If the magnified cell had a diameter of 40mm on the computer screen using the 10x ocular lens with the 40x objective lens, what would be the actual diameter of the cell in millimeters?.

The values you found are incorrect.

The sum/resultant vector is

[tex]\hat R = \hat A + \hat B \\\\ \hat R = (5.00\,\mathrm m)\,\hat\imath + (6.00\,\mathrm m)\,(-\cos(30.0^\circ)\,\hat\imath - \sin(30.0^\circ)\,\hat\jmath) \\\\ \hat R = (2.00\,\mathrm m) \,\hat\imath - (3\sqrt3\,\mathrm m)\,\hat\jmath \\\\ \hat R \approx \boxed{(2.00\,\mathrm m)\,\hat\imath - (5.20\,\mathrm m)\,\hat\jmath}[/tex]

The magnitude of the resultant is

[tex]\|\hat R\| = \sqrt{(2.00\,\mathrm m)^2 + (-5.20\,\mathrm m)^2} \approx \boxed{5.57\,\mathrm m}[/tex]

The direction or angle the resultant makes with the positive horizontal axis is [tex]\theta[/tex] such that

[tex]\tan(\theta) \approx \dfrac{-5.20\,\mathrm m}{2.00\,\mathrm m} \approx -2.60[/tex]

Note the signs of the [tex]\hat\imath[/tex] and [tex]\hat\jmath[/tex] components of [tex]\hat R[/tex]. They tell us that [tex]\hat R[/tex] points into the fourth quadrant, and this means we can take the inverse tangent of both sides without any extra steps*. We then get

[tex]\theta \approx \tan^{-1}(-2.60) \approx \boxed{-67.0^\circ}[/tex]

* There would have been an extra step if [tex]\hat R[/tex] were pointing into either the second (negative [tex]\hat\imath[/tex], positive [tex]\hat\jmath[/tex]) or third quadrant (both negative [tex]\hat\imath[/tex] and [tex]\hat\jmath[/tex]). The inverse tangent function has a range of -90° to 90°, which means upon taking the inverse tangent of both sides of

[tex]\tan(\theta) = \dfrac{R_y}{R_x} \implies \theta = \tan^{-1}\left(\dfrac{R_y}{R_x}\right)[/tex]

we would only recover some angle [tex]\theta[/tex] between -90° and 90°. Yet our resultant must have some angle between -180° and -90°, or between +90° and +180° to belong to quadrant II or III. To get around this, we add an appropriately chosen multiple of 180° to the right side after taking the inverse tangent.

The distance the red ball travelled between 12 s and 24 s is 2116.8 m

Free fall is motion under gravity.

If we assume the red ball is falling freely, it has an initial velocity of zero.

Using the equation of motion s = ut - 1/2gt², we find the distance it travels or height it drops after the given time. where

So, s = ut - 1/2gt²

s = 0 × t - 1/2gt²

s = -1/2gt²

Since the distance the red ball falls is s = -1/2gt² with t = 12 s, we have

s = -1/2gt²

= -1/2 × 9.8 m/s² × (12 s)²

= -1/2 × 9.8 m/s² × 144 s²

= -4.9 m/s² × 144 s²

= -705.6 m

Since the distance the red ball falls is s = -1/2gt² with t = 24 s, we have

s' = -1/2gt²

= -1/2 × 9.8 m/s² × (24 s)²

= -1/2 × 9.8 m/s² × 576 s²

= -4.9 m/s² × 576 s²

= -2822.4 m

So, the distance the red ball travelled between 12 s and 24 s is d = s' - s

= -2822.4 m - (-705.6 m)

= -2822.4 m + 705.6 m

= -2116.8 m

So, the distance the red ball travelled between 12 s and 24 s is 2116.8 m

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Time taken by the soccer ball in the air when we neglect the air resistance is 2.75s

projectile motion - It is the motion of an object which projected into the air  and moving under the gravity.

a soccer ball is kicked at an angle of 64° to the horizontal

initial speed = 15 m/s

Initial velocity in vertical direction is given as

[tex]V_{v} = V_{0}sin \theta[/tex]

[tex]V_{v} = 15sin(64)[/tex]

[tex]V_{v}[/tex] = 15× 0.8987

    = 13.48m/s

time taken to reach the maximum height is given by

T =[tex]V_{v}[/tex] /g

where

[tex]V_{v}[/tex]  is the velocity

g is the gravity

Ball comes downward with the same speed

then that time period is given by.

2[tex]V_{v}[/tex] /g

= 2× 13.48 /9.8

T = 2.75s

Time taken by the soccer ball in the air when we neglect the air resistance is 2.75s

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An object attached to one end of a spring makes 20 vibrations in 10 seconds, its angular frequency is 12.6 rad/s.

The quantity of complete waveforms produced per second is a wave’s frequency (f). This is equivalent to the quantity of cycles per second or oscillations per second.

In this instance, a spring-attached object causes 20 vibrations in 10 seconds. 20 vibrations in 10 seconds, in other words. S creates two vibrations in a second.

As a result, the object’s frequency is 2 Hertz.

Angular frequency, abbreviated “[tex]\omega[/tex]” is a scalar measure of rotation rate in physics. It describes the rate of change of the argument of the sine function, the rate of change of the phase of a sinusoidal waveform, or the angular displacement per unit of time.

у = 20/10

= 2 vibrations in 1 second

Then w = 2[tex]\pi[/tex]v = 4 x 3.14

=12.56 rad /s

Thus, the angular frequency is 12.56 rad /s

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The ball rises 53.361 m above the point where the bat hit the ball.

When a batter hits a ball high in a baseball game, the ball remains in the air for 6.6 seconds.

The acceleration of gravity is 9.8 m/s².

The vertex value of time is half of 6.6 seconds or 3.3 seconds.

Therefore, the final velocity at the maximum height is v = 0 m/s

Now, using the equation of motion:

v - u = gt

v = u + gt

u × sin(θ) = - gt

u × sin(θ) = 9.8 × 3.3

u × sin(θ) = 32.34 m/s

Now, by using the equation of motion:

v² - u² = 2gh

h = ( v² - u²) / 2g

h = ( 0 - (32.34)² ) / 2(9.8)

h = (1045.8756) / 19.6

h = 53.361 m

The ball rises 53.361 meter high.

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The approximate magnitude of the attractive gravitational force between ganymede and jupiter  is 16.35 x 10^21 N .

According to Newton’s Law of Gravitation, the gravitational force between two bodies is directly proportional to the masses of the two objects and is inversely proportional to the square of the distance between them.

The above statement can be represented by the following equation:

F = Gx (m1)x (m2)/r^2

Here G = Universal Gravitational Constant = 6.67 x 10^-11 N m^2/kg^2

m1 and m2 are the masses of two bodies

r is the distance between the bodies

Putting m1= Mass of Jupiter= 1.89 x 10^27 kg

m2 =Mass of Ganymede 1.48 x 10^23 kg

r = Distance between Jupiter and Ganymede = 1.07 x 10^9 meters

F = 6.67 x 10^-11 x 1.89 x 10^27 x 1.48 x 10^23/(1.07 x 10^9)^2

On solving the above equation F comes out to be 16.35 x 10^21 N.

Thus, the approximate magnitude of the gravitational force between Ganymede and Jupiter is 16.35 x 10^21 N.

Because it consistently attempts to pull masses together rather than pushing them apart, the gravitational force is known as attractive. In actuality, every thing in the cosmos, including you, is pulling on every other object.

Gravitation is the force in physics that draws two masses together. Unbelievably, every single particle of matter in the cosmos attracts every other particle through gravity. The phrases gravitation and gravity are sometimes used synonymously to refer to the attraction that exists between anything with mass or energy.

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The independent variable is the type of rose, and the dependent variable is the quantity of flowers.

In mathematical modelling, statistical modelling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables due to some law or rule.

Consider what is being recorded first in order to identify the variables; in this situation, it would be the variety and quantity of roses cultivated.

Asking yourself which one depends on which other will help you distinguish between which is reliant and which is independent.

Is it more likely that the number of flowers determines the type of rose?

Or does the type of rose affect how many blossoms are present?

Saying that a rose's kind depends on how many blossoms it has is illogical.

However, it does make sense to state that the type of rose affects how many blossoms are there.

As a result, the independent variable is the type of rose, and the dependent variable is the quantity of flowers.

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The correct answer is 21 m.

The term "uniformly accelerated motion" refers to a body or object moving at a consistent rate of acceleration. The absence of velocity does not imply constant acceleration. Therefore, if a body is in motion such that the amount of change in its velocity in equally spaced time intervals will be constant, then that is what is meant by uniform acceleration or uniform acceleration definition.

Given initial velocity = 0 m/s

acceleration = 6 m/s^2

The body's movement in nth seconds in terms of distance,

S_n = u + a/2 (2n-1)

S_4 = 0 + 6/2 ( 2 × 4 - 1 )

S_4 = 3 ( 8 -1 )

S_4 = 3 × 7

S_4 = 21 m

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The property of the rock that will change if it is transported from the moon to the earth, is the weight.

The weight of an object is directly proportional to the action of gravity on the mass of that object. It can be confirmed with the weight formula:

W = m * g

Where:

By contrast, the mass of an object indicates the amount of matter it contains, it is a constant magnitude.

It is the physical magnitude that expresses the force exerted by gravity on the mass of a body, this is expressed in units of the international system in Newton.

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The effect is that the electrons shield the nucleus from the magnetic field.

A magnetic field is a vector field that explains the magnetic influence on moving electric charges, electric currents, and magnetic materials.

A force perpendicular to the charge's own velocity and the magnetic field acts on it when it moves through a magnetic field.

Moving electric charges generate magnetic fields.

Everything is constructed of atoms, and each atom has an orbiting nucleus that is composed of protons and neutrons.

Compass, motors, refrigerator magnets, railroad tracks, and modern roller coasters are all examples of objects that use magnetic force.

Charges that travel across its areas feel a force. All moving charges produce a magnetic field.

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After a collision, there is no change in the momentum from the initial situation. This statement  satisfies the law of conservation of momentum. Hence, Option D is correct.

Momentum is the sum of an object's mass and velocity, and it is a property of all moving objects. This can be expressed mathematically as p=MV, where p stands for momentum. The momentum of an object can fluctuate because its velocity can. When describing the momentum of a system of objects, the Law of Conservation of Momentum is helpful. The Law of Conservation of Momentum, in its most basic form, states that the total momentum of an isolated system stays constant.

Hence, the momentum will be the same after the collision as it was before the collision.

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The  pressure at the bottom of the cylinder is two atmospheres at the depth d will be 202650 Pa.

The force delivered perpendicularly to an object's surface per unit area across which that force is dispersed is known as pressure. In comparison to the surrounding pressure, gauge pressure is the pressure. Pressure is expressed using a variety of units.

Calculate the size of that surface. Check to see that both numbers are expressed in the proper units, such as newtons/meters squared or pounds/inches squared. By the area, divide the force. The units of measurement for your pressure are pascals (Pa) or pounds per square inch (psi).

[tex]P = {P_{{\rm{atm}}}} + {\rho _1}gd + {\rho _2}g{h_2}[/tex]

[tex]{h_2} = \left( {1 - d} \right)\\P = 2\;{\rm{atm}}\\\begin{array}{c}\\P = \left( {2\;{\rm{atm}}} \right)\left( {\frac{{101325\;{\rm{Pa}}}}{{1\;{\rm{atm}}}}} \right)\\\\ = 202650\;{\rm{Pa}}\\\end{array}[/tex]

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The rate constant increases by a factor of 1.3 when the temperature increases from 200k to 400k for a reaction with an activation energy of 845 j/mol.

ln k2/k1 = 845/8.314 (1/200 - 1/400)

ln k2/k1 = 0.254

k2/k1 = 1.3

The Arrhenius equation, which has the form lnk=RE(T1T1), relates the activation energy (Ea) and rate constants (k1 and k2) of a chemical process at two distinct temperatures (T1 and T2).

Where T1 and T2 are the temperatures of rates k1 and k2 (respectively) in K, k1 and k2 are rate constants, Ea is the activation energy in J/mol, and R is the gas constant which has a value of 8.314 J/K mol.

The activation energies employed were 20.1 kJ/mol and 59.8 kJ/mol.

The rate constants K1 and K2 are 1016 e-2000/T and 1015 e-1000/T, respectively, for two distinct reactions.

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0.1 J of elastic potential energy will be stored by the spring when it gets compressed by 0.2 m if it has the spring constant of 5 N/m.

Elastic potential energy can be defined as the potential energy stored by the spring when it is stretched or compressed.

According to the question.

Compression in the spring, x = 0.2 m

Spring constant, k = 5 n/m

Elastic potential Energy, U = [tex]\frac{1}{2} (0.2)^{2} (5)[/tex]

U = 0.1 J

0.1 J of elastic potential energy will be stored by the spring.

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Because protons and electrons in an atom carry opposite charges, they are attracted to each other and thus maintain the boundaries of the atom as a  singular closed system.

An atom consist of equal number of electrons and protons, due to which the attractive force between them binds the atom together and hence no exchange of matter takes place, therefore an atom posses closed system.

If we consider that energy is emitted, when electrons emit energy, then this energy is absorbed in the atom, thus preventing the electrons from hitting the nucleus. More specifically, as the electron wave travels around the nucleus, it emits energy, but this energy is recaptured when the wave doubles back on itself in 1/2 or full wavelengths to form a standing wave.

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The mass of the electric car moving at the given speed and kinetic energy is determined as 920 kg.

The kinetic energy of an object is the energy possessed by the object due to the motion of the object. The kinetic energy of an objects is determined from the product of object's mass and its velocity.

The mass of the electric car is calculate by applying kinetic energy formula as follows;

K.E = 0.5 mv²

where;

Substitute the given parameters and solve for the mass of the electric car.

m = (K.E)/(0.5v²)

m = (222640) / (0.5 x 22²)

m = 920 kg

Thus, the mass of the electric car moving at the given speed and kinetic energy is determined as 920 kg.

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Answer:

A "resistor" can be connected in "parallel" to the meter

Suppose that an ammeter reads from 1-10 amps.

Now add a resistor in parallel to the ammeter where the resistor has the same value as the resistance of the ammeter - Now the ammeter will read 1-20 amps because only 1/2 the current passes thru the ammeter.

A sled is initially moving on a straight track at 3.5 m/s. The final velocity of the sled will be 3.75m/s. When the acceleration is 2.0 m/s².

The rate at which an object's velocity with respect to time changes is referred to as acceleration in mechanics. They are vector quantities, accelerations. The direction of the net force applied on an item determines the direction of its acceleration.

Given parameters:

Initial velocity  = 3.5m/s

Final velocity  = ?

Time taken  = 2s

acceleration = 2m/s²

[tex]a = v_f - v_i/t[/tex]

2 = x - 3.5/2

x = 3.75 m/s

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41.4 x 104 Nm2/C is the electric flux through the sheet.

The electric flux through a planar area A is calculated as the product of the electric field, the area of the plane, and the cosine of the angle between the electric field and a vector that is perpendicular to the area.

Φ = E A cos θ -----1  

By the question;

E = 4.6 x 10⁴ N/C

A = Area of the square = l²          [l = length of the square]

=> A = (3m)² = 9m²

θ = 0°    [since the electric field is perpendicular to the square sheet, then the area vector is parallel to the field]

Substitute the values in equation 1

Φ = 4.6 x 10⁴ x 9 x cos 0°

Φ = 4.6 x 10⁴ x 9 x 1

Φ = 41.4 x 10⁴ Nm²/C

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The speed and the direction of motion of player 2 is 2.2 = M1xV1 + M2xV2

2.2 = 47x1.1 + 38×V2

2.2 = 51.7 + 38xV2

-49.5 = 38×V2

V2 = -1.3 m/sec.

It means that the second object is moving opposite to first object.

Momentum is product of mass and velocity. It is a vector quantity and it's S.I unit kgxmeter/sec.

In above question

Player one has

M1 = 47 kg

V1 = 1.1 m/sec

Player two has

M2 = 38 kg

V2 = not given

Total momentum = 2.2 kgxm/sec

Total momentum = momentum of first body + momentum of second body

2.2 = M1xV1 + M2xV2

2.2 = 47x1.1 + 38×V2

2.2 = 51.7 + 38xV2

-49.5 = 38×V2

V2 = -1.3 m/sec.

It means that the second object is moving opposite to first object.

Therefore, The speed and the direction of motion of player 2 is 2.2 = M1xV1 + M2xV2

2.2 = 47x1.1 + 38×V2

2.2 = 51.7 + 38xV2

-49.5 = 38×V2

V2 = -1.3 m/sec.

It means that the second object is moving opposite to first object.

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In the mass spectrum of pentane, the presence of a peak with m/z = 15 is most likely due to the detection of A) methyl radical cation that has been lost from the spectrum.

The m/z ratios of any ions contained in a sample displayed against their intensities that forms a mass spectrum.

The height of the peaks in any kind of mass spectrum denotes the relative abundance of the various components in the sample, and each peak in a mass spectrum displays a component that a distinct m/z is in the sample.

Only when a molecule has been transformed into a gas-phase ion can a mass spectrometer calculate the mass of the molecule.

In order to do this, it gives molecules an electrical charge and transforms the flow of electrically charged ions that results into a proportional electrical current that a data system can subsequently read.

Whenever any molecules are ionized in an ionization box, many different kinds of ions have been created.

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Complete Question

In the mass spectrum of pentane, the presence of a peak with m/z = 15 is most likely to the detection of: _________-

A) Methyl Radical

B) Ethyl Radical

C) Propyl Radical

D) Butyl Radical

The magnitude of the force exerted by the electric field on the proton will be 4.80 × 10—¹⁷ N.

The force exerted by the electric field on the electron =

4.80 × 10—¹⁷ N.

The direction of the electric field that is exerting force on the electron = West

The magnitude of the electric field is,

[tex] = \frac{4.80 \times 10 ^{ - 17} }{1.6 \times 10 - 19} [/tex]

= 300 N/C

The magnitude of the electric field is 300 N/C.

The magnitude of the force exerted by the electric field on the proton will be,

The magnitude of the force exerted by the electric field on the electron = The magnitude of the force exerted by the electric field on the electron.

[tex] = 4.80 \times 10 ^{ - 17} [/tex]

Therefore, the magnitude of the force exerted by the electric field on the proton will be 4.80 × 10—¹⁷ N.

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In cartesian coordinates, we can write the position vectors as-

a) → r = 12.4 m , θ = 170°    ↔     - 12.21 i + 2.15 j

b) → r = 4 cm , θ = 50°   ↔    2.57 i + 3.06 j

c) → r = 20 inches , θ = 210°   ↔    - 17.32 i - 10 j

It is two-dimensional coordinate system which uses a straight line distance (from a reference point) and the angle made by it (with respect to reference direction) to represent a point in the X-Y plane.

Given are the position vectors in polar coordinates of three points in X-Y coordinate system.

The transformation from polar coordinates (r, θ) into cartesian coordinates (x, y) is done using the following formulae -

x = r cosθ

y = r sinθ

a) → r = 12.4 m , θ = 170°

x = 12.4 x cos (170°) = 12.4 x -0.98480775301 = -12 .21

y = 12.4 x sin (170°) = 12.4 x 0.17364817766 = 2.15

In cartesian form → ( -12.21 i + 2.15 j )

b) → r = 4 cm , θ = 50°

x = 4 x cos (50°) = 4 x 0.64278760968 = 2.57

y = 4 x sin (170°) = 4 x 0.76604444311 = 3.06

In cartesian form → ( 2.57 i + 3.06 j )

c) → r = 20 inches , θ = 210°

x = 20 x cos (210°) = 20 x -0.86602540378 = -17.32

y = 20 x sin (210°) = 20 x -0.5= -10

In cartesian form → ( -17.32 i - 10 j )

Therefore, in cartesian coordinates, we can write the position vectors as -

a) → r = 12.4 m , θ = 170°    ↔     - 12.21 i + 2.15 j

b) → r = 4 cm , θ = 50°   ↔    2.57 i + 3.06 j

c) → r = 20 inches , θ = 210°   ↔    - 17.32 i - 10 j

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Answer:

(174^2 + 88.4^2)^1/2 = 195 m       magnitude of resultant vector

(tan θ = 88.4 / 174 = .508 or 26.9 deg)

Answer:

D. All of the above

Explanation:

Because it's the most logical answer.

The deflecting electric field is 0.83mv/m

Acc. to the newtons 2nd law - there is an acceleration when a force acts on an object.

F = ma     (equation 1)

where

F is force

m is mass of object

a is acceleration

Electric field intensity- it is defined as force experienced by a unit positive charge placed at that point.

it is denoted by E = F/q

where

F is force

q is the charge

F = Eq     (equation2)

from 1 and 2 equation we get

ma = Eq

E = ma /q

Charge on the drop of ink.is q.

(e is the charge on an electron.)

so,

q = 751896×e

q = 751896×1.6 ×⁻¹⁹

q = 12.03 ×10⁻¹⁴

m = 10⁻¹¹kg

a = 10⁴ m/s²

using above values

E = ma /q

E = 10⁻¹¹×10⁴/12.03 ×10⁻¹⁴

E = 0.83mv/m

The deflecting electric field is 0.83mv/m

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Kepler used the extensive records of planetary positions measured by  Tycho to discover that the orbits of the planets are elliptical.

The planets would be listed from smallest to largest in order of size: Mercury, Mars, Venus, Earth, Neptune, Uranus, Saturn, and Jupiter. The gas giants are Jupiter and Saturn, whereas the more distant Uranus and Neptune are known as the ice giants.

The International Astronomical Union (IAU) downgraded Pluto to a dwarf planet since it failed to satisfy all three criteria for a full-sized planet. Pluto essentially meets all the criteria, with the exception of the one that it "has not cleared its nearby vicinity of other objects."

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The egg is traveling at least at a speed due to gravity of 20 m/s.

The force of gravity causes items to fall toward the ground. The force of gravity accelerates items as they descend to the ground. Velocity is a measure of the speed and direction of motion, and acceleration is a change in velocity. The longer an object is in free fall, the faster it descends toward the ground due to gravity.

In actuality, an object's velocity rises by 9.8 m/s2, so it reaches 9.8 m/s by the time it begins to fall. By the time it has been falling for 2 seconds (9.8 m/s plus 9.8 m/s), it is moving at 19.6 m/s, and so on.

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The mass of an object that requires 15.0N to accelerate it at rate of 3 m/s² is 1.17 kg.

The mass of an object is the quantity of matter present in an object.

The mass of an object is related to its acceleration and the applied force by the given formula below:

force = mass * acceleration

mass = force/acceleration

From the data provided:

force applied = 15.0 N

acceleration = 3 m/s²

The force applied overcomes the weight of the body.

Total force applied = weight + net force

Total force = mg + ma

Total force = m(g + a)

m = force/(g + a)

mass = 15(9.8 + 3)

m = 1.17 kg

Therefore, the mass of the object is 1.17 kg.

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The continuous circular motion of the wind (air mass) between the equatorial low pressure belt and the subtropical high pressure belts is known as Trade winds

These winds helps ships to travel west. It also steers hurricanes. These winds are air currents that are closer to the Earth's surface. These winds start as warm air from equator and as it travels to polar regions it gets cooler. Trade winds can be found 30 degrees North and South of the equator.

The subtropical high pressure belts extends from 35 degrees North and South of the equator. It is also called as Horse latitude. The equatorial low pressure belt is the area where the trade winds from Horse latitudes of both hemispheres converges.

Therefore, the continuous circular motion of the wind (air mass) between the equatorial low pressure belt and the subtropical high pressure belts is known as Trade winds

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