Which of the following graphs represents the equation y-2 = 3(x-1)?

0.23 mm far apart are the second-order fringes for these two wavelengths on a screen 1.5 m away.

Position of n the order fringe = n λ D / d

for n = 2

position = 2 λ D / d

λ = 710 nm , D = 1.5m

d = .65 x 10⁻³

position 1 = 2 x 710 x 10⁻⁹ x 1.5 / .65 x 10⁻³

= 3276.92 x 10⁻⁶ m

= 3.276x 10⁻³ m

= 3.276mm .

For λ = 660 nm

position = 2 λ D / d

λ = 660 nm , D = 1.5 m

d = .65 x 10⁻³

position 2 = 2 x 660 x 10⁻⁹ x 1.5 / .65 x 10⁻³

= 3046.15 x 10⁻⁶ m

= 3.046 x 10⁻³ m

= 3.046 mm .

Difference between their position

= 3.276mm ₋ 3.046 mm

= 0.23 mm .

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Light bulbs 1, 2, and 4 will continue to shine when Linh switches off bulb 3.

The battery-powered electrical circuit where a voltage differential is generated across a capacitor, a resistor, or an inductor.

As soon as Linh cuts the middle branch, the bulbs in positions 1, 2, and 4 will function as a resistor in a series circuit. Except for resistor number 3, the current through the other resistors will be constant.

In conclusion, if Linh switches off Bulb 3, only Bulbs 1, 2, and 4 will still be on.

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Answer:

1. no

2. yes

Explanation:

on edge 2022

Answer:

Approximately [tex]2.05\; {\rm m\cdot s^{-2}}[/tex].

Explanation:

The net force on the girl would be:

[tex]\begin{aligned}m(\text{girl}) \, a(\text{girl}) &= 41\; {\rm kg} \times 3.0\; {\rm m\cdot s^{-2}} \\ &= 123.0\; {\rm N} \end{aligned}[/tex].

Under the assumptions, the net force on this girl would be equal to the tension force in the rope. All other forces on the girl would be balanced.

In other words, the tension force that the rope exerted on the girl would be [tex]123.0\; {\rm N}[/tex]. The girl would exert a reaction force on the rope at the same magnitude ([tex]123.0\; {\rm N}\![/tex]) in the opposite direction. This force would translate to a [tex]123.0\; {\rm N}\!\![/tex] force on the boy towards the girl.

Under similar assumptions, the net force on the boy would also be [tex]123.0\; {\rm N}[/tex]. Since the mass of the boy is [tex]m(\text{boy}) = 60\; {\rm kg}[/tex], the acceleration of the boy would be:

[tex]\begin{aligned}a(\text{boy}) &= \frac{(\text{net force})}{m(\text{boy})} \\ &= \frac{123.0\; {\rm N}}{60\; {\rm kg}} \\ &= 2.05\; {\rm m\cdot s^{-2}}\end{aligned}[/tex].

Answer:

 W = 1960 N

T = 1960 N     in the upward direction

Explanation:

Let's apply Newton's second law to this exercise with acceleration equal to zero, translational equilibrium

Weight is

            W = m g

            W = 200 9.8

            W = 1960 N

In the attachment we can see a diagram

             T -W = 0

             T = W

             T = 1960 N

in the upward direction

credit - somebody else

The wavelength of the standing wave at fourth harmonic is; λ = 0.985 m and the frequency of the wave at the calculated wavelength is; f = 36.84 Hz

Given Conditions:

mass of string; m = 0.0133 kg

Force on the string; F = 8.89 N

Length of string; L = 1.97 m

1. To find the wavelength at the fourth normal node.

At the fourth harmonic, there will be 2 nodes.

Thus, the wavelength will be;

λ = L/2

λ = 1.97/2

λ = 0.985 m

2. To find the velocity of the wave from the formula;

v = √(F/(m/L)

Plugging in the relevant values gives;

v = √(8.89/(0.0133/1.97)

v = 36.2876 m/s

Now, formula for frequency here is;

f = v/λ

f = 36.2876/0.985

f = 36.84 Hz

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In an isometric transformation, the shape does not change size.

A shape-preserving transformation (movement) in the plane or in space is called an isometric transformation (or isometry). The isometric transformations include translation, rotation, and combinations thereof, such as the glide, which combines a translation with a reflection.

A stiff transformation called an isometry keeps perimeter and area constant while preserving length and angle measurements.

As a result, while dilations are not isometric since the image and preimage are comparable figures rather than congruent figures, translations, reflections, and rotations are.

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The great astronomer of ancient times who summarized and improved...in a book now called The Almagest) is Ptolemy This is further explained below.

Generally, Claudius Ptolemy was a Greek mathematician, astronomer, and geographer who lived in the second century CE and is best known for proposing the geocentric model of the cosmos, which was used to explain planetary and stellar movements for the next thousand years.

In conclusion, Ptolemy, the ancient world's preeminent astronomer, compiled and refined a system of circles inside circles to describe the complexities of planetary motion, publishing his work in what is now known as The Almagest.

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After 5 seconds the velocity of the projectile is 71m/s

Given that Initial velocity is 120m/s

Time t = 5s

We need to find the velocity after 5 sec

Projectile motion is the movement of an item hurled or projected into the air, which is only subject to the acceleration of gravity. The trajectory of the object is referred to as its trajectory.

The horizontal velocity of a projectile is constant,

There is a vertical acceleration caused by gravity and  its value is 9.8 m/s

Now the velocity for 5 seconds

[tex]v(t)=v_0-gt\\[/tex]

[tex]v(t)=120-(9.8)(5)\\\\v(t) =71m/s[/tex]

Hence the velocity after 5 seconds is 71m/s

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20 m/s is the speed of the heavier fragment just after the explosion.

Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.

F = ma                   where, F = Force (Newton)

                                          m= mass

                                          a = acceleration

Given:

mass of rocket = M = 1500 kg

acceleration of rocket = a = 10 m/s²

elapsed time = t = 2.00 s

mass of lighter fragment = m₁ = m = 500 kg

mass of heavier fragment = m₂ = 2m = 1000 kg

maximum height of lighter fragment = h = 530 m

Let's calculate the final speed of the rocket just before the explosion:

v = u + at

v = 0 + 10(2)

v = 20 m/s

Then, we will calculate the height of the rocket just before the explosion:

[tex]h' = ut + \frac{1}{2}at^{2}[/tex]

[tex]h' = 0 + \frac{1}{2} (10)(2.00)^{2}[/tex]

[tex]h' =20m[/tex]

The initial speed of lighter fragment just after the explosion:

[tex]v^{2}[/tex]₁ [tex]= u^{2}[/tex]₁ - [tex]2g[/tex]Δ[tex]h[/tex]

[tex]v^{2}[/tex]₁ [tex]= u^{2}[/tex]₁ - [tex]2g[/tex] [tex](h - h')[/tex]

[tex]0^{2} = u^{2}[/tex]₁[tex]- 2(9.8) (530-20)[/tex]

[tex]u^{2}[/tex]₁[tex]=9996[/tex]

[tex]u[/tex]₁ [tex]=\sqrt{9996} m/s[/tex]

Using Conservation of Momentum Law :

[tex]M v=m[/tex]₁ [tex]u[/tex]₁ [tex]+ m[/tex]₂[tex]u[/tex]₂

[tex]1500 (20)= 500(\sqrt{9996} ) + 1000u[/tex]₂

[tex]u[/tex]₂ ≅ [tex]- 20 m/s[/tex]

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The average power required to stop the wheel is 2795 Joule.

To find the answer, we need to know about the linear velocity, acceleration and force on the wheel.

= 2×π×(283/60) rev/s

= 30 rad/s

So, velocity= 30×1.21 m = 36.3 m/s

The force on the wheel= mass× acceleration

= 31.4 × 2.45 = 77 N

Thus, we can conclude that the average power of the wheel is 2795 J.

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Answer:

Both will be attractive in nature.

Explanation:

In the given case, the direction of the magnetic field is same in both loops as the direction of the current is same in both loops. When two parallel straight wire carrying current in the same direction are brought close to each other, the force between them is attractive in nature. In the same way,  when two coplanar, circular and concentric loops of wire are carrying current in the same direction, the force between them is attractive in nature. It can be checked by using right hand thumb rule.

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Answer:

Therefore, the number of electrons moving through the receiver circuit per second is 6250 electrons/s.

Explanation:

Given:

Power of radio wave, P = 1 × 10⁻²⁴ W

Potential of signal, V = 1 × 10⁻⁹ V

Solution:

Consider the number of electrons flowing through the receiver circuit per second be 'n'.

The current flowing through the circuit will be:

I = P/V

 = (1 × 10⁻²⁴ W)/(1 × 10⁻⁹ V)

 = 1 × 10⁻¹⁵ A

Then, the number of electrons moving through the receiver circuit can be  calculated as:

ne = I

where, e is charge on an electron

            I is current flowing through the circuit

Applying values in above equation we get:

n(1.6×10⁻¹⁹ C) = (1 × 10⁻¹⁵ A)

n = (1 × 10⁻¹⁵ A)/(1.6×10⁻¹⁹ C)

n = 6250 electrons/s

Therefore, the number of electrons moving through the receiver circuit per second is 6250 electrons/s.

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Friction yields equal amounts of positive and negative charge as positive and negative charges occur in pairs.

What is frictional electricity:

When two charged particles are rubbed together, transfer of charge takes place. This leads to production of electricity, as one object loses electrons and gains positive charge while the other object gains electrons and becomes negatively charged.

All objects contain equal amounts of positive and negative charge. Thus, when friction is caused between them, it yields equal amounts of positive and negative charge which is known as static electricity.

One of the prime example of static electricity is rubbing silk cloth over glass rod. Here, the glass rod loses electrons while silk gains electrons. thus, the glass rod becomes positively charged and silk becomes negatively charged.

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Answer:

The answer is B

Explanation:

The section C of the heating curve represents the liquid phase, which is where liquid water is heated. Hence option D is correct.

The body or particle is considered to be heating up as the temperature rises.

100°C is the boiling point of water at 1 atm of pressure.

The term "enthalpy of vaporisation" refers to the amount of heat energy needed to change liquid water into steam.

Enthalpy of vaporisation has a greater value than enthalpy of fusion.

The amount of power needed to melt ice into liquid water is known as the enthalpy of fusion.

As a result, section C illustrates the heating of liquid water.

Hence option D is correct.

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The skater's final angular speed is equal to 12 rad/s.

When implemented to angular momentum, the regulation of conservation means that the momentum of a rotating item is no longer exchanged until some form of external torque is carried out. Torque, in this sense, can check with any outside pressure that acts upon the object for the purpose to twist or rotate.

The law of conservation of angular momentum states that once no external torque acts on an item, no trade of angular momentum will occur. The angular momentum of a machine is conserved as long as there may be no net external torque performing on the machine.

In angular kinematics, the conservation of angular momentum refers back to the tendency of a device to keep its rotational momentum inside the absence of outside torque. For a round orbit, the system for angular momentum is (mass) ×(pace) ×(radius of the circle): (angular momentum) = m × v × r.

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The resultant wave at point (5, 2) is Ψ = 5.99 cos [ 7.15 - (20/s) t]

What are the plane waves:

Here,

Two plane waves are given:

c (5, t) = 4 cos [(8π/3) - (20/s) t]

c (2, t) = 2 cos [(3π/2) - (20/s) t]

now, the waves as imaginary exponentials,

separating the spatial parts, and then adding them together

we get The resultant:

Ψ = [  4 sin (8π/3) +  2 sin (3π/2) ]^2 +  [ 4 cos(8/3 π) +  2 cos(3/2π) ]^2

Ψ = 5.99 tan(a) = 0.747/ 5.95

a = 7.15

Ψ = 5.99 cos [ 7.15 - (20/s) t]

hence,

The resultant wave is Ψ = 5.99 cos [ 7.15 - (20/s) t]

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Your question is incomplete, but most probably the full question was:

Two plane waves with the same frequency and with vibrations (measured by Psi) in the z-direction are given by c (x, t) = (4cm.) cos [pi/3cm. x - 20/s t + pi] c (y, t) = (2cm.) cos[pi/4cm. y - 20/s t + pi]

Express the waves as imaginary exponentials, separate the spatial parts, and add them together using a phasor diagram to find the resultant at the point x = 5cm. y = 2cm

c. A current is induced in the coiled wire, which lights the light bulb.

If we kept the bar magnet stationary and moved the coil back and forth within the magnetic field an electric current would be induced in the coil.

Then by either moving the wire or changing the magnetic field we can induce a voltage and current within the coil and this process is known as Electromagnetic Induction and is the basic principle of operation of transformers, motors and generators.

When the magnet shown below is moved “towards” the coil, the pointer or needle of the Galvanometer, which is basically a very sensitive center zeroed moving-coil ammeter, will deflect away from its center position in one direction only.

When the magnet stops moving and is held stationary with regards to the coil the needle of the galvanometer returns back to zero as there is no physical movement of the magnetic field.

Therefore ,

If you move a bar magnet back and forth along the axis of the coiled wire shown below then a current is induced in the coiled wire, which lights the light bulb.

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The width of the central diffraction peak is 0.0754 m.

What is central diffraction:

It is distance between the 1st order minima from the center of the screen on both sides of the center.

The first diffraction minimum from the center is given as:

where

y is the location of first minimum diffraction.

Distance of screen from slit (L) = 2.40 m

Width of the slit (a) = 0.0328 mm = 0.0328 × 10⁻³ m

Wavelength of light (λ) = 588 nm = 588 × 10⁻⁹ m

Width of central diffraction peak is,

Now, plug in the values given and solve for width 'W'.

This gives,

W = 2 * 2.40 * 588 × 10⁻⁹ / ( 0.0328 × 10⁻³ )

W = 0.0860 m

Therefore,

The width of the central diffraction peak is 0.0754 m.

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Answer:

See below

Explanation:

There is the normal force of the book on the table.....the table exerts the same force ( upwards) on the book.

All of the forces result in a net zero force on the book so it does not move (there are no horizontal forces on the book)

Answer:

We have the formula,

V=λ×v

where,

V is the velocity of sound =330ms

−1

v is the frequency

λ is the wavelength

We have a range of frequencies from 20Hz to 20,000Hz

Hence for frequency v=20Hz, we have

330=20×λ

Therefore, λ=

20

330

m

Explanation:

Answer:

Most exceptions to the trend of decreasing radius moving to the right within a period occur in the d-block.

What are the characteristics of d-block elements?

Therefore, most exceptions to the trend of decreasing radius moving to the right within a period occur in the d-block.

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When a planet temporarily moves westward in the sky over the course of several weeks or months (instead of eastward, as it typically does), we call it retrograde motion.

In astronomy, retrograde motion refers to a body's actual or apparent motion in the opposite direction from the majority of solar system objects or other astronomical systems having a favored direction of motion.

Planets usually appear to migrate eastward when compared to the fixed stars.

However, on occasion, they appear to briefly stall in their eastward travel and then migrate westward (backward) in front of the stars for a few months.

They then pause once again. They resume their eastward movement after that.

This motion is known as retrograde motion and sometimes it is just an illusion.

Hence, when a planet temporarily moves westward in the sky over the course of several weeks or months (instead of eastward, as it typically does), we call it retrograde motion.

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May have to swing wide to complete the right turn

In any vehicle which makes any turn, the rear wheels follow a shorter path as compared to the front wheels. While the truck being larger than any usual vehicle, the distance between the wheels are even more, which makes it harder to complete the turn by going in its own lane or the other two right lanes.

So, the truck will try to go wide in left and then complete the right turn as by doing this the distance between the rear and front will get compensated by the width of the lanes making it easier for the truck to complete its turn.

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[Your question is incomplete, but most probably your full question was

May not turn without engaging its hazard lights

May complete its turn in either of the two lanes

Must stay in the right lane at all times while turning

May have to swing wide to complete the right turn]

a)The total distance she walks will be 1100 m.

b)The magnitude and direction of the budgie's path will be 854.4 m at 69.44°.

c)Sally's average speed for the journey will be 2.82 m/sec

d)The average velocity of Sally's budgie willl be 2.19 m/sec North of East.

Displacement is defined as the shortest distance between the two points.

Distance travelled in north direction,d₁ = 8.0 x 10² m

Time elapsed  travelled in north direction,t₁ = 5.0 minutes

Distance travelled in east direction,d₂ = 0.30 km = 3.0 × 10² m

Time elapsed  travelled in east direction,t₂= 1.5 minutes

The total distance she walks,d =? m

The magnitude and direction of the budgies path will be, D

Sally's average speed for the journey, [tex]\rm S_{avg}[/tex]

The average velocity of Sally's budgie,[tex]\rm V_{avg}[/tex]

a)

The total distance she walks is found as;

d=d₁+d₂

d=800 m +300 m

d = 1100 m

b)

The magnitude and direction of the budgies path will be;

[tex]\rm D = \sqrt{d_1 ^2 + d_2^2 } \\\\ D = \sqrt{800^2 +300^2 } \\\\ D = 854.4 \ m[/tex]

The direction of the displacement is;

[tex]\rm \theta = tan^{-1} \frac{800}{300} \\\\ \theta = tan^{-1}(2.6) \\\\ \theta = 69.44 ^ 0[/tex]

c)journey is found as;

Sally's average speed for the

[tex]\rm S_{avg} = \frac{d}{t} \\\\ S_{avg} =\frac{100}{300+900} \\\\ S_{avg} =2.82 \ m/sec[/tex]

d)

The average velocity of Sally's budgie is found as;

[tex]\rm V_{avg} = \frac{854.4}{300+ 900 } \\\\ V_{avg} = 2.19 \ m/sec[/tex] North of east

Hence, the total distance she walks, the magnitude and direction of the budgie's path, Sally's average speed, and the average velocity of Sally's budgie will be 1100 m,854.4 m at 69.44°,2.82 m/sec, and 2.19 m/sec North of East.

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Mature wind waves of one wavelength that form orderly undulations of the ocean surface and often precede a major storm system is known as swells.

Meaning of mature wind and waves:

The waves in a fully developed sea outrun the storm that creates them, lengthening and reducing in height in the process.      

There are 3 types of wind generated waves:

we can say that,

Mature wind waves are known as swell, when they left the formation region.

They have traveled away from where they were raised by the wind, and have to a greater or lesser extent dispersed.

Hence,

Mature wind waves of one wavelength is known as swell.

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The ratio of the mass of copper to water will be 10.8

The quantity of heat energy needed to raise a body's temperature per unit of mass is known as specific heat. Other names for specific heat include mass specific heat and specific heat capacity.

The quantity of heat in joules needed to elevate one gram of a material by one Kelvin is known as specific heat in SI units (symbol: c). The standard way to report specific heat is in joules (J).

We know that

The product of mass of copper and mass of water is equal to the product of the specific heat of copper and Water

Therefore ,

[tex]m_wc_w = m_cc_c[/tex]

We know that

Specific heat of water is 4.18 J

Specific heat of copper is 0.39 J

Therefore,

[tex]m_c*(0.39)=m_w*(4.18)\\\frac{m_c}{m_w} = \frac{4.18}{0.39}\\ = 10.8[/tex]

Hence  The ratio of the mass of copper to water will be 10.8

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Answer:

The approximate magnitude of the force of air resistance is 540 N.

Explanation:

The acceleration of a 600,000 kg freight train, if each of its three engines can provide 100,000N of force is 0.167m/s².

The acceleration of a freight train can be calculated using the following formula:

Force = mass × acceleration

According to this question, a 600,000kg freight train can produce 100,000N of force. The acceleration is as follows:

100,000 = 600,000 × a

100,000 = 600,000a

a = 0.167m/s²

Therefore, the acceleration of a 600,000 kg freight train, if each of its three engines can provide 100,000N of force is 0.167m/s².

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