2m east, then 3m north, then 4m west
What the total distance travelled and the net displacement?

The focal length (in cm) of the lens is 400

The distance between a lens's center and its focus is known as the focal length of a convex lens. An optical device's focal length, which is just the inverse of the system's optical power, measures how strongly/sharply the system converges or diverges light.

A plane mirror is one having a flat surface, as those found frequently in home mirrors. It has an infinite focal length. Its optical power is 0 since it does not cause light to converge or diverge.

Given:

n=1.5

R2 = 20 cm

R1= ∞ since it is a flat surface

1/f = (n-1) (1/R1-1/R2)

Substituting values,

1/f = (1.5- 1) (1/∞-1/20)

1/f = (0.5) (-1/20)

= 1/400

F=400

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The energy absorbed outdoor copper sculpture heats up during the day q = 1.79 x 10⁵ J.

To find energy using formula,

q = mcΔT

where,

q is energy

m is mass

c is specific heat

ΔT is change in temperature

Given,

m = 7.8 kg

c = 390 J/kg

T₁ =  28°C

T₂ = 87°C

To find ΔT,

ΔT = T₂ - T₁

ΔT = 87° - 28°

ΔT = 59°C

Now, putting values,

q = mcΔT

q = 7.8 kg x 390 J/kg x 59

q = 1.79 x 10⁵ J

The best materials for sculpture are copper and copper alloys for a variety of reasons. They offer countless artistic possibilities because they can be molded into any desired shape. Copper components can be mechanically joined or assembled by bolting or bonded by welding, enabling works of enormous size.

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The runway should be 253.5m for a light plane that needs to reach a speed of 39 m/s for takeoff.

The rate at which the speed and direction of a moving object vary over time is called as acceleration. A point or object going straight ahead is accelerated when it accelerates or decelerates.

Even if the speed is constant, motion on a circle accelerates because the direction is always shifting.

In physics, acceleration is the rate at which the velocity of an object changes in relation to time.

According to Newton’s Second Law, the sum of all forces acting on an item results in its acceleration.

Meter per second squared (m s2) is the unit of acceleration used in the SI system.

We know from the equation,

V^2 = u^2 + 2as → 1

Here a = acceleration of the light plane

v = final velocity of the light plane

u = initial velocity of the light plane

s = length of the runway

Then we also know that

s = (v^2 - u^2) / 2a → 2

v = 39m/s

u = 0m/s

a = 3 m/s^2

Then substituting these values in equation 2,

s = (39^2 - 0) / (2x3)

s = 1521/6

s = 253.5 m

The runway needed is 253.5m long.

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If net work is done by a system containing an ideal gas, the sign of is negative according to convention, and represents a(n) decrease in the volume and a(n)  decrease By convention, in the internal pressure of the gas.

A theoretical gas known as an ideal gas is made up of several randomly moving point particles and only interacts through completely elastic collisions.

There are two equations of state that can be used to describe the classical thermodynamic characteristics of an ideal gas: The equation of state for an ideal gas, as determined by: Absolute temperature is denoted by T.

The ideal gas law is a development of the gas laws that were found through experiment. It may also result from analysis of microscopic factors. As a result, if we shift the ideal gas law's pressure, volume, and temperature onto the same side, we obtain This demonstrates that as long as a gas's mole (or molecule) count stays constant, its amount will not change.

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The complexity of your algorithm is O(nm).

Algorithmic complexity is a measure of how long an algorithm would take to complete given an input of size n. If an algorithm has to scale, it should compute the result within a finite and practical time bound even for large values of n. For this reason, complexity is calculated asymptotically as n approaches infinity.

Now,

Text: T

Pattern: s

Algorithm   String Matching(T,s)

n=len(T)

m=len(s)

for i = 0 to n-m

j=0

while j<m and s[j]=T[ i + j]

j=j+1

if j==m

  return i

end if

end while

return -1

end for

the complexity of your algorithm: O(nm)

reason: nested loop runs one run (n-m) times and second run m times. so it becomes (n-m)(m) = (nm-m2) = O(nm)

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Acceleration of a ball rolling down hill, a = 3.5 m/s².

Given in details,

Initial velocity of ball,

u = 3 m/s

Final velocity of ball,

v = 34.5 m/s

Time taken for changing velocity,

t = 9 s

To find acceleration of ball,

a =?

Using formula,

First equation of motion

 v = u + a t

where,

v is final velocity,

u is initial velocity,

t is time taken

a is acceleration

Using this first equation of motion,

v = u + a t

34.5 = 3 + a × 9

34.5 - 3 = 9 a

31.5 = 9 a

a = 31.5 / 9

a = 3.5 m/s²

Newton's first law: the law of inertia

According to Newton's first law, if a body is at rest or moving in a straight line at a constant speed, it will continue to move at that speed or remain at rest until acted upon by a force.

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The data which Marcus most likely collected during his investigation is a quantitative data.

A quantitative data is also referred to as a numerical data and it can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a quantitative data (numerical data) simply refers to a data set consisting of numbers rather than words.

In Science, there are different types of graph and these include the following:

A line graph is sometimes referred to as scatter chart, scatter plot, scatter diagram or scattergram and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables in a quantitative data, with the resulting points showing any association (correlation) between the data set.

In this context, we can reasonably infer and logically deduce that the data which Marcus most likely collected during his investigation is a quantitative data because a line graph is generally used to represent quantitative data.

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The solid pieces of lead with a mass of 29.92 g has a density of 11,164 Kg/ m3.

To find the density the given values are,

v = 2.68 cm3

m = 29.92 g

The density is a mass of a unit volume of a material substance. It is a physical quantity that expresses the ratio of the body mass to the volume it occupies.

Density is a scalar quantity.

The unit of density is kg/m³.

The density formula and the procedure we will use is:

ρ = m/v

Where:

v= volume

ρ= density

m= mass

Applying the density formula, we get:

ρ = m/v

ρ = 29.92 g/ 2.68 cm3

ρ(g/cm3) = 11.164 g/cm3

Converting the density from (gram g /cm3) to (kilogram/m3), we get:

11.164 g/cm3 * (1 kg/1000g) * (1000000 cm3/1 m3) = 11,164 Kg/ m

11.164 g/cm3 is equivalent to 11,164 Kg/ m3

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The magnitude of the acceleration of the ball while it is on the ramp is 2.4 m/s² approximately

Acceleration is the rate at which velocity changes. It is a vector quantity.

Given that a ball is given a brief push and then is allowed to roll up a ramp. It travels 53.1 cm up the ramp before stopping and rolling back down. It takes a total of 1.34 s to roll up and back down to its initial position.

Let us take the account of rolling down.

The magnitude of the acceleration of the ball while it is on the ramp can be calculated by using the below formula

s = ut + 1/2at²

Substitute all the parameters into the formula

0.531 = 0 + 1/2 × a × 0.67²

0.531 = 0.22445a

a = 0.531/0.22445

a = 2.365 m/s²

Therefore, the magnitude of the acceleration of the ball while it is on the ramp is 2.4 m/s² approximately

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The prediction of the meteorologist, the family is to expect a severe rain as they embark on the vacation. Option A

The term climate refers to the average weather condition of a place over a long period of time. The weather in a place changes from time to time. The weather of a place could be forecasted by a meteorologist. The meteorologist is a scientist that has been trained in the science of how to interpret weather patterns and also make predictions.

The meteorologist can be able to use the tools of the profession to discern what could be the weather condition of a place at any given point in time and announces the same by the process of giving a weather forecast.

Hence, the local meteorologist predicts that a cold front will move in; this implies that there is a cooler mass of air near the surface.

This implies that from the prediction of the meteorologist, the family is to expect a severe rain as they embark on the vacation.

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Explanation:

interesting let's see it is very confusing

Answer:

See below

Explanation:

Motion as the change of position of an object with respect to time.

Uniform motion covers equal distance at an equal time interval. The velocity is constant. For example, a car traveling at 55 mph constant speed for 2 hours has uniform motion

Non-uniform motion covers unequal distance at equal time intervals. For example, in heavy traffic, a car may travel at 20mph for the first 10 minutes, then 10mph for the next 10 minutes etc. Thus velocity changes over equal time periods

It takes 3.16s to hit the bottom of the well.

g = 9.8 m/[tex]s^{2}[/tex]

y = 9.8t m/[tex]s^{2}[/tex]

y = [tex]\frac{9.8 t^2}{2}[/tex] = 4.9[tex]t^{2}[/tex] m

When y =49, we have to find t

49 = 4.9[tex]t^{2}[/tex]

10 = [tex]t^{2}[/tex]

t = [tex]\sqrt{10}[/tex] = 3.16 s

Gravity causes a body to descend faster, and as it does, the air resistance that slows it down rises.

This keeps happening until the weight of the object and the force of air resistance are equal. The terminal velocity is the pace at which the item now falls instead of accelerating any longer.

When an object moves, it is said to be in motion under gravity since gravity has an impact on the object’s motion.

GRAVITY is the force that pulls things downward. In actuality, gravity pulls objects toward the Earth’s center.

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Answer: A position- time graph shows how far an object has traveled from its starting position at any given time since it started moving. The steeper the line is, the greater the slope of the line and the faster the object's motion is changing

Explanation:

Answer:

Independent variable is the variable that causes the changes in the experiment. Dependent variable is the variable that is affected by the changes.

Explanation:

14.8m/s is  minimal horizontal velocity must the cliff divers leave the top of the cliff is they are to miss the rock.

Ledge divers in Acapulco leap into the water from a 36-meter-high cliff. A rock protrudes 10.4 meters horizontally from the water, level. 9.8 m/s2 is the acceleration of gravity. If the cliff divers are to miss the rock, they must depart from the top of the cliff with a minimal horizontal velocity.

from above statements, we assume that

there is no initial vertical velocity, then we calculate the time it takes to reach the water, then divide the horizontal distance by that time to get the minimum required horizontal speed.

h=gt^2/2

h= 36 m

t = [tex]\sqrt{2h/g}[/tex]

put h = 36 m g = 9.8 m/s^2

t=2.7 second

Then the minimum required horizontal velocity is

v = d/t

by putting value

v= 10.4 m/2.7 s

v=14.8m/s

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The average velocity of the ball is - 14 m / s if it rolls from x = 10 to x = - 25 in 2.5 seconds.

We know that,

v = Δd / t

where,

v = Average velocity

Δd = Displacement

t = Time taken

Given that,

t = 2.5 sec

Δd = - 25 - 10

Δd = - 35 m

v = - 35 / 2.5

v = - 14 m / s

Average velocity is the average value of velocity from the starting point to ending point in a given amount of time.

Therefore, the average velocity of the ball is - 14 m / s

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The height through which the player will jump is determined as 44.1 m.

The height through which the player will jump at the given time is calculated as follows;

h = vt + ¹/₂gt²

where;

v is the initial velocity of the basketball player

Substitute the given parameters and solve for the height jumped by the player.

h = 0 + ¹/₂(9.8)(3²)

h = 44.1 m

Thus, the height through which the player will jump is determined as 44.1 m.

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The transformer secondary turns should be 83 turns.

We need to know about the transformer to solve this problem. Transformer is a device that can increase or reduce the voltage. The changed voltage depends on the current and number of coil turns. It can be written as

Vi / Vs = Ni / Ns = Is / Ii

where Vi is input voltage, Vs is output voltage, Ni is primary turn, Ns is secondary turn, Is i output current and Ii is input current.

From the question above, we know that

Vi = 120 V

Ni = 1000 turns

Vs = 10V

By substituting the following parameters, we can calculate the secondary turns

Vi / Vs = Ni / Ns

120 / 10 = 1000 / Ns

Ns = 1000 / 12

Ns = 83 turns

Hence, the transformer secondary turns should be 83 turns.

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When the mass is increased by 4, the frequency would decrease by a factor of 2 hence we have 0.795 Hz.

We know that a simple harmonic motion is a motion that is directed towards the center of the motion. The acceleration has the center as its direction.

We must first be able to obtain the angular velocity and then use it to obtain the velocity of the body that is undergoing the simple harmonic motion.

Now, we have;

ω = √k/m

ω = angular velocity

k = spring constant

m = mass of the object

ω = √10 N/m/1 kg

ω = 10 rad/s

And

ω = 2πf

f = ω/2π

f = 10 rad/s 2 * 3.14

f = 1.59 Hz

If we increase the mass by 4, the frequency would decrease by a factor of 2 hence we have 0.795 Hz.

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The electric potential from proton 52.92 pm from a proton is 27.21 V that is the average distance between the proton and electron.

Electric potential is the effort required to transport a unit charge from one point to another in the presence of an electric field.

Earth is typically chosen as the reference point, but any location outside the range of the electric field charge can be used.

The work required to accelerate a unit positive charge from infinity to a specific point in an electric field is known as the electric potential (or potential) at that location.

Electric potential is the amount of labor or energy that an electric charge can produce. A 1.5 V battery, for instance, has an electric potential of 1.5 volts.

Distance from proton,

r= 52.92pm

= 52.92 x 10^(-12)

Charge on a proton

q = 1.6 x 10^(-19) C

Therefore, electric potential at distance r from a proton is

Vp = Kq/r

=Vp = (9x 10^3 x 1.6 x 10^(-19)) / 52.92 x 10^(-12) volts

Vp = 27.21 V

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The acceleration of the car after leaving the pit to reach a speed of 75 m / s in 9 s is 8.3 m / s²

a = v / t

a = Acceleration

v= Velocity

t = Time

v = 75 m / s

t = 9 s

a = 75 / 9

a = 8.3 m / s²

Acceleration is the rate of change of velocity with respect to time. It is denoted as a.

The given question is incomplete. The complete question is:

At an international auto race, a race car leaves the pit after a refueling stop and accelerates uniformly to a speed of 75 m/s in 9 s to rejoin the race. What is the race car's acceleration during this time?

Therefore, the acceleration of the car after leaving the pit is 8.3 m / s²

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The relative velocity with respect to my friend is 32.7 m/s.

We need to know about relative velocity to solve this problem. The relative velocity depends on the object and observer velocity. It can be written as

v = vo ± v'

where v is relative velocity, vo is object velocity and v' is observer velocity.

From the question above, we know that

vo = 29 m/s

v' = 3.7 m/s

The velocity will be added each other because the direction of the observer is different from the object.

v = vo + v'

v = 29 + 3.7

v = 32.7 m/s

Hence, the relative velocity with respect to my friend is 32.7 m/s.

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The international system of units is also known as SI units. It was introduced to remove the confusion between many units. According to standard international form, the SI units of various quantities are listed below:

Mass = kg

Length = m

Time = s

Force = N

To obtain the SI units of the following dimensions, they must be converted to universal standard by expressing them by the given relations:

mm-mN = ×10-3 * x10-3 = 1 x10-6 N.m

mg/mm = ×106 kg /10-3m = 1×109 kgm-1

km/ms = ×103 m /x10-3 s = 1×106 ms-1

kN/(mm)2 = ×103 / ×10-3 = 1×106 Nm-2

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18 Mg/ L is the amount of work done.

It should be converted to energy in order to move an object. Energy can be transferred by the use of force. Work done refers to the amount of energy used by a force to move an object. A force must be applied in order for work to be completed, and there must also be motion or displacement in the force's direction. The amount of force multiplied by the distance moved in the force's direction is known as the work done by a force acting on an item.

Assume that the element's length at distance x from the table is dx.

Let's assume that W= M/L* dx*g(x) and that the entire work completed will take up 1/3 of the table.

W=M/L g(x)dx W=M/L g(x)dx

W= 18 MgL

​

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The orbit is an ellipse for the space probe that is sent into the orbit around the sun that brings it as close as 0.3 au and as far away as 5.4 au.

Kepler’s 3rd law

According to Kepler’s Third Law, the cubes of the semi-major axes of the orbits of the planets are directly proportional to the squares of the planets’ orbital periods. As an orbiting planet’s radius increases, so does the time of its orbit around the Sun.

T = 2πr3GME Remember that the semi-major axis of an ellipse is equal to the product of the perihelion and the aphelion divided by two. The semi-major axis (a) for a circular orbit is equal to the orbital radius.

P2 = a3, which means that the period of an orbit (P) squared is equal to Kepler’s Third Law.

As per Kepler's law and his explanation of eccentricity,

Eccentricity = Distance to the focus/ Distance to the directrix.

According to Kepler, an elliptical orbit is a Kepler orbit with an eccentricity of less than 1 and for a circular orbit, it is exactly 0 eccentricity.

So here Eccentricity = 0.3/5.4

= 0.055

So according to this, the space probe is moving in an ellipse orbit.

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The Law of Universal Gravitation,  states that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Newton's law of gravitation, states that any particle of matter in the universe draws another with pressure varying at once as the manufactured from the loads and inversely as the rectangular.

Newton, the pressure of gravity appearing between the earth and another item is at once proportional to the mass of the earth, directly proportional to the mass of the item, and inversely proportional to the square of the distance that separates the centers of the earth and the item. Gravitational steady, G is unbiased of the nature of the particle, medium among the debris, and time. Its cost is constant anywhere within the Universe.

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The change in internal energy of a gas as it cools is 94 J.

According to the First Law of Thermodynamics,

ΔU = q + w

Here  ΔU represents the change in internal energy

Q represents the heat added to the system

W represents the work done on the system

In the given case, work is done on the system, and heat is removed from the system.

Hence, W = 200 J AND Q= -106 J.

Putting the above values in the standard equation

ΔU = 200 - 106

ΔU = 94 J.

Hence, the change in internal energy is 94 J.

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By using the blackbody radiation formula, the temperature of the filament inside the bulb is changed by a factor of 10⁰'²⁵.

We need to know about black body radiation to solve this problem. The energy radiated by a black body object is proportional to the area and the fourth power of temperature. It can be determined as

P = A . e . σ . T⁴

where P is power, A is surface area, e is emissivity, σ is Stefan Boltzmann's constant ( 5.67 x 10¯⁸ W/m²K⁴) and T is temperature.

From the question above, we know that

P1 = 10 watt

P2 = 100 watt

T1 = T1

By using the black body radiation formula, the ratio of temperature is

T1⁴ / T2⁴ = P1 / P2

Hence,

T1⁴ / T2⁴ = P1 / P2

T1⁴ / T2⁴ = 10 / 100

T1⁴ / T2⁴ = 1 / 10

T2⁴ = 10T1⁴

T2 = ⁴√(10T1⁴)

T2 = T1 x 10⁰'²⁵

Thus, the temperature of the filament inside the bulb is changed by a factor of 10⁰'²⁵.

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The value to strain  is 0.00105.

When an object or medium is stressed, it deforms. Strain is the number that describes this distortion (deformation is experienced by objects or physical medium as a result of external forces—for). Strain is expressed as a fractional change in length (when under tensile stress), volume (when under bulk stress), or shape (under shear stress). As a result, strain is a dimensionless quantity. Tensile strain is strain produced by tensile stress, bulk strain (or volume strain) is strain generated by shear stress, and shear strain is strain induced by shear stress.

Strain = changes in length/ Original length

Strain = dL/L

= 0.21/200

= 0.00105

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