Help on solving this single logarithm

Answer:

Formula

Resolve:

Hope this helped

Hello..!

We first apply the data to the problem.

Data:

Then, we apply the formula that is.

Formula:

Finally we develop the problem.

Developing:

The speed is 2 meters per second.

The relative humidity (RH) where the Wet Bulb Depression is 3° and the Dewpoint is 24° is given as 78.92%.

Relative humidity (RH) is a percentage ratio of the quantity of atmospheric moisture available to the amount that would exist present if the air was saturated.

The relationship between Relative Humidity, Air Temperature, and Dewpoint is given as follows:

RH = 100 *[[tex]e^{\frac{(\beta * Dp)}{(\lambda + Dp)}}[/tex] / [tex]e^{\frac{(\beta * T)}{(\lambda + T)}}[/tex]]

Where

RH = Relative Humidity

T = Air Temperature

Dp = Dewpoint

β = 17.625 and λ = 243.04°C; (revised Magnus coefficients)

e = 2.7182818 [exponential constant]

Note that Air temperature (T) is determined using the attached Dewpoint Psychrometer Table /chart

As given on the chart and in the question;
T = 28°

Dp = 24°

Hence,

RH = 100 x [[tex]e^{\frac{(17.625 * 24)}{(243.04+ 24)}}[/tex] / [tex]e^{\frac{(17.625 * 28)}{(243.04+ 28)}}[/tex] ]
RH = 100 x [ [tex]e^{(423/267.04)}[/tex] )/ [tex]e^{(493.5/271.04)}[/tex]]

RH = 100 x [[tex]e^{1.584}[/tex]/[tex]e^{1.8207}[/tex]]

RH = 100 x (4.874414/6.176578)

RH = 100 x 0.789177113929

RH = 78.9177113929

RH [tex]\approx[/tex] 78.92%

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The correction options indicating a decomposition reaction are:

This a reaction in which a compound breaks down into smaller elements or compound by the application of heat. Example is given below:

AB₂ -> A + B₂

We can see that AB₂ decomposed to produce A and B₂

With the above information in mind, we can easily determine which reaction is decomposition reaction from the given options.

The options from the question are:

Observing the given options with the knowledge of decomposition reaction, we can conclude that the correct options are:

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The force that is applied 100 N.

We know that a lever is one of the kinds of simple machine that we have. The lever works by the fact that there is a load and an effort arm. We have been told that a  lever with an effort arm of 10 meters and a load arm of 2 meters is used to lift an object weighing 220 Newtons to a height of 4 meters.

We can get the force that must be applied from the fact that;

Work = Force * distance

Force = Work/Distance

Force = 400/4

Force = 100 N

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The initial speed of the ball is 4.12 m/s.

Speed is distance travelled by the object per unit time. Due to having no direction and only having magnitude, speed is a scalar quantity With SI unit meter/second.

Given parameters:

Mass of the ball; M = 10.0 g.

Height from where ball straight down from : h = 2.0 m.

Final speed of ball; v = 7.5 m/s.

And we known that, acceleration due to gravity; g = 9.8 m/s²

We have to find:  the initial speed of the ball: u = ?

We know that, v² = u² + 2gh

⇒ u² = v² - 2gh

⇒ u² =( 7.5)²  - 2×9.8 ×2

⇒ u² = 17.05

⇒ u = 4.12 m/s.

Hence,  the initial speed of the ball is 4.12 m/s.

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Answer:

the power used is 0.18kW and the energy used is 0.36kWh

Explanation:

from power= current × voltage

power= 1.5A × 120V

power= 180W or 0.18kW

energy used = power × time

= 0.18kW ×2h

energy used = 0.36kWh

Answer:

Explanation:

The rms speed:

Vrms = (500 + 600 + 700 + 800 + 900) / 5 = 700 m/s

The Honda Civic is the car that would have greater impulse, momentum change and acceleration due to Collison.

The term impulse has to do with the product of force and time. The impact is literally the force that acts on an object for a short time. We know that the mass of the object is very important when we are discussing the impulse on the object.

When there is a  head-on collision that occurs between the  Mack truck and a Honda Civic, the Honda Civic would have the greater impulse and the greater change in momentum and thus the greater acceleration.

If we do not understand the concept of the effect of momentum and the acceleration of an object, we would not be able to understand the basic interaction that occur between objects using the principles of physics.

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a) Tractor trailer will have more kinetic energy

b) kinetic energy of pickup truck will be more than a SUV

c) school bus will have the maximum kinetic energy

a) Tractor trailer will have more kinetic energy because its mass is way to heavy than that of compact car as kinetic energy is not only just dependent on velocity but also depend upon mass of that body .

b) since , speed of SUV and truck is same , but mass of the truck is more than SUV , hence kinetic energy of pickup truck will be more than a SUV .

C) Since , school bus carries number of passengers than SUV or compact car , hence school bus will have the maximum kinetic energy .

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A projectile is fired horizontally at 180 m/sec from an altitude of 734.7 m. The final vertical velocity of the projectile as it hits the ground will be 216.36 m/s

s = u*t + 1/2 * a * [tex]t^{2}[/tex]

734.7 = 180 * t + 1/2 * g  * [tex]t^{2}[/tex]

734.7 =  180 * t + 1/2 * 9.8  * [tex]t^{2}[/tex]  

         = 4.9  [tex]t^{2}[/tex]   + 180 t - 734.7

by solving the above quadratic equation , we get

t = 3.71 seconds

v = u + at

v = u + g*t

v = 180 + (9.8)(3.71)

 = 216.36 m/s

The final vertical velocity of the projectile as it hits the ground will be 216.36 m/s

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(a) The magnitude of the magnetic field at the point of the proton moving in the negative direction is 2.1 x 10⁻⁹ T.

(b) The magnetic force direction experienced by the proton moving in the negative direction is 4.71 x 10⁻²² N.

The magnitude of the magnetic field at the point of the proton moving in the negative direction is calculated as follows;

F = qvB = kq²/r²

qvB = kq²/r²

B = kq²/qvr²

B = kq/vr²

where;

B = (9 x 10⁹ x 1.602 x 10⁻¹⁹) / (1.4 x 10⁶ x 0.7 x 10⁻³ x 0.7 x 10⁻³ )

B = 2.1 x 10⁻⁹ T

The magnetic force direction experienced by the proton moving in the negative direction is calculated as follows;

F = qvB

F = 1.602 x 10⁻¹⁹ x 1.4 x 10⁶ x  2.1 x 10⁻⁹

F = 4.71 x 10⁻²² N.

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According to particle model of light, speed of light decreases as it enters a optically denser medium.

Refraction occurs when a light beam crosses a barrier between two different materials. The ray changes direction and speed in accordance with the following relationship:

where n is the material's index of refraction, which is greater for a medium with a higher optical density, and v and c are the speed of light in a vacuum and the ray of light, respectively, in the material. As a result, the equation shows that the wave's speed decreases with increasing optical density.- Since the frequency of the light is independent of the characteristics of the medium, it is constant.

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The color of the wire is a factor that will not affect the magnetic strength of a solenoid.

A solenoid is a device that consists of a coil made of wire, a housing and a moveable armature. When an electrical current is flowing in the solenoid, a magnetic field forms around the coil which draws the plunger inside. A solenoid has the ability to convert electrical energy in the form of mechanical work.

The magnetic field created by a solenoid depends on the current and density of rounds. The energy density of the magnetic field depends on the strength of the magnetic field and also depends upon the magnetic permeability of the material present in it. Iron has a larger permeability as compared to a vacuum.

So we can conclude that option C is the correct answer.

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Answer:

no coaster car does not travel as high

Sound waves are mechanical waves. They need a medium for propagation. In air the sound waves will travel smoothly and we can get it. Whereas  in vacuum, no medium is there and the sound waves cannot propagate.No sound can be produced there.

Mechanical waves are waves propagating through a medium such as air, water etc. There are two types of mechanical waves namely transverse wave and longitudinal waves.

In transverse waves, the vibration of particles is in a direction perpendicular to the wave whereas, in longitudinal waves,  both are in one direction. Sound wave is a longitudinal wave.

Unlike electromagnetic waves mechanical waves cannot be travelled in vacuum. Hence if we try to produce sound in space or vacuum,no effect will be there but in air and water sound waves can be propagated.

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1. The time taken for the car to stop is 5 s

2. The distance travelled during the reaction time is 50 m

3. The distance travelled during the stopping time is 62.5 m

1. How do I determine the time taken for the car to stop?

The time taken for the car to stop can be obtained as follow:

a = (v - u) / t

-5 = (0 - 25) / t

-5 = -25 / t

Cross multiply

-5 × t = -25

Divide both sides by -5

t = -25 / -5

t = 5 s

Thus, the time taken to stop is 5 s

2. How do I determine the distance travelled during the reaction time?

The distance travelled during the reaction time can be obtained as follow:

Distance travelled = velocity × reaction time

Distance travelled = 25 × 2

Distance travelled = 50 m

3. How do I determine the distance travelled during the stopping time?

s = ut + ½at²

s = (25 × 5) + (½ × -5 × 5²)

s = 125 - 62.5

s = 62.5 m

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The horizontal velocity of the projectile as it leaves the launcher is 35 m/s.

The time of motion of the projectile is calculated by applying the following kinematic equation as shown below.

h = vt + ¹/₂gt²

where;

h = 0 + ¹/₂gt²

h = ¹/₂gt²

t = √(2h/g)

t = √(2 x 0.4 / 9.8)

t = 0.286 s

The horizontal velocity of the projectile as it leaves the launcher is calculated as follows;

v = x/t

where;

v = 10 m / 0.286 s

v = 35 m/s

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The work done by a 20-newton force applied at an angle of 45.0° is 565.69 J.

Calculation:-

Force = 20 N

distance = 40 meters

angle = cos 45°

Work done = F.d cosθ

                 = 20×40 × 1/√2

                 = 800 / √2

                =  565.69 J

Force is a push or pulls upon an item because of the object's interaction with some other object. pressure is a power that can exchange the motion of an object. A force can reason an object with mass to alternate its speed, i.e., to boost up. pressure also can be described intuitively as a push or a pull. A force has each significance and course, making it a vector amount.

The phrase 'Force' has a unique meaning. At this degree, it is absolutely appropriate to describe a force as a push or a pull. A force is not something that an object consists of or 'has in it. A force is exerted on one object through another. The concept of a force isn't always restricted to living matters or non-living matters.

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The force exerted on the body is 12.66 N.

Linear momentum, translational momentum, or clearly momentum is the made of the mass and velocity of an item. it's miles a vector amount, possessing significance and a path. If m is an object's mass and v is its speed.

Given;

mass = 2 kg

height = 8m

bounce height = 2 m

let velocity just before striking the floor is initial velocity 12.65 m/s

the potential energy at 8 m = mgh

                                        = 2 ×10× 8

                                        = 160 J

same converted into kinetic energy 160 J = 1/2 mv²

                                                               V² = 320/2

                                                                v = 12.65 m/s

Final velocity

mgh = 1/2 mv²

2×10×2 = 1/2×2 × v²

v² = 6.32 m/s

Acceleration = change in velocity per unit of time

                      = - 6.32 - (-12.65)  = 6.33 m/s² / 0.1

Force = mass × acceleration

          = 2 ×  6.33 m/s²

           = 12.66 N

Momentum may be described as a mass in motion. All objects have mass; so if an object is transferring, then it has momentum - it has its mass in movement. the quantity of momentum that an item has depends upon variables: how an awful lot of stuff is moving and the way speedy the stuff is moving.

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3.2) the magnitude and direction of the reaction to the nail is 26.5 N towards the wall.

3.3) the person's resultant displacement measured from the starting point is  239.99 m.

3.2)

The tension in the rope 1 = 10N

The tension in the rope 2 = 20N

the angle between them = 120degrees

We have;

R² = 10² + 20² - 2(10 x 20)Cos(120°)

R² = 100 + 400 - 400Cos(120°)

R² = 500 + 200

R² = 700

R = 26.5 N

towards the wall.

3.3)Let alone having the graph's x axis and the West-East axis in a Cartesian coordinate system coincide.

Let's split the vectors up using trigonometry.

Aₓ = 100.0 m  

By = -300.0 m

angle measured from the positive side of the x-axis counterclockwise is

θ = 180 + 30 = 210

Cy = C sin 210° =  -75.0 m

Cₓ = C cos 210° = -129.9 m

The angle from the positive side of the x-axis counterclockwise.

θ = 180-60 = 120º

Dy = D sin 120 =  173.2 m

Dₓ = D cos 120 = -100.0 m

add the component Then we get :

x = Aₓ + Cₓ + Dₓ

x =  100 - 129.9 -100 = -129.9 m

y = By + Cy + Dy

Y = -300 - 75.0 + 173.2 = -201.8 m

Resulting vector calculated as :

[tex]R = \sqrt{x^2 + y^2}[/tex]

R = 239.99 m

3.2) the magnitude and direction of the reaction to the nail is 26.5 N towards the wall.

3.3) the person's resultant displacement measured from the starting point is  239.99 m.

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In order to determine the density of the pebble, Nabil requires a balance to measure the mass of the pebble.

The density of a substance is the measure of how tightly-packed the particles in the substance are.

Density is the ratio of the mass and volume of the substance.

To determine the density of a substance, the mass of the substance is measured with a balance and the volume of the substance if it is solid is measured using a displacement can and a beaker.

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The electrostatic force between the two charged spheres is determined as 6 x 10⁻³ N.

The electrostatic force between two charged objects, according to Coulomb's law, is directly proportional to the product of the charges and inversely proportional to the square of the distance between the charges.

F = kq₁q₂/r²

where;

F = (9 x 10⁹ x 2 x 10⁻⁷ x 3 x 10⁻⁷) / (0.3²)

F = 6 x 10⁻³ N

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Metals are great conductors because the electrons are able to move freely between the different energy levels within the atom.

What are conductors?

A substance or material that has the capability of conducting electricity or allows the passage of electricity to flow through it is known as conductor or electric conductor. The electrical charge carriers i.e., electrons or ions move easily from one atom to another when a voltage is applied on it.

The outer bound electrons of the metals are loosely bound  as the nucleus gets very less attracted on the electrons present on the outermost shell and because of this the charge carriers in them can move the current applied easily when there is a potential difference. Therefore, metals are considered to be the best conductors.

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Answer:  C.  5V

Explanation:

Since P = VI, power is directly proportional to voltage

If current is constant, then the lower the voltage, the lower the power. The lowest voltage shown is 5 Volts.

16.52 m/s is the velocity  and  vcosθ is the velocity in component vector form.

velocity in vector form= vcosθ

vector form= vcosθ

vector form=18cos53

v=16.52 m/s

"The rate at which an item changes its location" is described by a vector number called velocity. Imagine someone walking quickly, one step forward, one step back, and starting each step from the same location. Velocity is a vector quantity. Therefore, velocity is cognizant of direction. The direction must be taken into account when determining an object's velocity. A velocity of 55 miles per hour is not sufficient information. It is necessary to account for the direction in order to accurately describe the object's velocity. Simply put, the direction of the velocity vector represents the motion of the object.

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It is important for the measurements that the track is level for rolling motion in physics because the rolling objects only move on the tract that is leveled correctly.

The rolling motion is a fusion of translational motion and rotational motion. For a body, the motion of the center of mass is the adaptation motion of the body. During the rolling motion of a body, the exterior contact gets disfigured a little temporarily. A combination of translational and rotational motions happens during the rolling motion of an object. To define rolling motion, we must recognize the forces like angular momentum and torque. It is a merger of two types of motion i.e. translational and rotational motion. The translational motion of a body is the movement of the whole body from one place to another.

So we can conclude that Rolling motion is that usual combination of encircling and translational motion that we see everywhere and every day.

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D. air resistance

Hope it helps

The gravitational force exerted on the Station by the gravity of the Earth is approximately 0.00026680N.

The gravitational force is the force that the earth exerts on a body to attract it. Examples of motion caused by gravitational force include the downward motion of water in rivers and streams, the upward motion of thrown objects such as balls, and the downward motion of the leaves and fruits of trees as they fall to the earth.

All objects with mass are attracted to one another by the gravitational attraction, which has a magnitude that is directly proportional towards the masses of the two objects & directly proportional to the distance of their distance from one another gravitational force

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The answers include the following:

This is referred to as the force per unit area of a substance and the unit is Pascal. This parameter varies with depth such that the higher the pressure, the deeper the ocean or water body and vice versa.

The pressure variations affects the ability to explore the ocean such that it exerts a force on the diver thereby slowing him/her down and also not being able to reach certain areas.

The challenges of scuba diving include drowning and decompression sickness which is characterized by dissolved gasses exiting solution to form bubbles inside the body.

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