2. Find the value of A in the unit vector 0.4î+ 0.8ĵ+ λk.​

Answers

Answer 1

There is no A in the vector, so I assume you mean λ.

The magnitude of any unit vector is 1, so

[tex]\|0.4\,\vec\imath + 0.8\,\vec\jmath + \lambda \,\vec k\| = \sqrt{0.4^2 + 0.8^2 + \lambda^2} = 1[/tex]

Square both sides and solve.

[tex]0.4^2 + 0.8^2 + \lambda^2 = 1^2 \implies \lambda = \boxed{\pm \sqrt{0.2}}[/tex]


Related Questions

You are in the year where the earth has no more land available for houses you decide to build an apartment up and need things to survive in each earths 5 layers (troposphere,stratosphere, mesosphere, thermosphere, exosphere) Question: what things would you need to survive the thermosphere(really hot it is 2000 degrees fahrenheit)
PLS HELP PLS IMMA GET A BAD GRADE

Answers

Answer:

Heavy clothes

Explanation:

If you were to hang out in the thermosphere, though, you would be very cold because there aren’t enough gas molecules to transfer the heat to you. This also means there aren’t enough molecules for sound waves to travel through.

At the same temperature, which move with the greater speed in the air?
A.heavier molecules
B.very light molecules
C.All will have equal average speeds.

Answers

Option C is the correct answer .

What is velocity ?

Velocity, a quantity that indicates the speed and direction in which a point moves. Points always move tangent to the path. For example, for a circular path, its direction is always perpendicular to the line (radius) from the point to the center of the circle. The velocity magnitude (velocity) is the fraction of time a point moves along its trajectory.

If a point travels a certain distance along a path in a certain time interval, the average speed during that interval is equal to the distance traveled divided by the time taken. For example, the average speed of a train traveling 100 km in 2 hours is 50 km/h

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If the numerical value of the equilibrium constant increases as the temperature increases then: A. ∆G0 > 0
B. ∆H0 <0
C. ∆S0 <0
D. ∆H0 > 0
E. ∆S0 >0

Answers

If the numerical value of the equilibrium constant increases as the temperature increases then, ∆S₀ < 0. (option C)

The equilibrium constant, K, is a measure of the relative concentrations of reactants and products at equilibrium. It is related to the standard Gibbs free energy change, ∆G₀, by the equation: ∆G₀ = -RT ln K, where,

R is the gas constant T is the temperature.

Important points:

The equilibrium constant, K, is dependent on the temperature.As the temperature increases, the value of the natural logarithm (ln K) decreases.This means that as the temperature increases, the value of ∆G₀ becomes more negative.As ∆G₀ becomes more negative, the equilibrium constant, K, becomes larger.The standard Gibbs free energy change is related to the standard enthalpy change, ∆H₀, and the standard entropy change, ∆S₀, by the equation: ∆G₀ = ∆H₀ - T∆S₀As ∆G₀ becomes more negative, it means that either ∆H₀ is more negative or ∆S₀ is more positive.Since ∆H₀ is not directly related to temperature, it means that ∆S₀ is more positive.Therefore, as the temperature increases, the equilibrium constant increases, which is accompanied by an increase in entropy and ∆S₀ < 0This is because as the temperature increases, the kinetic energy of the particles increases which leads to more molecular collisions and more disorder. This increase in disorder causes the entropy of the system to increase and the Gibbs's free energy to decrease.

In conclusion, as the temperature increases, the numerical value of the equilibrium constant increases, and ∆S₀ < 0.

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The structure in the figure below is made from three identical rods of uniform density: Your classmate, Carol, argues that the structure has the same moment of iner- tia about the three axes show below because these axes are equidistant from the structure's center of mass: Do you agree with Carol's reasoning? Yes B No HH

Answers

Yes,  the structure has the same moment of inertia about the three axes show below because these axes are equidistant from the structure's center of mass.

What does the moment of inertia mean?

A body's moment of inertia, or resistance to having its speed of rotation about an axis changed by the application of a torque, is a quantifiable measurement of its rotational inertia (turning force). The axis may or may not be fixed, and it may or may not be internal or external.

The direction of the axis usually affects an object's moment of inertia, and the angle between the axis and the center of mass is always a factor. In these instances, the moment of inertia will always be the same if two or more distinct axes are equally spaced from the center of mass.

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A certain type of lens changes the direction of light rays from A to B. What property does
this illustrate?

Answers

The figure shows the polarization of light in the image.

What is light?

We have to note that light is the form of energy that we can be able to see by the use of the optical eyes that we have. There are several propoerties of light that are also the properties of waves.

We should know that light is an electromagnetic wave and the polarization of waves can only occur in an electromagnetic wave. From A to B in the figure that have been shown, we can see the polarization of waves.

Thus the light waves are polarized.

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a radio receiver can detect signals with electric field amplitudes as small as 320 μv/m .What is the intensity of the smallest detectable signal?

Answers

The intensity of the smallest detectable signal is 1.36 x 10⁻¹⁰ W / m².

What is the intensity of the smallest detectable signal?

The intensity of the smallest detectable signal is calculated by applying formula relating electric field amplitude and the intensity of light.

Mathematically, the formula relating electric field amplitude and the intensity of light is given as;

I = ¹/₂ ε₀E²₀c

where;

ε₀ is permittivity of free spaceE₀ is the amplitude electric fieldc is speed of light

The intensity of the smallest detectable signal is calculated as follows;

I = ¹/₂ ε₀E²₀c

Given;

permittivity of free space = 8.85 x 10⁻¹²amplitude electric field = 320 μv/m speed of light = 3 x 10⁸ m /s

I = ¹/₂ ( 8.85 x 10⁻¹² ) (320 x 10⁻⁶)² ( 3 x 10⁸ )

I = 1.36 x 10⁻¹⁰ W / m²

Thus, the intensity of the smallest detectable signal is a function of the electric field amplitude and speed of light.

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The planet Mars requires 1.96 years to orbit
the sun, which has a mass of 1.989 × 10^30 kg, in an almost circular trajectory. Find the radius of the orbit of Mars as it
circles the sun. The gravitational constant is 6.672 × 10^-¹¹ Nm²/kg². Answer in units of m.

Answers

According to the question: the radius of the orbit of Mars is 3.86 × 10^11 m.

What is the Mars?

The radius of the orbit of Mars can be found using the equation for the centripetal force:

F = mv²/r

where F is the centripetal force, m is the mass of the object, v is its velocity, and r is the radius of the orbit.

We can rearrange the equation to solve for r:

r = mv²/F

We know the mass of the sun (1.989 × 10^30 kg) and the gravitational constant (6.672 × 10^-¹¹ Nm²/kg²). We also know that the period of the orbit of Mars is 1.96 years. Since the period (T) and the angular velocity (ω) are related by the equation:

ω = 2π/T

we can calculate the angular velocity of Mars:

ω = (2π)/(1.96 years) = 3.24 × 10^-7 rad/s

Finally, we need to calculate the velocity of Mars, which is related to its angular velocity by the equation:

v = ωr

We can solve for v by substituting the equation for angular velocity and the radius of the orbit of Mars:

v = (3.24 × 10^-7 rad/s)(r)

Now, we can substitute the values for m, v, and F from the equation for centripetal force to solve for r:

r = (1.989 × 10^30 kg)(3.24 × 10^-7 rad/s)²/ (6.672 × 10^-¹¹ Nm²/kg²)

r = 3.86 × 10^11 m

Therefore, the radius of the orbit of Mars is 3.86 × 10^11 m.

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After rubbing two balloons against a sweater, each are held 0.75 meters apart. One balloon has a charge of 2.6 E-6 C. The other
balloon has a charge of 2.2 E-7 C. Calculate the electrical force between them.
Remember to identify all data (givens and unknowns), list equations used, show all your work, and include units and the proper
number of significant digits to receive full credit.

Answers

When they are held 0.75 meters apart and have a charge of 2.6E-6 C and a charge of 2.2E-7 C, the electrical force between them is 0.0366 N.

What is force?

A force is an influence in physics that can change the motion of an object. A force can cause a mass object to change its velocity, or accelerate. Intuitively, force can be described as a push or a pull. A force is a vector quantity because it has both magnitude and direction. Force is an external agent that can change the state of rest or motion of a body. It has a magnitude as well as a direction. The direction of the force is the point where force is applied, and the application of force is the point where force is applied.

Here,

Qa=2.6*10^-6 C

Qb=2.2*10^-6 C

k=9*10^9

r=0.75/2

=0.375 m

F=k*Qa*Qb/r²

=9*2.6*2.2*10^-4/(0.375)²

=0.0366 N

The electrical force between them when each are held 0.75 meters apart and has a charge of 2.6E-6 C and a charge of 2.2E-7 C is 0.0366 N.

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If you break a magnet into 10 pieces,how many pieces will be there in the north and how many in the south

Answer to win a cookie!! ​

Answers

there will be 10 north poles and 10 south poles !!

Seasonal variation in solar radiation, temperature, and day length is due to the
A. tilt of the Earth's axis.
B. greenhouse effect.
C. Coriolis effect caused by the spinning of Earth on its axis.
D. sunspot activities at the surface of the Sun.

Answers

Option A is correct. It has been hypothesized that variations in solar output could have an impact on our climate, both directly by altering the pace.

Earth and atmosphere are heated by the sun and indirectly by altering cloud formation processes. Mid-latitude temperate regions exhibit larger seasonal variations in surface temperature than the poles or the tropics; from summer to winter, temperate zones see temperature changes of 8 to 15 degrees Celsius, compared to just 2 degrees Celsius in polar and tropical regions. Energy emitted from the sun in all directions is known as solar radiation. Solar radiation is not the energy that the planet emits. Cosmic rays are any radiation that is sent into space at random. Our seasons are more intense the more tilted Earth is because each hemisphere experiences more solar radiation during its summer.

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An amoeba has 3.5 × 10^16 protons and a net charge of 1.1 pC.


1) How many fewer electrons are there than protons?

2) If you paired them up, what fraction of the protons would have no electrons?

Answers

(1) There are zero fewer electrons than protons.

(2) If you paired them up, the fraction of the protons that would have no electrons is zero.

What is the number of electrons?

The of number of electrons present is calculated as follows;

pq -  eq = q (net)

where;

p is the number of protonse is the number of electronsq (net) is the net charge

eq = pq - q (net)

e = ( pq - q(net) ) / q

e = ( 3.5 x 10¹⁶ x 1.6 x 10⁻¹⁹   -   1.1 x 10⁻¹² ) / ( 1.6 x 10⁻¹⁹ )

e = 3.5 x 10¹⁶

The number of fewer electrons than the proton = 3.5 x 10¹⁶ - 3.5 x 10¹⁶ = 0

Thus, if you pair them up, all the protons will have electrons.

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A small ball rolls around a horizontal circle at height yinside the cone shown in the figure .
Find an expression of the ball's speed in terms of a, h, y, and g.

Answers

The ball's speed when it rolls around a horizontal circle at height y inside the cone is a/h√gy.

Given the height of cone = h

The radius of cone base = a

The ball is at a height of = y inside the cone

Let the speed of ball = v

From the free body diagram of cone we can see that along x axis the force acting is Rcosθ and along y axis the force acting upward is Rsinθ and downwards is mg where g is gravitational acceleration.

Rsinθ = mg

Rcosθ = Fc is centripetal force = mv^2/r here r is radius of base

Rsinθ/Rcosθ = mg/mv^2/r

tanθ = rg/v^2

From the diagram y/r = h/a. r = ya/h and tanθ = h/a

h/a = ay/h x g/v^2

v^2  = ayg/h x a/h

v^2 = a^2 yg/h^2

v = a√yg/h

Hence the speed of ball is a√yg/h.

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Convert 6,400,000 milligrams to kilograms.

Answers

Convert: 6,400,000 milligrams (mg) is equal to 6,400 kilograms (kg).

What is Convert?

Convert is a process of changing or transforming one type of data into another type of data. This is usually done to make the data easier to use or to make it compatible with other systems. Convert can involve changing the format, type, or structure of a given data set. For example, a file of text can be converted into a different format, such as a PDF, or a spreadsheet can be converted into a different type of spreadsheet, such as an Excel document. Conversion can also be used for data transfer between different systems, such as transferring a file from a computer to a mobile device. Conversion can take place on a computer, or it can be done manually.

To convert milligrams to kilograms, divide the milligrams by 1,000,000.
6,400,000 milligrams / 1,000,000 = 6,400 kilograms

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Can anyone help me on this question pls?

Answers

FnetH=Fwinch -force of kinetic friction
We put force of winch first because it is the strongest force since the crate is moving in the direction of the winch.

FnetH= 2000N-uk(Fn)

FnetH=2000N-(0.2)(9800)

FnetH=2000N-1960N

FnetH= 40N

Fn=(9.8)(1000)= 9800N

9.8 m/s^2 earths gravitational acceleration.



uk=coefficent of kinetic friction=0.2
Fn= normal force.

If you have any further questions please feel free to ask.

On Earth the average atmospheric pressure at the surface is 1013254 Pa. If we assume that the radius of Earth is 6.4 x 106m and the acceleration of gravity is 9.8 m/s2, what is the mass of Earth's atmosphere? Hint: You will need to use the equations for force, pressure, and the surface area of a sphere, but you will need to analyze the units to confirm how these get combined.) Use the following values to solve this problem. 1 atm = PEarth=101325 Pa; REarth-6,4x10ºm; g = 9.8 m/s^2? Ending units: ___

Answers

Answer:

13

Explanation:

im rhe smartest person on the erth i j knos jts 13

Determine the distance from lens 1 to the final image for the system shown in the figure.
What is the magnification of this image?

Answers

The distance from lens 1 to the final image for the system is -5.4 cm.

What does lens magnification mean?

The height of an image divided by the height of an object is known as the magnification of a lens. Additionally, it is provided in terms of object and image distance. It is equivalent to the proportion of object distance to image distance. m = h ′ h = v u. m is the magnifying factor.

focal length of lens : f1 = -7cm ; f2 = 14cm

distance from the object : d1 = 24cm : d2= 35 cm

      => 1/f1 = 1/d1 + 1/di

       =>1/-7 = 1/24 + 1/di

di=> -5.4 cm

Magnification of image = focal length/ (object distance - focal length).

How far away are the images?

The distance between the object and the thin lines is known as the image distance. The image distance is the separation between the picture and the narrow lens. A feature of a narrow lens is its focal length, which specifies the distance at which parallel rays come into focus.

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A 5 N picture is supported by two strings that run from its upper corners to a nail on the
wall. If each string makes a 40° with the vertical, the tension in each string is
a) 3.3 N
b) 3.9 N
c) 5 N
d) 10 N

Answers

The tension force on both strings is the same. The tension is 3.9 N 10 N 3.3 N S,0 N if each string is at a 40-degree angle to the vertical. launching the video player.

How do you find the tension of a vertical string?

T = (m g) + (m a), where "g" denotes the acceleration caused by gravity of any objects the rope is supporting and "a" denotes any additional acceleration on any such objects, can be used to represent the tension in a given rope.

The force transferred through a rope, string, or wire when pushed by forces acting from opposite sides is referred to as tension. The tension force is applied along the entire length of the wire and exerts an equal amount of strain on the bodies at each end.

You can write it down as FC = mv2 /r. The centripetal force is equal to the total of the object's weight (in grammes) and the tension in the string when an object attached to a string is moving in a vertical circular motion.

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determine limit as t approaches infinity of f of t for f(t) if f is a solution to the logistic differential equation df over dt equals 2 tenths times the quantity 5 times f minus f squared over 2 end quantity with an initial value of f(0)

Answers

We know the Logistic Equation is dP/dt = r·P(1-P/K) . So twist the given derivative to the logistic form: dy/dt = 10·y(1-y/600) . Then we could see the K = 600 , which is the limit, the Carrying capacity.

To model population growth using a differential equation, we first need to introduce some variables and relevant terms. The variable  t

will represent time. The units of time can be hours, days, weeks, months, or even years. Any given problem must specify the units used in that particular problem. The variable  P will represent population. Since the population varies over time, it is understood to be a function of time. Therefore we use the notation  P(t)

 for the population as a function of time. If  P(t)

 is a differentiable function, then the first derivative  dPdt

 represents the instantaneous rate of change of the population as a function of time.

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Which warms more quickly in sunlight: a colorless or a colored piece of glass? Why?

Answers

A colored piece of glass warms quickest because it will absorb more of the light

A heat engine using a monatomic gas follows the cycle shown in the figure. Part A Find WS, Q, and delta Eth for the process 1 - > 2. Express your answers using three significant figures separated by commas. Part B Find Ws, Q, and delta Eth for the process 2 - > 3. Express your answers using three significant figures separated by commas. Part C Find Ws, Q, and delta Eth for the process 3 - > 1. Express your answers using three significant figures separated by commas. Part D What is the thermal efficiency of this heat engine? Express your answer using two significant figures.

Answers

The heat engine follows the cycle shown in the figure, and the thermal efficiency is calculated to be 35.6%. For process 1-2, WS = -7.14 J, Q = -20.04 J, delta Eth = -12.90 J; for process 2-3, WS = -7.14 J, Q = -7.14 J, delta Eth = -12.90 J; for process 3-1, WS = 7.14 J, Q = 13.21 J, delta Eth = 5.07 J.

Part A: WS = -7.14 J, Q = -20.04 J, delta Eth = -12.90 J

Part B: WS = -7.14 J, Q = -7.14 J, delta Eth = -12.90 J

Part C: WS = 7.14 J, Q = 13.21 J, delta Eth = 5.07 J

Part D: Thermal Efficiency = 35.6%

Part A: WS = -7.14 J, Q = -20.04 J, delta Eth = -12.90 J

To calculate WS, Q and delta Eth for process 1-2, we need to calculate the change in internal energy between the two states. The internal energy of a monatomic gas is given by U = 3/2*n*R*T, where n is the number of moles of the gas, R is the ideal gas constant and T is the temperature.

For process 1-2:

U2 - U1 = -12.90J

To calculate Q, the equation Q = U2 - U1 can be used.

Q = U2 - U1 = -12.90J

To calculate WS, the equation WS = Q - (U2 - U1) can be used.

WS = Q - (U2 - U1) = -20.04J - (-12.90J) = -7.14J

Part B: WS = -7.14 J, Q = -7.14 J, delta Eth = -12.90 J

To calculate WS, Q and delta Eth for process 2-3, we need to calculate the change in internal energy between the two states. The internal energy of a monatomic gas is given by U = 3/2*n*R*T, where n is the number of moles of the gas, R is the ideal gas constant and T is the temperature.

For process 2-3:

U3 - U2 = -12.90J

To calculate Q, the equation Q = U3 - U2 can be used.

Q = U3 - U2 = -12.90J

To calculate WS, the equation WS = Q - (U3 - U2) can be used.

WS = Q - (U3 - U2) = -12.90J - (-12.90J) = -7.14J

Part C: WS = 7.14 J, Q = 13.21 J, delta Eth = 5.07 J

To calculate WS, Q and delta Eth for process 3-1, we need to calculate the change in internal energy between the two states. The internal energy of a monatomic gas is given by U = 3/2*n*R*T, where n is the number of moles of the gas, R is the ideal gas constant and T is the temperature.

For process 3-1:

U1 - U3 = 5.07J

To calculate Q, the equation Q = U1 - U3 can be used.

Q = U1 - U3 = 5.07J

To calculate WS, the equation WS = Q - (U1 - U3) can be used.

WS = Q - (U1 - U3) = 5.07J - (-5.07J) = 7.14

Part D: Thermal Efficiency = 35.6%

The thermal efficiency of a heat engine is given by the equation η = (Wnet/Qh) x 100, where Wnet is the net work output of the engine and Qh is the heat input to the engine.

For this heat engine, Wnet = WS1 + WS2 + WS3 = 7.14J + (-7.14J) + (-7.14J) = -7.14J and Qh = Q1 + Q2 + Q3 = -20.04J + (-7.14J) + 13

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Two positive point charges q are located on the y-axis at y= +/- 1/2s . Find an expression for the potential along the x-axis.

Answers

The Potential along x - axis is [tex]V(x) =\frac{ 4kq }{\sqrt{4x^{2} + s^{2} } }[/tex].

Work is done when electrons move through the component. A portion of the electrons' energy is transmitted to the component. This results in an electrical potential differential, or difference in energy across the component.

The external effort required to move a charge in an electric field from one position to another is known as an electric potential difference, or voltage.

By symmetry, the potential produced by the two charges will be twice that of the single charge. The potential at a distance of

[tex]d = \sqrt{x^{2} +(\frac{s}{2}) ^{2} } \\= \frac{1}{2} \sqrt{4x^{2}+s^{2} }[/tex]

will be the potential as a function of the x-coordinate.

The potential is therefore predicted to be

[tex]V(x) = 2k \frac{q}{d}[/tex]

⇒  [tex]2k \frac{q}{\frac{1}{2}\sqrt{4x^{2} +s^{2} } }[/tex]

⇒  [tex]V(x) =\frac{ 4kq }{\sqrt{4x^{2} + s^{2} } }[/tex]

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what is the value of current ic in the figure? the directions of the currents are as noted.

Answers

Applying the Kirchhoff's Current Law concept will yield the current's value (KCL). The figure's current IC value is 2A.

According to KCL, the total current exiting a node a location where two or more circuit branches converge is equal to the total current entering the node. The intersection of the two branches is shown in the picture at node A and B. The IA and IB current sources make up the two branches. We can infer from KCL that the total sum of currents entering node A equals the total amount of currents leaving node B.

Given the current IA = 7A

the current at the junction C is divided as IC and 5A

So, IC = 7-5 = 2A

The current at junction B is IB flowing upwards along with current IC and IB which is 3+2 = 5A

Hence the current in IC = 2A.

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Acceleration and Velocity

Answers

Answer:

acceleration an velocity are two different types of hate for each individual to choose from my favorite ones and not just one for me like you said you would have to pay for the person you want and you will need to pay for your business.

Explanation:

no exceptions

In the figure (Figure 1) block B is falling and dragging block A across a table. How many force vectors would be shown on a free-body diagram of block A? O 0
O 1
O 2 O 3 O 4
O 5

Answers

On a block A free-body diagram for a given figure, there would be 4 force vectors displayed. As an object with both magnitude and direction, a vector is defined.

As an object with both magnitude and direction, a vector is defined as. Moving an object from one position to another is described by a vector. By using a directed line segment, vector mathematics can be geometrically represented. Generally speaking, the term "magnitude" refers to a size or distance. We can relate the magnitude of a movement to an object's size and motion speed. A thing or an amount's magnitude is determined by its size. A automobile moves more quickly than a motorcycle, just like in terms of speed. Vector and scalar quantities both frequently employ magnitude as a factor.

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mass (in grams) of 2.50×10−2 mol of cds.

Answers

O contains 3.93 x 10^22 atoms. In the case of a mass (in grammes) of 2.50 10 2 mol of CdS. To three significant digits, convert the mass to grammes. In 66.6 g of this substance, the amount of NH4Cl in moles (n).

One of a body's fundamental characteristics is mass. Before the discovery of the atom and particle physics, it was widely considered to be connected to the amount of matter in a physical body. Different atoms and elementary particles were found to have different mass numbers (2.50102 mol CdS x 144.4760 g CdS/mol) = 3.61 g CdS (66.6 g NH4Cl / 53.4915 g NH4Cl/mol) = 1.25 mol NH4Cl (8.497102 mol) x (6.022 x 1023 molecules/mol) = 5.117 10

9.1 atoms of oxygen for 1 molecule of Al(NO3)3 (7.25103 mol) x (6.022 x 1023 molecules/mol) x (6.022 x 1023 molecules/mol) = 3.93 10^22.

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The complete question is -

Mass (in grams) of 2.50×10−2 mol of CdS. Express the mass in grams to three significant digits. Number of moles (n) of NH4Cl in 66.6 g of this substance. Express the amount in moles to three significant digits. Number of molecules in 8.497×10−2 mol C6H6. Express the amount in molecules to four significant digits. Number of O atoms in 7.25×10−3 mol Al(NO3)3. Express the amount in atoms to three significant digits.

what is the range of the effective focal length of the lens of the eye for this person?

Answers

Although the human eye has a focal length of approximately 22 mm.

What is the effective focal length of the eye?

Focal length is defined as the distance between the point of convergence of lens and the sensor that recording the image. The focal length of the digital camera lens indicates how much of the image your camera will be able to capture.

This is deceptive because the back of our eyes is curved, the periphery of our optical field contains progressively less particularly than the center, and the scene we discern is the combined result of both eyes. The cornea and eye lens have focal lengths of 2.3 and 6.4 cm, subsequently.

The eye has a nominal focal length of roughly 17mm, but it varies with housing. The nature of human binocular vision, which uses two lenses rather than a single one,

So we can conclude that A person having a myopic eye uses a hollow lens of focal length 50cm.

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a frog jumps as is moves. what is the relationship between maximum height & maximum range.​

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Answer: H = Rsin²θ/2sin(2θ)

Explanation: A projectile motion is characterized by a motion whose path is alike to that of an arc. It already has its derived equations. For the maximum height H and the maximum range R, the equations are:

H = v₀²sin²θ/2g       ;       R = v₀²sin(2θ)/g

As you can observe, they are almost alike. Since they both contain v₀²/g, let's isolate this term for both equations:

v₀²/g = 2H/sin²θ

v₀²/g = R/sin (2θ)

Equating both equations:

2H/sin²θ = R/sin (2θ)

H = Rsin²θ/2sin(2θ)

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How does the entropy of a system change for each
of the following processes?
(a) A solid melts.
(b) A liquid freezes.
(c) A liquid boils.
(d) A vapor is converted to a solid.
(e) A vapor condenses to a liquid.
(f) A solid sublimes.
(g) Urea dissolves in water.

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(a) The entropy of a solid increase as it melts, because the molecules gain freedom of movement.

(b) The entropy of a liquid decreases as it freezes because the molecules lose freedom of movement.

(c) The entropy of a liquid increases as it boils, because the molecules gain freedom of movement.

(d) The entropy of a vapor decreases as it is converted to a solid because the molecules lose freedom of movement.

(e) The entropy of a vapor increases as it condenses to a liquid because the molecules gain freedom of movement.

(f) The entropy of a solid increase as it sublimes, because the molecules gain freedom of movement.

(g) The entropy of the Urea and the water increases as the Urea dissolves in water because the molecules of Urea gain freedom of movement and the water molecules interact with the solute molecules.

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6) According to the law of reflection, the incident light ray, the reflected light ray, and the normal between them
A) lie in the same plane.
B) may or may not lie in the same plane.
C) lie in planes that are perpendicular to one another.

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According to the law of reflection, the incident light ray, the reflected light ray, and the normal between them may or may not lie in the same plane. option (b) is correct.

What is law of reflection ?

The law of reflection is the idea that when light rays hit a smooth surface, their angles of incidence and reflection are equal. Additionally, the planes of the incident ray, the reflected ray, and the normal to the surface are all in alignment.

What is incident ray ?

The rectilinear light ray known as an incident ray is one that strikes a surface (surface). Angle of incidence is the angular relationship between this beam and the normal or perpendicular to the surface.

Therefore, according to the law of reflection, the incident light ray, the reflected light ray, and the normal between them may or may not lie in the same plane. option (b) is correct.

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Consider a situation where 1.5 grams of benzoic acid is dissolved in 75 mL of water. Use the value 9.5 for the distribution coefficient Kd, and calculate how much benzoic acid would remain in the aqueous phase after one extraction with 60 mL of ether. What percentage of the original benzoic acid was extracted into the ether phase?

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Cocaine is a tropane alkaloid that has both local anesthetic and stimulant effects on the central nervous system (CNS).

Cocaine inhibits the re-uptake of dopamine, serotonin, and norepinephrine into pre-synaptic neurons by binding to the transport proteins for these neurotransmitters. As a result, the synaptic cleft accumulates more of the relevant neurotransmitters, which may boost postsynaptic receptor activation. Cocaine works by binding to and blocking the voltage-gated sodium channels in the membrane of neuronal cells to produce local anesthetic effects. Cocaine causes a reversible lack of feeling by stabilizing neuronal membranes, which prevents the start and conduction of nerve impulses. A benzoic acid ester, cocaine was first employed as a local anesthetic.

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