Suppose a consumption function is given as c = $500 0.75yd. the marginal propensity to consume is:______

The mass of the electron is [tex]1.72\times 10^{-30}[/tex] Kg.

To calculate the mass of the electron we are using the formula,

[tex]m=\frac{m_{0} }{\sqrt{1-\frac{v^{2} }{c^{2} } } }[/tex]

Here we are given,

[tex]m_0[/tex]=The rest mass of an electron =  [tex]9. 11 \times 10^{-31}[/tex] kg.

v= The velocity of electron =  0. 85c.

c= The velocity of light = c.  (c=[tex]3\times 10^8[/tex] m/s)

We have to found the mass of an electron = m Kg.

Now we substitute the known values, we found that,

[tex]m=\frac{9. 11 \times 10^{-31} }{\sqrt{1-\frac{(0.85c)^{2} }{c^{2} } } }[/tex]

Or,[tex]m=\frac{9. 11 \times 10^{-31} }{\sqrt{1-(\frac{0.85c}{c})^2 } }[/tex]

Or,[tex]m=\frac{9. 11 \times 10^{-31} }{\sqrt{1-({0.85})^2 } }[/tex]

Or, [tex]m=1.72\times 10^{-30}[/tex] Kg.

From the above calculation we can conclude that, The mass of the electron is [tex]1.72\times 10^{-30}[/tex] Kg.

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The change in potential energy of the proton is  5.6 x [tex]10^{-17}[/tex] Joule

A uniform electric field is where the electric field strength is the same at all points in the field. In the uniform field, the force experienced by a charge is the same no matter where it is placed in the field.

Given that a proton moves a distance 10 cm in a uniform electric field of 3.5 kN C, in the direction of the field.

The Work done = Fd

but F = Eq

Recall that Electric field E = F/q = V/d

Where V = potential difference.

Let us first calculate the V

E = V/d

V = Ed

Substitute all the parameters into the formula above

V = 3.5 × 10³ × 0.1

V = 350 v

from F/q = V/d

make F the subject of formula and substitute it in work formula

F = Vq/d

W.D = Vq/d x d

W.D = Vq

Substitute all the parameters into the formula above

W.D = 350 x 1.6 x [tex]10^{-19}[/tex]

W.D = 5.6 x [tex]10^{-17}[/tex] J

Work done = Energy = Potential Energy

Therefore, the change in potential energy of the proton is 5.6 x [tex]10^{-17}[/tex] Joule

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Answer:

The key difference between air pressure and liquid pressure is that air pressure allows the gaseous state of matter to be compressible, whereas liquid pressure makes a liquid incompressible.

Liquid pressure is the pressure that we can observe in a liquid. Air pressure is also known as atmospheric pressure, and it is the pressure as the force exerted by the collisions of particles in the air.

(a) The average velocity of the car in m/s for the first leg of the run is 36.2 m/s.

(b) The average velocity (in m/s) for the total trip is 0.

The average velocity of the car in m/s for the first leg of the run is calculated as follows;

Average velocity = total displacement/total time

Average velocity = (760) / (21) = 36.2 M/S

The average velocity (in m/s) for the total trip is calculated as follows;

v =  total displacement/total time

v = 0/(26 + 21)

v = 0

Thus, the average velocity of the car in m/s for the first leg of the run is 36.2 m/s.

The average velocity (in m/s) for the total trip is 0.

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Higher frequencies are present in more dramatic events and have thus been the first to be noticed, but the frequencies of ordinary gravitational waves are relatively low and considerably more difficult to detect.

A gamma-ray burst (GRB), which was discovered by the orbiting Fermi gamma-ray burst monitor on 2017 August 17 at 12:41:06 UTC, triggered an automatic notice throughout the world in addition to a merger of black holes. Six minutes later, a gravitational-wave observatory in Hanford, Washington, detected a gravitational-wave candidate that occurred 2 seconds before the gamma-ray explosion.

This collection of data supports the merger of two neutron stars, as shown by a multi-messenger transient event that was detected by gravitational waves as well as electromagnetic (gamma-ray burst, optical, and infrared) spectrum observations.

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The resulting velocity of marble B after the collision is 2.4 m/s.

The object with the faster velocity, and thus larger momentum, will impart more energy to the slower object during the collision than vice versa. Following the collision, the object with the lower beginning velocity will travel away from the other object with a higher speed and momentum.
Marble A's mass, marble B's mass, marble B's initial velocity, marble A's final velocity, marble B's final velocity, and marbles A and B's combined mass and initial velocity

Applying the mass-conservation principle
Momentum is conserved.

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

(0.08 kg)(0.5 m/s) + (0.05 kg)(0 m/s) = (0.08 kg)(-0.1 m/s) + (0.05 kg) v

0.04 kg m/s = -0.08 kg m/s + (0.05 kg) v

0.12 kg m/s = (0.05 kg) v

v = 2.4 m/s

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(a) The gravitational force received by each 1 kg mass is 8.66 N.

(b) The magnitude of gravitational acceleration is 8.66 m/s².

(c) The orbital speed of the ISS is  7,663.6 m/s.

(d) The time take  for the ISS to orbit round the Earth is 5,558.75 seconds which is equal to 1.54 hours.

The gravitational force received by each 1 kg mass is calculated as follows;

F = Gm₁m₂/r²

where;

F = (6.67 x 10⁻¹¹ x 5.97 x 10²⁴ x 1) / (6780,000)²

F = 8.66 N

mg = GMm/r²

g = GM/r²

where;

g = (6.67 x 10⁻¹¹ x 5.97 x 10²⁴ ) / (6780,000)²

g = 8.66 m/s²

v = √GM/r

v = √(6.67 x 10⁻¹¹ x 5.97 x 10²⁴  / 6780,000)

v = 7,663.6 m/s

T = 2πr/v

T = (2π x 6780,000) / (7663.6)

T = 5,558.75 seconds

1 hour = 3600 seconds

=  5,558.75/3600

= 1.54 hours

Thus, the gravitational force received by each 1 kg mass is 8.66 N.

The magnitude of gravitational acceleration is 8.66 m/s².

The orbital speed of the ISS is  7,663.6 m/s.

The time take  for the ISS to orbit round the Earth is 5,558.75 s = 1.54 hours.

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A satellite is 1200 k above the earth (radius = 6400 k); it completes one revolution in 90min. what is the linear speed?

530.58 (1200+6400)*pi*2/90

The measurement of a moving object's actual distance traveled is called linear speed. Linear speed is the rate of motion of an object along a straight line. In plain English, it is the distance traveled along a linear path in the allotted amount of time.

A pseudovector used in physics to express how quickly the angular location or orientation of an item changes over time is called an angular velocity or rotational velocity  The pseudovector's direction is normal to the instantaneous plane of rotation or angular displacement, and its magnitude corresponds to the object's angular speed, or the rate at which it rotates or revolves. The right-hand rule is a common way to specify the direction of angular velocity.

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The spring stiffness constant is  796.25 N/m.

A spring's "spring constant" is a property that quantifies the relationship between the force acting on the spring and the displacement it produces.

The slope of the plot of the straight line W vs x represents the spring constant, K. Weight (W) is defined as mass times the gravitational acceleration (g), where g is equal to approximately 980 cm/sec².

Mass of the fish = 2.6 kg

Length of the fisherman's scale, x = 3.2 cm

                                                          = 3.2/100 m

                                                          = 0.032 m

We have to find the value of k;

We know that,

                       F = - kx

Where k is the spring constant,

           F is the force applied over x

           x is the displacement by the spring expressed in N/m.

                       mg = - kx

                       g = 9.8 m/s²

                       [tex]K = \frac{mg}{x}[/tex]

                           [tex]= \frac{2.6*9.8}{0.032}[/tex]

                           [tex]= 796.25 N/m[/tex]

Therefore, the spring's constant is 796.25 N/m.

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Aluminium has a work function of 4. 08 eV. The cutoff wavelength and cutoff frequency for the photoelectric effect is 303.9nm and 911.7× 10¹⁷ s⁻¹ respectively.

Work Function is the minimum energy required to eject an electron from a photoelectric material.

Cutoff Wavelength is the maximum wavelength below which electron will be ejected

Cutoff Frequency is the minimum frequency required to eject electron.

Let the work function of Aluminium be Φ

Given,  work function Φ = 4.08eV

We know that hc/λ =  Φ

where, h is Planck constant

c is speed of light

λ is wavelength of light used

Hence, on subsitution

1240 / λ = 4.08 eV          (hc = 1240)

⇒ λ = 303.9 nm

Hence, cutoff wavelength used is 303.9 nm

We know that ν = c/λ

ν = 3 × 10⁸ / 303.9

⇒ ν = 911.7 × 10¹⁷ s⁻¹

Hence, cutoff frequency used is 911.7 × 10¹⁷ s⁻¹

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150 kJ of energy was given out over the course of the reaction and 200kJ is required for the reactants to be converted into products.

We know that the combination of the reactants is what leads to the formation of products. The interaction of the reactants and the products is what is shown on the potential energy curve. The hump at the highest point of the graph is the activation energy while the difference between the energy of the reactant and the products is the enthalpy of the reaction.

Now; the enthalpy change is given as;

ΔH = 200 kJ - 50 kJ = 150 kJ

Ea = 250 kJ - 50 kJ = 200kJ

We can see that 150 kJ of energy was given out over the course of the reaction and 200kJ is required for the reactants to be converted into products.

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Answer:

Apparently, a measuring rod had been used incorrectly and the telescope was not focusing properly - changes were later made to the telescope to correct this problem.

The current in the ideal diode with forward biased voltage drop of 65V is 132.6 mA.

To find the answer, we have to know more about the ideal diode.

                       [tex]V_2=65V\\V_1=0V\\R_1=490Ohm.[/tex]

                [tex]I=\frac{V_2-V_1}{R_1} =\frac{65}{490} =132.6mA[/tex]

Thus, we can conclude that, the current in mA of the ideal diode with forward biased voltage drop of 65 V is 132.6.

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The rate of heat transfer from the entire plate is 710.8 kW

The properties of mercury at the film temperature of (75+25)/2= 50°C

k = 8.83632 W/m °C

v = 1.056 × [tex]10^-^7[/tex] m²/s

Pr = 0.0223

The local Nusselt number relation for liquid metals is given by

 [tex]N_u =\frac{h_sx}{k} = 0.565 9Re_x Pr)^\frac{1}{2}[/tex]

The average heat transfer coefficient for the entire surface can be determined from

[tex]h = \frac{1}{L} \int\limits^1_0 {h_x} \, dx[/tex]

Substituting the local Nusselt number relation into the above equation and performing the integration we obtain

[tex]N_u = 1.13 (Re_s Pr)^\frac{1}{2}[/tex]

The Reynolds number is

[tex]Re_L = \frac{VL}{v} = \frac{(0.01)(3m)}{1.056 * 10^-^7 m^2/s} = 0.028 * 10^7[/tex]

Using the relation for the Nusselt number, the average heat transfer coefficient and the heat transfer rate are determined to be

                       Q = 710.8 kW

Therefore, the rate of heat transfer from the entire plate is 710.8 kW

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C. Molecules in the original disturbance disturb (move) adjacent molecules which disturb more adjacent molecules and so the wave travels.

A wave can be defined as a propagating dynamic disturbance of one or more quantities.

A wave can be propagated in longitudinal or transverse method.

When waves start as a disturbance (an input of energy) in a medium (water, air, the earth etc).

The energy of the disturbance is moved from the starting point to other places in the medium by molecules in the original disturbance disturb (move) adjacent molecules which disturb more adjacent molecules and so the wave travels.

Thus, the correct option is C.

"Molecules in the original disturbance disturb (move) adjacent molecules which disturb more adjacent molecules and so the wave travels".

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The wavelength of radiowaves is 3.042 m.

The electromagnetic spectrum's longest wavelengths, which are found in radio waves, are normally found at frequencies of 300 gigahertz and below.

Frequency given, f = 98.6 MHz = 98.6 x [tex]10^{6}[/tex] cycles/second

Electromagnetic waves including radiowaves also travel at the speed of light.

Therefore, c = 3.0 x [tex]10^{8}[/tex] m/sec

Wavelength = speed/frequency

wavelength of 98.6 MHz = 3.0 x [tex]10^{8}[/tex]/98.6 x [tex]10^{6}[/tex] meters

=3.042 meters

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Answer: b. inversely proportional to each other

Explanation:

The wave with the greatest frequency has the shortest wavelength. Twice the frequency means one-half the wavelength.

A wooden block contains some nails so that its density is exactly equal to that of water. if it is placed in a tank of water and released from rest when it is completely submerged, it will remain where it is released.

The concept of density seeks to measure the weight of an object in relation to its size. It is the measure of how packed together the particles of that object are. An object placed in a liquid displaces a certain volume of the liquid, based on the relative density of the object and the liquid.

If an object is less dense than a liquid in which it is placed, it displaces a smaller volume of the liquid than its volume, hence only some part of the object will be seen to be under the liquid, the other part will float.

If an object is denser than the liquid in which it is placed, it displaces a larger volume of the liquid than its own volume, making the object to sink and is submerged, sometimes to the bottom of the liquid, but mostly below the point at which it was released.

Finally, if the density of an object and the liquid into which it is submerged is the same. the object's mass per unit volume is the same as the liquid's mass per unit volume, hence the weight and force created due to density will balance and cancel each other out hence making the object to remain where it was submerged.

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The intensity of electric field E midway between these two charges is 2.52*10^7N/C.

To find the answer, we have to know more about the electric field.

                      [tex]E=\frac{kQ}{r^2}[/tex]

where, k is the constant equal to 8.99*10^9.

                [tex]E_1=\frac{8.99*10^9*20*10^{-6}}{10*10^{-2}} =1.79*10^7N/C[/tex]

                 [tex]E_2=\frac{8.99*10^9*8*10^{-6}}{(10*10^{-2})^2} =7.19*10^6N/C[/tex]

                [tex]E=1.79*10^7+7.19*10^6=2.52*10^7N/C[/tex]

Thus, we can conclude that, the intensity of electric field e midway between these two charges is 2.52*10^7N/C.

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The focal Length of the eye is 0.37cm.

The retina, which is always 2.70 cm away from the lens, serves as the image's primary imaging medium. Image distance is 2.70 cm as a result.

The object is located 265 cm away from the eye's lens.

Based on lens formula:

[tex]\frac{1}{f} = \frac{1}{u} + \frac{1}{v}[/tex]

where the object distance is u, the image distance is v, and the focal length is f.

Consequently, u is 265.00 cm and v is 2.70 cm.

[tex]\frac{1}{f} = \frac{1}{265} + \frac{27}{10}[/tex]

[tex]\frac{1}{f} = \frac{7165}{2650}[/tex]

[tex]f = \frac{2650}{7165}[/tex]

f = 0.37

Thus, the focal length of the eye is 0.37cm.

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Answer:

if a car is increasing it's acceleration uniformly in a unit time, the graph will be moving away from it's origin. that's how you get this kind of graph.

Magnetic Flux is the magnetic force acting on a unit positive charge moving perpendicular to the magnetic field with a unit velocity

The magnetic flux or field lines linking a coil depends on;

According to the question, the Magnetic force acting on a unit positive charge moving perpendicular to the magnetic field with a unit velocity is called magnetic flux

To obtain a large induced electromotive force, we cause a coil of many turns to move at a high speed across a strong magnetic field.

According to Faraday's law, which state that whenever there is a change in the magnetic lines of force, an electromotive force is induced, the strength of which is proportional to the rate of change of the flux linked with the circuit.

Therefore, Magnetic Flux is the magnetic force acting on a unit positive charge moving perpendicular to the magnetic field with a unit velocity

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The final speed of the sprinter is 4.8 m/s.

According to the second law, the mass of the item or the net force acting on it both affect how quickly an object accelerates.

An object's acceleration is directly proportional to the net force applied on it and inversely proportional to its mass.

An object's acceleration increases as the amount of force exerted on it does.

A decreasing acceleration is caused by a rise in an object's mass.

Calculation of final velocity;

The sprinter exerts an average force of 518 newtons backward on the ground.

The taken by sprinter is 0.75 sec.

The wight of the sprinter is 89Kg.

According to Newton's second law

Force = mass×acceleration

F  = m×a

a = F/m

a = 518/89

a = 6.4 m/sec²

Now, apply the equation of motion of straight line;

final velocity = initial velocity + acceleration×time

As, the sprinter starts from rest; initial velocity = 0.

Substitute all the values;

final velocity = 0 + 6.4×0.75

                     = 4.8 m/sec

Therefore, the final velocity of sprinter comes out to be 4.8 m/sec.

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        800 = 0 + [tex]\frac{1}{2}[/tex]a(30)[tex]^{2}[/tex]

        800 = 450a

        a = 1.77m[tex]s^{-2}[/tex]

        s = 0+  [tex]\frac{1}{2}[/tex]1.77[tex]t^{2}[/tex]

        s =  [tex]\frac{1}{2}[/tex]1.77(30)[tex]^{2}[/tex]

        s = 796.5m

        t = 800/8

        t = 100 sec

       2000 -800

      length = 1200m

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The total mass of the earth's atmosphere is 5×[tex]10^{8}[/tex] kg.

To calculate the total mass of the earth's atmosphere we use the expression

[tex]P=\frac{F}{A}[/tex]

or, [tex]F=P\times A[/tex]

or,[tex]M\times g=P\times A[/tex]

or,[tex]M=\frac{P\times 4\times \pi\times r^{2} }{g}[/tex]

Here, P= Atmospheric pressure at the surface = [tex]10^{5}[/tex] N/m2

F= Force at the earth surface.

A= Area of the earth.

r= Radius of the earth=6.4 × [tex]10^{6}[/tex] m

g= Acceleration due to gravity. = 9.8 m/s2 ≈ 10 m/s2

Let, M be the total mass of the earth's atmosphere.

Now, [tex]M=\frac{10^{5}\times4\times\pi\times(6.4\times10^{6} )^{2} }{10}[/tex]

M= 5×[tex]10^{8}[/tex] kg.

Thus from the above calculation we can show that, the total mass of the earth's atmosphere is 5×[tex]10^{8}[/tex] kg.

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Answer:

blank 1: close together

blank 2: more

The 60 degrees is needed between the direction of polarized light and the axis of a polarizing filter to cut its intensity to one-fifth of its initial value.

It is given that axis of a polarizing filter to cut its intensity to one-fifth of its initial value.

It is required to find the angle between the direction of polarized light and the axis of a polarizing filter to cut its intensity to one-fifth of its initial value.

Suppose the angle between the polarizer and the axis of filter is θ.

The intensity of light that is passing after the filter is 0.2 l₀.

From the law of Malus, we have

I = I₀ [tex]cos^{2}[/tex]θ

0.2I₀= I₀ [tex]cos^{2}[/tex]θ

0.2 =  [tex]cos^{2}[/tex]θ

[tex]cos\\[/tex]θ = 0.447

θ = 60°

Thus the angle between the direction of polarized light and the axis of a polarizing filter is 60 degree.

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Answer:

C

Explanation:

Use conservation of momentum

Momentum before collision = mv = 50 (4) = 200  kg-m/s

AFTER collision

  30 * 3    + Blue momentum    = 200

    blue momentum = 110   kg-m/s

The refrigerator is removing 300 watts of heat every hour.

Energy can only be changed in form; it cannot be created or destroyed, according to the basic law of thermodynamics. For any system, energy transfer examples include mass crossing the control boundary, external work, or heat transfer across the barrier. These have an impact on the energy reserves of the control volume.

The rate of heat removal from within the refrigerator may be calculated using the formula below thanks to the First Law of Thermodynamics and the definition of a refrigeration cycle.

Rate of heat transfer to the space, measured in watts.

Q=800 W W=500

The refrigerator removes heat at a rate of (800-500) 300 watts per hour.

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The applied effort represents the time devoted to the analysis of theory, attendance at theory classes, and the authentic performance of all practical skills.

The applied effort represents the time devoted to the analysis of theory, attendance at theory classes, and the authentic performance of all practical skills.

The effort, application, endeavor, and exertion imply activities directed or force expended toward a definite end. Effort exists as an expenditure of energy to perform some objective: He created an effort to control himself. The application exists continuous struggle plus careful attention: constant application to duties.

Length of crow bar = 2m

length of load arm = 0.1M

length effort arm = length of crow bar -length of load arm

=2−0.1=1.9m

so, velocity ratio = length of effort arm/length of load arm = 1.9/0.1 = 19

use formula, velocity ratio = load/effort

19 = 100kgf/effort

effort = 100/19= 5.26 kgf

hence,5.26 effort is required.

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