours

So it would take approximately 965.5 hours to travel from Earth to Mars at the time of closest approach. This is equivalent to about 40 days. However, this estimate is only for the ideal scenario in which Mars does not move relative to Earth during the entire trip.

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A 75 kg object is moved a distance of 44 m with a force of 55 N at an angle of 53 above the horizontal. How much work is done?

Answers

To move a distance of 44 m Work is done 1456.4 Joule.

What is work?

A force must be applied and there must be movement in the force's direction for a work to be done scientifically. Having said that, we may state that: Work is the product of the displacement's magnitude and the component of force acting in that direction.

Mass of the object: m = 75 kg.

Force applied on it: F = 55 N.

Angle of applied force: α = 53°

Displacement: d = 44 m

Hence, work done: W = Fd cosα = 55 N × 44 m × cos53° Joule = 1456.4 J.

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The pr interval begins at the first sign of the p wave and ends at the first sign of the next deflection, which is called the:__________.

Answers

The PR interval in an electrocardiogram (ECG) represents the time it takes for the electrical impulse to travel from the atria (depicted by the P wave) to the ventricles. It begins at the first sign of the P wave and ends at the first sign of the next deflection, which is called the QRS complex.

The QRS complex represents the depolarization of the ventricles, which results in ventricular contraction and the pumping of blood out of the heart. It consists of three main deflections: Q, R, and S waves.

The Q wave is the first downward deflection after the P wave, the R wave is the first upward deflection after the Q wave, and the S wave is the second downward deflection following the R wave.

The PR interval is important in assessing the conduction time through the atrioventricular (AV) node, which connects the atria and ventricles. Abnormalities in the PR interval can indicate conduction abnormalities or disturbances in the electrical pathways of the heart.

In summary, the PR interval in an ECG begins at the first sign of the P wave and ends at the first sign of the QRS complex, which represents the depolarization of the ventricles.

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When the energy of a wave increases, what happens to the amplitude?

Answers

Answer:

The energy transported by a wave is directly proportional to the square of the amplitude. So whatever change occurs in the amplitude, the square of that effect impacts the energy. This means that a doubling of the amplitude results in a quadrupling of the energy.

Explanation:

When the energy of a wave increases, the amplitude also increases. This is because the amplitude of the wave is directly proportional to the energy of a wave.

What is the amplitude of a wave?

The amplitude of a wave may be defined as the maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position. It is equal to one-half the length of the vibration path.

It is the principle of physics that when the amplitude of the wave is higher, the energy also gets higher. To summarise, waves carry energy. The amount of energy they carry is related to their frequency and their amplitude. The higher the frequency, the more energy, and the higher the amplitude, the more energy.

Therefore, when the energy of a wave increases, the amplitude also increases. This is because the amplitude of the wave is directly proportional to the energy of a wave.

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does the battery appear to be a source of constant current, constant voltage, or neither when different elements are added to a circuit?

Answers

Adding additional components to a circuit gives the impression that the battery is a source of consistent voltage.

A battery is typically considered to be a source of constant voltage, meaning that it maintains a fixed potential difference between its terminals, regardless of the elements that are added to the circuit. However, the current supplied by the battery may vary depending on the resistance of the circuit and the characteristics of the elements that are added. Ohm's Law states that the current in a circuit is directly proportional to the voltage and inversely proportional to the resistance. Therefore, adding elements with higher resistance to the circuit will result in a decrease in the current supplied by the battery.

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A projectile is launched with an initial velocity of 25 m/s at an angle of 30° above the horizontal. The projectile reaches maximum height at point p then falls to point a, which is 65 m below the cliff. What is the horizontal distance that it travels (labeled x in the diagram)

A projectile is launched with an initial velocity of 25 m/s at an angle of 30 above the horizontal. The

Answers

Answer:

x ≈ 56 m

Explanation:

vertical initial velocity =\(v_{0y}(t)\) = 25 m/s* sin(30°)= 12.5 m/s

height = h

\(h =v_{0y}t+\frac{at^{2}}{2} \\\\65m = 12.5m/s*t + \frac{9.8m/s^{2}*t^{2}}{2} \\\\t=2.584 s\)

t- time is found solving quadratic equation.

horizontal velocity = \(v_{0x}=25m/s*cos(30^{o})=21.65 m/s\)

Horizontal velocity is constant, so distance \(x=v_{0x}*t =21.65 m/s *2.584 s=55.9 = 56 m\)

The horizontal distance travelled by the object will be "111.07 m".

According to the question,

\(u_v = u sin\Theta\)

    \(= 25 \ sin30^{\circ}\)

    \(= 12.5 \ m/s\)

As we know,

→  \(s = ut +\frac{1}{2} at^2\)

 \(-y = u_vt-\frac{1}{2}gt^2\)

\(-65 =12.5t - \frac{1}{2}\times 9.8t^2\)

   \(0 = 4.9t^2-12.5t-65\)

    \(t = \frac{12.5 \pm \sqrt{(-12.5)^2-4\times 4.9\times (-65)} }{2\times 4.9}\)

       \(= 5.13 \ s\)

hence,

The horizontal distance will be:

→ \(u_x = ucos \Theta\)

       \(= 25 cos 30^{\circ}\)

       \(= 21.65 \ m/s\)

or,

→ \(x = 21.65\times 5.13\)

     \(= 111.07 \ m\)

Thus the response above is right.  

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A projectile is launched with an initial velocity of 25 m/s at an angle of 30 above the horizontal. The

How to integrate 1/ 1 + x2

Answers

The integral of 1/(1 + x²) is (1/2)ln|1 + x²| + C where C is the constant of integration.

Integration is a mathematical process of finding the antiderivative of a function. To integrate the given expression 1/(1 + x²), we will use the substitution method.

Let u = 1 + x², du/dx = 2x dx, then dx = du/2x and the integral becomes:

∫1/(1 + x²) dx = ∫1/u * (1/2x) du= (1/2)∫1/u du

The antiderivative of 1/u is ln|u| + C, where C is the constant of integration.

Therefore, the final solution of the integral is (1/2)ln|1 + x²| + C.

Let us work through the steps:

Step 1:Let u = 1 + x² and then differentiate both sides with respect to x to obtain du/dx. du/dx = 2x

Substitute 2x dx = du into the integral ∫1/(1 + x²) dx to get the integral in terms of u:∫1/u * (1/2x) du = (1/2) ∫1/u du

Step 2:Calculate the antiderivative of 1/u, which is ln|u|. Thus, the final solution is (1/2)ln|1 + x²| + C, where C is the constant of integration. The constant C will vary depending on the initial conditions of the problem.

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