A 21.1 A current flows in a long, straight wire. Find the strength of the resulting magnetic field at a distance of 67.7 cm from the wire.

The expression to be simplified is, A + BC + ABCD. Using De Morgan's theorem, we can convert complementation bars extending over multiple variables into complementation bars over single variables. The De Morgan's theorem states that the complement of a product is equal to the sum of complements. De Morgan's Theorem:

 1.   (AB) = A + B2.  (A + B) = A B The steps to simplify the given expression using De Morgan's theorem are as follows: A + BC + ABCD = A + (BC + ABCD) = A + (BC). (ABCD) = A + (B + C) (A + B + C + D) = A + AB + AC + BC + BD = A + AC + BC + BD.

Hence, the simplified expression is A + AC + BC + BD. Thus, using DeMorgan's Theorem and other applicable rules of Boolean algebra, the given expression is simplified to A + AC + BC + BD.

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 It would take the runner approximately 10,268.29 seconds (or about 2 hours, 51 minutes, and 8 seconds) to complete a marathon race of 42.2 km, maintaining an average speed of 4.1 m/s.

We can use the formula:

time = distance ÷ speed

to calculate the time it would take the runner to complete a marathon race of 42.2 km, given an average speed of 4.1 m/s.

First, we need to convert the distance to meters, as the speed is given in meters per second:

42.2 km = 42,200 m

Now, we can substitute the values into the formula:

time = distance ÷ speed

time = 42,200 m ÷ 4.1 m/s

time ≈ 10,268.29 s

Thus the time that the runner would take is  10,268.29 seconds  to complete a marathon race.

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Complete question :

Tony drives his car . He drives the first 13 miles in 13 minutes. He then drives at an average speed of 68mph for 1 hour 24 minutes . Find how much petrol he uses using the information in the table.

Requires table to answer question is attached below

Answer:

2.64 gallons

Explanation:

Given that:

First 13 miles takes 13 minutes

Average rate = 13 miles / 13 minutes = 1mile/minute ; Average rate per hour = (1 mile /minute * 60) = 60 miles /hour

If average speed = 65mph or less ; 50 miles per gallon (it uses 1 gallon for 50 miles)

Hence, since first phase rate is 60 mph,; then miles per gallon is 50 miles

Therefore,gallon of petrol used for 13 miles will be :

13 miles / 50 mpg = 0.26 gallons

2nd phase:

Average rate of 68 mph for 1 hour 24 minutes (1.4 hours)

Here, miles per gallon = 40 (that is; 40 miles for 1 gallon).

Total distance covered = 68 * 1.4 = 95.2 miles

Petrol used = 95.2 miles / 40 mpg = 2.38 gallons

Hence,

Total petrol used : (0.26 + 2.38) = 2.64 gallons

The chief factor that determines what type of electromagnetic radiation that objects give off in the absence of a strong magnetic field is their temperature.

The radioactive activity refers to the energy that a atomic nucleus can release in a given period of time due to the emission of different types of radiation.

This activity (radioactive activity) increases as temperature rises due to a higher collision of subatomic particles that form molecules.

In conclusion, the chief factor that determines what type of electromagnetic radiation in the absence of a magnetic field is temperature.

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To calculate the normal force exerted by the seat of the car on the passenger when the car is at the bottom of the depression, we need to consider the forces acting on the passenger.

At the bottom of the depression, the passenger experiences an inward net force directed towards the center of the circular path. This force is provided by the normal force exerted by the seat. To determine the normal force, we need to consider the centripetal force acting on the passenger.

The centripetal force can be calculated using the formula:

F_c = m * a_c

where F_c is the centripetal force, m is the mass of the passenger, and a_c is the centripetal acceleration.

The centripetal acceleration is given by:

a_c = v² / r

where v is the velocity of the car and r is the radius of the circular depression.

Given:

Velocity of the car (v) = 10 m/s

Radius of the depression (r) = 30 m

Mass of the passenger (m) = 60 kg

First, we calculate the centripetal acceleration:

a_c = (10 m/s)² / 30 m = 100 m²/s² / 30 m = 10/3 m/s²

Now, we can calculate the centripetal force:

F_c = (60 kg) * (10/3 m/s²) = 200 N

Since the normal force exerted by the seat is equal to the centripetal force, the normal force is 200 N. Therefore, the normal force exerted by the seat on the 60 kg passenger at the bottom of the depression is 200 N.

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Answer:

The magnitude of the coefficient of kinetic friction is approximately 1.304 × 10⁻⁵

Explanation:

The given parameters are;

The time it takes for the box to stop, "t" = 600 seconds

The distance the box moves before coming to a stop, "d" = 23 meters

The work done by the friction force to stop the block = The kinetic energy lost by the box

The work done by the friction force to stop the block = \(\mu _k\)·m·g·d

The kinetic energy change of the block = 1/2·m·u²

Where;

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

m = The mass of the box

\(\mu _k\) = The coefficient of kinetic friction

d = The distance travelled by the block = 600 m

u = The initial velocity of the block

∴ \(\mu _k\)·m·g·d = 1/2·m·u²

\(\mu _k\)·g·d = 1/2·u²

\(\mu _k\) = 1/2·u²/(g·d) = 1/2·u²/(9.8 × 23) = u²/450.8

∴  \(\mu _k\) = u²/450.8...(1)

The kinematic equation of motion of the block can be presented as follows;

v = u - a·t

Where;

v = The final velocity = 0 m/s (The block slides to a stop)

u = The initial velocity

a = The acceleration of the block (the minus sign indicates that the block's velocity is decreasing)

t = The time of motion of the block = 600 seconds

Therefore, by substituting the above values, we have;

0 = u - 600·a

∴ u = a·600

The kinematic equation of motion for the distance moved by the block, "s" can be expressed as follows;

s = u·t - 1/2·a·t²

Where;

s = The distance moved by the bloc = 23 meters

∴ 23 = a·600·600 - 1/2·a·600² = 360,000·a - 1/2·a·360,000 = 180,000·a

a = 23/(180,000)

u = 600 × (23/(180,000)) = 23/300

The initial velocity, u = 23/300 m/s

From equation (1), we have;

\(\mu _k\) = u²/(450.8) = (23/300)²/450.8 = 23/1764000 ≈ 1.304 × 10⁻⁵

The magnitude of the coefficient of kinetic friction, \(\mu _k\) ≈ 1.304 × 10⁻⁵

Both discharge and velocity will increase because there is more water flowing and it is flowing faster. This is option E.

Discharge and velocity are both affected by floods. Discharge is defined as the volume of water that flows through a certain area during a specified period of time.

During a flood, the water level increases, resulting in an increase in discharge. Velocity is defined as the rate at which water moves through a stream channel. The force of water is determined by the slope of the land.

During a flood, the velocity of water flowing through the stream channel increases because the slope is steeper. As a result, both discharge and velocity will increase because there is more water flowing and it is flowing faster.

Hence, option (E) is the correct answer.

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Answer:

V = - 1 m/s

Explanation:

Given:

m₁ = 8 kg

V₁ = 4 m/s

m₂ = - 9 m/s

__________

V - ?

Law of conservation of momentum for inelastic impact:

m₁·V₁ + m₂·V₂ = (m₁ + m₂)·V

8·4 - 5·(-9) = (8 + 5)·V

- 13 = 13·V

V = - 13 / 13 = - 1 m/s

Sticky bars move to the left at a speed of 1 m/s

The system described by the transfer function G(s) = -co² s² + 2a + w², with a damping ratio of 1.3 and a natural frequency of 0.5, has an overdamped unit step response. So, the correct option is (E)

The transfer function of the system is given as G(s) = -co² s² + 2a + w², where co represents the damping ratio, a represents an arbitrary constant, and w represents the natural frequency of the system. We are given that the natural frequency is 0.5 and the damping ratio is 1.3.

To determine the type of unit step response, we need to analyze the damping ratio (co) in relation to the critical damping value (co_critical).

The critical damping ratio (co_critical) is defined as the value where the system is on the threshold between being overdamped and underdamped. It is given by the formula co_critical = 2 * sqrt(a * w²).

In our case, the natural frequency (w) is 0.5, so we can calculate co_critical as follows: co_critical = 2 * sqrt(a * 0.5²).

Since the damping ratio (co) is given as 1.3, we can compare it with co_critical to determine the type of unit step response.

If co > co_critical, the system is considered overdamped (Option E).

If co = co_critical, the system is considered critically damped (Option D).

If co < co_critical, the system is considered underdamped (Option C).

Based on the given values, we can determine that the system is overdamped (Option E) because the damping ratio (1.3) is greater than the critical damping ratio.

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Answer:

The alkali metals (Group 1) are the most reactive metals. Group 2 consists of the alkaline Earth metals.

Explanation:

The most reactive groups in the periodic table are the alkali earth metals (group 1) and the halogens (group 17).

The periodic table is composed of 18 groups of elements with varying degrees of reactivity.

However, the first group of elements called the alkali earth metals (group 1) and the second to the last group of elements called the halogens (group 17) are the most reactive all the elements in the periodic table.

Their elements can never occur free in nature, they always occur in combined form owing to their high reactivity.

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The following which is true, according to newton’s laws of motion with friction being ignored is that none of the above is true, according to the third law and is therefore denoted as option E.

This law was coined by Isaac Newton and it states that for every action (force) in nature there is an equal and opposite reaction.

A semitrailer truck crashing all the way through a wall and since the wall collapses, the wall sustains a greater force than the truck does which doesn't depict the third law of motion as the force are meant to be equal.

They pushing off against each other and fly apart and Sam flying off with the greater acceleration also disobeys the third law due to the action and reaction not being equal.

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The options are:

A. A sports utility vehicle (SUV) hits a stationary motorcycle. Since it is stationary, the motorcycle sustains a greater force than the SUV does.

B. A semitrailer truck crashes all the way through a wall. Since the wall collapses, the wall sustains a greater force than the truck does.

C. Sam (18 years old) and his sister (9 years old) go ice skating. They push off against each other and fly apart. Sam flies off with the greater acceleration.

D. Two astronauts on a space walk are throwing a ball back and forth between each other. In this game of catch the distance between them remains constant.

E. None of the above is true, according to the third law.

The speed of sound in the pipe is 150m/s and that found to be enhanced when air column is 150 mm long.

a two-pronged metal tool used for tuning musical instruments and determining standard pitch that produces a set tone when struck.

ΔL = 150mm => 0.15m = λ/2

               =>  λ = 2 x 0.15 => 0.3 m

The velocity of sound => frequency x wavelength

                                         500hz x 0.3 m  => 150m/s

The length of a tuning fork's prongs determines the pitch it produces. Each fork has a stamp that says the note it makes (for example, A) and the frequency in Hertz (e.g. 440 Hz). Higher pitch (frequency) noises are produced by shorter prongs than by longer prongs.

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According to the given statement the value of :

a -  \(\overrightarrow{\mathrm{A}}=\mathrm{A}_{\mathrm{x}} \hat{\mathrm{i}}+\mathrm{A}_{\mathrm{y}} \hat{\mathrm{j}}=-3.00 \hat{\mathrm{i}}+2.00 \hat{\mathrm{j}}\)

b - θ is in the second quadrant so θ = 180⁰ + (-33.7⁰) = 146⁰

c-\(\overrightarrow{\mathrm{B}}=3.00 \hat{\mathrm{i}}+6.00 \hat{\mathrm{j}}\)

In science, anything that has both a direction and a magnitude is referred to as a vector. They are typically represented by pointing arrows, the length of which denotes the size of the vector.

The component description of  A is just restated to constitute the answer to part (a):

A\(_x\) = -3.00 , A\(_y\) = 2.00

(a) \(\overrightarrow{\mathrm{A}}=\mathrm{A}_{\mathrm{x}} \hat{\mathrm{i}}+\mathrm{A}_{\mathrm{y}} \hat{\mathrm{j}}=-3.00 \hat{\mathrm{i}}+2.00 \hat{\mathrm{j}}\)

(b) \(|\overrightarrow{\mathrm{A}}|\) =  √(A\(_z\)² + A\(_y\)²) = √( (-3.00)² + (2.00)²) = 3.61

θ = tan -1 \(\left(\frac{\mathrm{A}_{\mathrm{y}}}{\mathrm{A}_{\mathrm{x}}}\right)\) = tan-1 \(\left(\frac{2.00}{-3.00}\right)\) = -33.7⁰

θ is in the second quadrant so θ = 180⁰ + (-33.7⁰) = 146⁰

(c) R\(_x\) = 0, R\(_y\) = -4.00 and \(\overrightarrow{\mathrm{R}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}\)   thus \(\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{R}}-\overrightarrow{\mathrm{A}}\)   and

B\(_x\) = R\(_x\) -A\(_x\) = 0-(-3.00) = 3.00,

B\(_y\) = R\(_y\) - A\(_y\) = -4.00-2.00= -6.00

therefore \(\overrightarrow{\mathrm{B}}=3.00 \hat{i}+6.00 \hat{j}\).

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The complete question is -

Vector  A  has a negative x component 3.00 units in length and a positive y component 2.00 units in length. (a) Determine an expression for  A in unit-vector notation. (b) Determine the magnitude and direction of  A. (c) What vector  B  when added to  A  gives a resultant vector with no x component and a negative y component 4.00 units in length.

Given what we know, we can confirm that investigative questions are used to develop and test hypotheses and often lead to the formation of an experiment.

These are questions posed by scientists that will often lead to a hypothesis. They are the crucial first step in the scientific process. Some examples of investigative questions include:

etc.

Therefore, we can confirm that investigative questions such as these are often the basis on which hypotheses are created and experiments are made in order to test the speculated results.

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Answer:

A. So that you can see if the answer to a problem makes physical sense.

Explanation:

Science can be defined as a branch of intellectual and practical study which systematically observe a body of fact in relation to the structure and behavior of non-living and living organisms (animals, plants and humans) in the natural world through experiments.

An experiment can be defined as an investigation which typically involves the process of manipulating an independent variable (the cause) in order to be able to determine or measure the dependent variable (the effect).

This ultimately implies that, an experiment can be used by scientists to show or demonstrate how a condition causes or gives rise to another i.e cause and effect, influence, behavior, etc in a sample.

Measurements refers to the process which typically involves the process of identifying and determining the dimensions of a physical object. The dimensions include important parameters such as width, height, length, area, volume, circumference etc.

In Science, making rough estimates of physical quantities is useful so that you can see if the answer to a problem makes physical sense.

For example, you could make a rough estimate of a storage tank and deductively determine whether or not it's in tandem with its physical size in reality.

The tapered shape of the wheel rims that ride on railroad tracks allows for both opposite wheels to vary their diameters and travel at different linear speeds for the same rotational speed. This design is crucial for ensuring that trains can smoothly and efficiently travel along the tracks without causing damage or excessive wear and tear.

When a train travels along a curved track, the outer wheel must travel a greater distance than the inner wheel in order to stay on the track. If the wheels were the same diameter, the outer wheel would have to rotate faster than the inner wheel, causing it to slip and slide along the rails. This can result in a phenomenon known as "railroad tracks," where the wheels leave behind a series of flat spots on the rails.

To avoid this problem, train wheels are designed with a tapered shape, where the diameter of the wheel gradually decreases towards the center of the axle. This allows the outer wheel to effectively increase its diameter and travel at a slightly faster linear speed than the inner wheel, while still maintaining the same rotational speed. As a result, the train can smoothly travel along the curved track without causing any damage or excessive wear and tear.

Overall, the tapered shape of train wheel rims is an essential design feature that helps to ensure the safe and efficient operation of trains on railroad tracks.

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Complete cancellation will occur for a path difference equal to an odd multiple of half the wavelength.

The phenomenon of cancellation occurs in wave interference when two waves with the same frequency and amplitude are out of phase by 180 degrees, meaning that the crests of one wave coincide with the troughs of the other wave.

The path difference between the two waves determines whether or not complete cancellation will occur. When the path difference is equal to an odd multiple of half the wavelength (λ/2, 3λ/2, 5λ/2, etc.), the waves will be out of phase by 180 degrees and complete cancellation will occur.

Mathematically, we can express this condition as:

path difference = (m + 1/2) λ

where;

For example, if the wavelength of the waves is 1 meter and the path difference is 1/2 meter (m = 0), the waves will be in phase and constructive interference will occur. However, if the path difference is 1 meter (m = 1), the waves will be out of phase by 180 degrees and complete cancellation will occur.

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Answer:

A popular set of Peg-Words

What is a Peg-Word?

They're easy to remember because they rhyme with the names of the first ten natural numbers, is: one is a bun, two is a shoe, three is a tree, four is a door, five is a hive, six is sticks, seven is heaven, eight is a gate, nine is wine, ten is a hen.

Explanation:

F = k |q1| |q2| / r^2

k = 9 * 10^9

q1 = - 2.5 C

q2 = 2 C

r = 100

r^2 = (10^2)^2 = 10^4

F = (9*10^9) * ( 2.5 ) ( 2) / ( 100)^2

F = 45* 10^9 / 10^4

F = 45 * 10^9 * 10 ^ -4 = 45 * 10^5 N

F = 45 * 10 ^ 5 N

The planet orbit Kepler was studying when he developed the law of orbital motion is Mars.

Kepler’s law of orbital motion are three laws  and can be stated as follows;

The first and second Kepler's law of orbital motion was proposed when Kepler discovered that the orbit of Mars was an ellipse.

Thus, the planet's orbit that Kepler was first studying when he began to develop his laws of orbital motion is Mars.

The correction that describes the planets orbit Kepler was studying is Mars.

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Answer:12

Explanation:Average speed=Total Distance divided by Total Time.

Answer: (d)inclined to time axis

Explanation:

For a moving object, the distance equation can be written as:

D = S*t

if S = 0, we will have a line parallel to the time axis.

if S = infinity we will have a line parallel to the distance axis.

Both options are discarded here, as S = ∞ is not possible, and S = 0 would mean that the object is not moving.

where D is the distance moved at the time t, t is the variable, and S is the speed of the object.

As S is constant, this equation defines a linear relationship.

The graph of this line will be a line that is not parallel either to the time axis nor the distance axis, this will be an inclined line that goes between them.

So the correct option is: (d)inclined to time axis

Answer:

c.................................

The resistance of a 20-cm-long column of blood in the femoral artery is approximately 40.6 ohms.

We can use the formula for the resistance of a cylindrical conductor:

R = (ρ * L) / A

where:

R is the resistance

ρ is the resistivity of the material

L is the length of the conductor

A is the cross-sectional area of the conductor

In this case, the conductor is a column of blood with length L = 20 cm and resistivity ρ = 1.6 ohm m. The cross-sectional area A is given by the formula for the area of a circle:

A = π * r^2

where r is the radius of the artery. Since the diameter of the artery is 1.0 cm, its radius is 0.5 cm = 0.005 m. Therefore:

A = π * (0.005 m)^2 = 7.85 × 10^-5 m^2

Substituting these values into the formula for resistance, we get:

R = (1.6 ohm m * 0.2 m) / 7.85 × 10^-5 m^2

R = 40.6 ohms

Therefore, the resistance of a 20-cm-long column of blood in the femoral artery is approximately 40.6 ohms.

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A.) The speed of Tarzan at the bottom of the swing when he starts from rest is 10.8 m/s.

B.) The speed of Tarzan at the bottom of the swing when he starts with 4 m/s is 11.6 m/s.

Let us solve this problem using law of conservation of energy. The kinetic energy at the bottom of the swing will be equal to the gravitational potential energy at the start of the motion.

U = K

m g h = 1/2 m v²

where,

m is Tarzan's mass

g is acceleration due to gravity

h is initial height

Tarzan's speed at the bottom is v

Re-arranging the equation for making v as subject, we have

v = √ (2 g h + u²)

Initial velocity u = 0.

Therefore, we must determine h, Tarzan's starting height. We know that the length of the swing is L= 30 m and it is initially inclined at θ = 37° with respect to the vertical, so the initial height of Tarzan is given by

h = L - L cosθ = L(1 - cosθ) = 30 ×(1 - cos 37 ) = 6 m

Tarzan's speed, then, at the swing's bottom is

v = √ ( 2 × 9.8 × 6) = 10.8 m/s

B.) If u = 4 m/s,

v = √ 2 g h + u² = √ [2 g L(1 - cosθ) + u²] = √ [ 2 × 9.81× 30 × (1 - cos 37 ) + 4²] = 11.6 m/s

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Explanation:

The work expended will be   mgh   ( which is also the GAIN in Potential energy)

Work = 80 kg * 9.81 m/s^2 * 30 m = 23544 J

The work required for a 80.0kg firefighter to climb a flight of stairs 30.0m high is 23,544 J.

To calculate the work required for an 80.0 kg firefighter to climb a flight of stairs 30.0 m high, we can use the formula:

Work = Force × Distance × cos(θ)

Here, Force = mass × acceleration due to gravity (m × g)
Since the firefighter is climbing vertically, the angle (θ) between the force and distance is 0°. Therefore, cos(0°) = 1.

Given: mass (m) = 80.0 kg, distance (d) = 30.0 m, and acceleration due to gravity (g) = 9.81 m/s².

Force = 80.0 kg × 9.81 m/s² = 784.8 N (Newtons)

Now, we can calculate the work:

Work = 784.8 N × 30.0 m × 1 = 23,544 J (Joules)

So, 23,544 Joules of work is required for the firefighter to climb the flight of stairs.

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Answer:

First one after Oxygen is Oxygen. Then Iron(Fe). Then Carbon(C). Then Potassium(K)

La actividad física posee muchos beneficios para la salud. Algunos de estos beneficios son la reducción en el riesgo de padecer enfermedades, control del peso, fortalecimiento de huesos y músculos, etc.

La actividad física regular previene la aparición de enfermedades cardiovasculares al evitar la acumulación de colesterol en las arterias que transportan sangre a diferentes áreas del organismo.

La actividad física consume calorías, especialmente aquellas provenientes de los lípidos (grasas), con lo cual permite controlar el peso y reducir el riesgo de obesidad.

La actividad física también ayuda al fortalecimiento de los tejido oseo, con lo cual previniendo enfermedades relacionadas tales como la osteoporosis.

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