If we ignore air resistance, a falling body will fall 16t2 feet in t seconds. what is the average velocity between t=5 and t=5.3? round your answer to two decimal places if necessary.

Answers

Answer 1

The average velocity between t=5 and t=5.3 262.4 m/s

The distance fallen s = 16t^2

The velocity v = [tex]\frac{d_{s} }{d_{t} }[/tex] = 32t

When we apply the values of t to the velocity v, we get

V1 = 32 x 8 = 256 m/s at time t = 8 seconds.

V2 = 32 x 8.4 at time 8.4 equals 268.8 m/s.

(V2 - V1)/2 = (268.8 + 256)/2 = 262.4 m/s is the average speed.

The concept of velocity refers to the rate and direction of motion of a point. For instance, the orientation of a circular path is always perpendicular to the line that connects a point to the centre of the circle. A point always advances down a route that is perpendicular to it (a radius).

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Related Questions

A fertilised egg (zygote) has a diameter of 0.01 cm. At birth the average baby measures 50 cm in length. Calculate the change in order of magnitude of length from fertilisation to birth.

does anyone know the answer??​

Answers

Differences in size are often described as differences in the order of magnitude. That's the difference calculated in factors of 10.

At the time of fertilization-

0.01cm = 1/100 = [tex]10^{-2}[/tex]

At the time of birth-

50cm = 5 ×  [tex]10^{1}[/tex]

Meaning there is 3 order of magnitude between the egg(zygote) (0.01cm) and child after the birth ( 50cm ).

Notice that when dividing numbers in standard form, we subtract the powers.

When comparing orders of magnitude, actual distances can be approximated. It’s the relative difference that is important.

Hence, the change in the order of magnitude of length from fertilization to birth of a child is 3 ( three )

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Which statement is true about vectors?
a. All quantities in physics are not vectors.
b. A vector may have either magnitude or direction.
c. The vector’s length should be proportional to its magnitude.
d. Two vectors can be added only if they have the same direction.

Answers

Answer:

b. A vector may have either magnitude or direction.

Explanation:

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If a car travels 270 meters in 30 seconds, then what is its
average speed?

Answers

Answer:

9m/s

Explanation:

Speed = Distance ÷ Time

Distance=270meters

Time =30 seconds

270m

30s

=9m/s

what is meant by temperature?​

Answers

Answer:

Average kinetic energy per molecule in a substance

Explanation:

The ability to buy a soda from a vending machine demonstrates which element of the marketing mix?

Answers

It demonstrates the place/distribution element.

Place, or its more popular name “distribution,” refers to the method by which a company delivers its goods to clients. It is one thing to have a fantastic product that is priced reasonably.

Which four forms of distribution are there?

Direct selling, selling through intermediaries, dual distribution, and reverse logistics channels are the four different categories of distribution channels.

What does distribution or place mean in marketing?

Distribution (or place) is one of the marketing mix’s four components. Making a good or service accessible to any consumer or any business user who is in requirement of it is the process of distribution.

The producer or service provider may carry this out directly or through indirect channels, such as distributors or intermediaries.

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heat supplied at the rate of 120W to 60g of ice raises it's temperature from -20°c to 0°c in 200s. Calculate the I. heat capacity of the ice Ii. specific heat capacity of the ice. III. time it will take to melt all the ice at 0°c. (s.f=336000 Jkg/K​

Answers

Answer:

aowbe9 wieveiq diqbedi diwbe

Explanation:

01837192

An incandescent light bulb has a power rating of 40 w when connected to a wall outlet of voltage 120 v. the resistance of the filament in the light bulb is?

Answers

An incandescent light bulb has a power rating of 40 w when connected to a wall outlet of voltage 120 v. the resistance of the filament in the light bulb is 360 ohms.

The relation between power, voltage and current is :

                                   P =VI ...(i)

According to Ohm's law:

                                  I =V/R

Substituting the value of I in power relation

                                  P = [tex]V^{2}[/tex]/R

Since we have to find the resistance

                               R = [tex]V^{2}[/tex]/P ...(ii)

Given:

V = 120 V

P = 40 w

Putting the values in eq (ii).

R = [tex]120^{2}[/tex]/40

R = 360 Ω

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The top speed of the blackbird is 2193 mph. given that 1 mile 1.61 km, what is this speed in km/h? (page 32).

Answers

The speed of 2193 mph expressed in km/h is: 3530.73 km/h

To solve this problem the we have to do the conversion of units with the given information.

Information about the problem:

v = 2193 miles/hv = expressed in (km/h) =  ?1 mile= 1.61 km

By converting the velocity units from  (miles/h) to (km/h) we have:

v = 2193 miles/h * 1.61 km/1 mile

v = 3530.73 km/h

What is unit conversion?

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

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9
> G.1 Calculate velocity from time and distance RXW
Submit
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Matthew was parasailing at a constant velocity behind a motorboat. As he was parasailing, he
passed over a kayak moving at 64 meters per minute, and he moved 200 meters west in
0.5 minutes. What was Matthew's velocity?
Write your answer as a whole number.
meters per minute to the west

Answers

As he was parasailing, he passed over a kayak moving at 64 m/minute, and he moved 200 meters west in 0.5 minutes. Matthew's velocity will be 400m/minute to the west.

The velocity of an object can be defined as the rate of change of an object's position relative to the frame of reference and over time. It sounds complicated, but basically, the speed is accelerating in a particular direction. It is a vector quantity, which means we need both magnitude (speed) and direction to determine speed. Its SI unit is meters per second (ms-1). If there is a change in magnitude or direction in the speed of an object, the object is said to be accelerating.

According to the question:

Velocity = Distance/ Time

Given in the question:

Distance= 200

Time= 0.5 minutes

Substitute the value,

Velocity= 200/0.5

Velocity = 400m/minute

Therefore, the velocity for the given question is 400m/minute.

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How long does it take light to travel through a 2.0- mm -thick piece of window glass?

Answers

Light travels at the exact speed of 299,792,458 meters (983,571,056 feet) per second in a vacuum.

The light passes through a 2.0-mm-thick section of window glass

= 1 × [tex]10^{-14}[/tex]    sec

                             

What is speed?

Speed is defined as the rate at which an object's position changes in any direction. Speed is calculated as the ratio of distance traveled to time spent traveling. Speed is a scalar quantity because it has a direction but no magnitude. The SI unit of speed is milliseconds per second.

There are several types of speeds:

Consistent speedSpeed controlSpeed in an instantThe average speedSpeed Relative

Speed is the street name for amphetamine sulphate, but it can also refer to other amphetamines. It's usually an off-white or pinkish powder that resembles crystals. It is also available in the form of a paste, which is usually white/grey or brown in color and can be damp and gritty.

Hence,

A thick piece of window glass = 2 mm

speed of light in medium = speed of light in vacuum / refractive index

      = (3×[tex]10^{8}[/tex])/1.5  

       = 2 ×[tex]10^{8}[/tex] m/s                                           

Time = distance / speed  

      = (2 × [tex]10^{-3}[/tex] )/(2 × [tex]10^{-11}[/tex])

      = 1 × [tex]10^{-14}[/tex]    sec

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A gas cylinder of cf2=cf2 is unexpectedly found to have lost all pressure. upon being sawn open, what was discovered? (a true story)

Answers

The correct answer is Teflon

Numerous applications can be found for polytetrafluoroethylene (PTFE), a synthetic fluoropolymer of tetrafluoroethylene. It is one of the most popular and often used PFAS. Teflon, manufactured by Chemours, a division of DuPont, which made the compound's initial discovery in 1938, is the term by which PTFE-based materials are most generally recognized. Polytetrafluoroethylene, a high-molecular-weight polymer made entirely of fluorine and carbon, is a fluorocarbon solid. PTFE is hydrophobic, meaning that neither water nor things containing water can bind to it. This is because fluorocarbons only exhibit weak London dispersion forces since fluorine has a poor electric polarizability. One of the lowest coefficients of friction of any substance is found in PTFE. For pans and other cookware, polytetrafluoroethylene is utilized as a non-stick coating.

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Consider an incandescent lightbulb. If you wanted to turn a 10-w lightbulb into a 100-w lightbulb, how would you change the temperature of the filament inside the bulb?.

Answers

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

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

P = A . e . σ . T⁴

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

From the question above, we know that

P1 = 10 watt

P2 = 100 watt

T1 = T1

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

T1⁴ / T2⁴ = P1 / P2

Hence,

T1⁴ / T2⁴ = P1 / P2

T1⁴ / T2⁴ = 10 / 100

T1⁴ / T2⁴ = 1 / 10

T2⁴ = 10T1⁴

T2 = ⁴√(10T1⁴)

T2 = T1 x 10⁰'²⁵

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

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A gold atom has a radius of 145 pm. if you could string gold atoms like beads on a thread, how many atoms would you need to have a necklace 36.0 cm long?

Answers

[tex]1.17\times 10^{9 }[/tex]atoms would you need to have a necklace 36.0 cm long.

The radius of the gold atom = 145pm

The diameter of gold atom = 2[tex]\times[/tex]145pm

 = 290Pm  

[tex]=290\times10^{-10} cm[/tex]

gold atoms   = [tex]34cm/290\times10^{-10}cm[/tex]

= [tex]1.17\times 10^{9}[/tex] atoms  will be find in 36.0 cm necklace

Atomic radius is the distance from the nucleus to the edge of the atom

atomic radius decreases as we  go across the periodic table

electronegativity is ability of an atom to attract electrons when the atom is in a chemically combined compound

Atomic Radius : Group Trend: as we go down a column, atomic radius increases.

Periodic Trend: as we go across a period, (L to R), atomic radius decreases.

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The escape speed from the moon is much smaller than from earth, around 2. 38 km/s. True or false?.

Answers

The statement is True.

What is the Escape speed of the Moon?

The Escape velocity of the Moon is 2.38km/s.

The conservation of energy and an energy field with a finite depth leads to the existence of escape velocity.

When moving under conservative forces (like a static gravity field), an object with a given total energy can only travel to combinations of locations and speeds that have that total energy; locations with higher potential energy cannot be reached at all.

The object's reachable locations increase as speed (kinetic energy) is added; with enough energy, the locations become infinite.

The minimum speed an object needs to travel at in order to "escape" gravity for a given gravitational potential energy at a given position is known as the escape velocity (i.e. so that gravity will never manage to pull it back).

Because it does not specify a direction of travel, escape velocity is actually a speed (not a velocity) and the object can escape the gravitational field in any direction (provided its path does not intersect the planet).

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Which would have the larger heat capacity, a large iron skillet or a small iron skillet?

Answers

A large iron skillet may hold more heat capacity than a small one because of its larger mass. Both skillet have the same specific heat because they are constructed of the same material.

A physical feature of matter known as heat capacity or thermal capacity is the quantity of heat that must be applied to an object in order to cause a unit change in temperature. J/K is the metric unit for heat capacity.

An extensive property is heat capacity.The heat is related to the substance's mass and the temperature change since the transferred heat is equivalent to the change in internal energy.

An object's mass and chemical makeup both affect its ability to hold heat. Therefore, a large iron skillet may hold more heat capacity than a small one because of its larger mass. Both skillet have the same specific heat because they are constructed of the same material.

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Oil drips from a car at a rate of 1 drip every 0.1 second. Which of the patterns below would best represent the pattern of drips from the car if it were accelerating constantly?

Answers

The equally spaced dots shows a car if it were accelerating constantly.

What is acceleration?

The term acceleration has to do with the rate of change of the velocity of a body with time. We know that velocity is a vector quantity. This implies that both the magnitude and the direction of the velocity are all important. The same goes for acceleration. The acceleration is a vector quantity so both its magnitude and direction are deemed as important.

Now we know that if the acceleration is uniform or constant, the velocity would increase by equal amounts in equal time intervals. We now have to check out to see the cases in which the image suggests that the velocity changes by equal amounts in equal time intervals.

Looking at the image as attached, the dots are equally spaced. The equal spacing of the dots shows us the way and manner in which the velocity of the car increases. Thus the image attached shows us that the velocity does increase by equal amounts in equal time intervals.

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A heat engine operates in a carnot cycle between reservoirs of temperatures 1000 k and 400 k. it is found to discharge 20 j of heat per cycle to the cold reservoir. what is the work output per cycle?

Answers

A heat engine operates in a Carnot cycle between reservoirs of temperatures 1000 k and 400 k. it is found to discharge 20 j of heat per cycle to the cold reservoir, then the work done by the engine would be 60 joules.

What is a Carnot engine?

It is a hypothetical engine that is presumable to have the highest efficiency of all engines in the universe.

The Carnot engine is the most efficient engine available.

If a heat engine runs in a Carnot cycle between reservoirs with temperatures of 1000 k and 400 k, as stated in the issue. It is discovered that it releases 20 j of heat to the cold reservoir per cycle.

The efficiency of the engine = 1 - 400/1000

                                               =0.6

Heat supplied = heat rejected + work done

The efficiency of the engine = 0.6 = work done/Heat supplied

                                               0.6 = work done/heat rejected + work done

                                                0.6 =W / 20 + W

The work done = 60 joules

Thus, the work done by the engine would be 60 joules.

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What are the magnitude and direction of electric field midway between these two charges?

Answers

No matter how far away or how large the charges are, the electric field in the middle of any two equal charges is always zero.

E is equal to Fe/q [where q is a positive test charge, Fe is the electric force vector, and E is the electric field vector].

According to the Coulomb Force, Fe = k Q q / r2,

and as a result, E = [K Q q / r2]/q

=K Q/r^2

Because similar charges repel one another, the field's orientation is away from the core charge.

The outcome is TWO FIELDS with the same magnitude but opposing directions, giving a value of ZERO.

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A workman stands on the roof of a 10 meter high building. Another worker tosses him a tool from the ground, which the first workman catches as the tool is falling to the ground. If the total time the tool is in the air is 2.5 seconds, what speed did the worker toss the tool into the air initially?

Answers

Answer:

4 Meters per second

Explanation:

This is assuming that the object is tossed straight up and without an angle since your question did not provide one

The acceleration of free fall is about 10 m/s^2. Why does the unit second appear twice?

Answers

In free fall, the fact that in the acceleration value (10 m/s^2) the unit of the second appears twice indicates that the object is moving at a rate of 10 meters per second every second.

The acceleration is the physical quantity that indicates the variation of velocity as a function of time,  and it is expressed in units of distance per time squared e.g.: m/sec2 ; km/h2

What is free fall?

It is when the object or mobile falls from a height (h) with a positive acceleration equal to the gravity, describing a vertical rectilinear travel.

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A farmer measures the distance around a rectangular field. The length of each long side of the rectangle is found to be 43.44 m, and the length of the short side is found to be 20.5 m. What is the total distance around the field?​

Answers

Answer:

115.88 m

Explanation:

The complete distance around the field (perimeter) is equal to the whole sum of the 4 sides:

Imagine you stroll trough the border of the field, you go 38.44m to the right, 19.5m up, 38.55m to the left, 19.5m down.

A uniform solid sphere rolls down an incline. what must be the incline angle if the linear acceleration of the center of the sphere is to have a magnitude of 0.10 g?

Answers

The uniform solid sphere rolls down an incident angel for solid sphere is θ = 9.6 degree .

What is incident angel?

The angle of incidence in geometric optics is the angle formed between a ray incident on a surface and the normal, or line perpendicular to the surface at the point of incidence. Any wave, including optical, acoustic, microwave, X-ray, and others, can create a ray.

required acceleration = .12 g

The term for the acceleration of a rolling body on an inclined surface

= gsinθ / 1 + k² / R²

Here rolling body is sphere

k² = 2/5 R²

k² / R² = 2/5

acceleration = g sinθ / 1 + k² / R²

.10 g = g sinθ / 1 + k² / R²

.10 g =g sinθ / 1 + 2/5

.10 = sinθ / 1.4

sinθ = .168

θ = 9.6 degree .

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The size of a certain insect population is given by p(t)=200e.02t, where t is measured in days. at what time will the population equal 800?

Answers

With the help of the mathematical concept of Functions in physics, the number of days for population to reach 800 will be approximately 69 days.

What are Functions in physics?

Functions in physics is a mathematical concept used to represent different types of physical quantities in nature. Some types of functions are- linear, quadratic, cubic, exponential and reciprocal functions. A functions relates a set of inputs with another set of desired outputs. Functions are essential for formulating physical relationships in theoretical and practical sciences. For example, functions can be widely used in the representation of electric and magnetic fields in space and time, they are used in quantum mechanics, it is very widely used in determining the position and motion of an object in space. We perform a variety of mathematical operations on functions to make some conclusions and to answer some typical questions related to a physical system.

Here in this question, we have a function which represents a certain population of insect, the function is given by,

[tex]P(t)=200e^0^.^0^2^t[/tex]

where [tex]t[/tex] represents the number of days.

We have to find the total time in days for the population to reach 800 insects, that means,

[tex]P(t)=800[/tex]

Hence,

[tex]200e^0^.^0^2^t=800[/tex]

[tex]e^0^.^0^2^t=\frac{800}{400}[/tex]

[tex]e^0^.^0^2^t=4[/tex]

Taking natural log both sides

[tex]ln e^0^.^0^2^t=ln 4\\[/tex]

[tex]0.02t=ln4[/tex]

[tex]t=\frac{ln4}{0.02}[/tex]

[tex]t=69.3\\[/tex]

[tex]t=69[/tex] days (appproximately)

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Acellus
Perform the following
mathematical operation, and
report the answer to the correct
number of significant figures.
7.125 x 8.00 = [?]
Copyright ©ang-an International Academy of All Rights Reserved

Answers

57.0 is the calculated value.

Any pair of non-zero digits separated by a zero is significant. The number 108.0097, for instance, includes seven significant digits. Every zero that is both to the right and left of a digit that is not zero and the decimal point has no significance. The number 0.00798, for instance, contained three significant digits. To calculate how many significant figures are in a number, use the three guidelines below: non-zero digits are always significant. Notable zeros fall inside the range of two significant digits. The importance of a final zero or subsequent zeros only applies to the decimal section.

Since there are only three significant figures in the operation, that would be the number to use: 8.00

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How do sub particles behave with each other

Answers

Answer:

The strong force binds quarks together within protons, neutrons, and other subatomic particles. Rather as the electromagnetic force is ultimately responsible for holding bulk matter together, so the strong force also keeps protons and neutrons together within atomic nuclei.

Explanation:

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If its volume remains unchanged, what will its pressure be at the temperature at which co2co2 solidifies?

Answers

The pressure for CO₂ will be 0.75atm when volume remains unchanged.

What is pressure?

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.

PV = nRT

[tex]\frac{P_{1} }{T_{1} } = \frac{P_{2} }{T_{2} }[/tex]

[tex]P_{1} = \frac{1.05atm}{273K} * (194.5K)[/tex]

P1 = 0.748atm

which on round figure gives us,

P1 = 0.75 atm

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A ball is dropped from the top of a tall building of height h = 29.47 m .
About how long does it take for the ball to hit the ground? Take acceleration due to gravity to be 9.81m/s/s (Neglect air resistance.)

Answers

With the use of motion under the gravity formula, It will take 2.45 seconds for the ball to hit the ground.

What is Linear Motion ?

Linear motion involves the movement of a body in a straight line. It can be horizontal motion or vertical motion which is also known as motion under gravity.

Given that a ball is dropped from the top of a tall building of height h = 29.47 m. To know how long it take the ball to hit the ground if acceleration due to gravity is to be 9.81m/s² and we neglect air resistance, we will make use of the formula below

h = ut + 1/2gt²

Since the ball is dropped from the top of a tall building, u = 0

29.47 = 1/2 × 9.81 × t²

29.47 = 4.905t²

t² = 29.47 / 4.905

t² = 6.008

t = √6.008

t = 2.45 s

Therefore, it take 2.45 seconds for the ball to hit the ground.

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Niobium (nb) has a bcc crystal structure, an atomic radius of 0.143 nm, and an atomic weight of 92.91 g/mol. compute and compare its theoretical density with the experimental value.

Answers

Both the theoretical density and experimental value is 8.57g/cm3

The term crystal structure, in crystallography, denotes that the structure in which the atoms (ions or molecules) are attached are arranged in an ordered manner. The smallest repeating unit of the crystal structure is called a unit cell.

Given that:

The radius of Nb is given as R=0.1430nm

The density of Nb is given as d=8.57g/cm3

The atomic weight of Nb is given as M=92.91g/mol

Also, given that the structure is BCC.

The value of the number of atoms per unit cell in BCC is Z=2

The formula for the edge length of BCC structure is,

a=4R/(√3)

Substitute the given values

a=(4*0.1430 nm)/(√3)

=3.3024×10−8cm

The formula for the density of the Nb in BCC structure is,

d2=(Z×M)/(a3×NA)

Substitute the given values.

d1=(2×92.91g/mol)/((3.3024×10-8cm)3 × 6.022 × 1023 mol-1)

=(185.82g/mol)/(21.68cm3/mola3×NA)

=8.57g/cm3

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What is the main reason for searing a roast at a high temperature before finishing it at a lower temperature?

Answers

Prior to cooking, searing meats at high heat seals the pores, preserving the juices and preventing shrinking.

Why is a roast seared at a high temperature before being finished at a lower temperature?

A roast looks and tastes good when it is roasted at high temperatures (400°F and above). For thin, tender meats that depend on a flavorful, well-browned crust for flavor, such beef tenderloin and pork tenderloin, this approach works best.

Why is a roast seared in the first place?

If you want to produce the most delectable roasts, steaks, chops, and other meat dishes, searing the meat is a necessary step.

Meat is seared to caramelize the natural sugars and brown the proteins, resulting in a thick, nutty crust.

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The first telescopic photo shows what appears to be a single star. The second photo shows the same object, now revealed to be two distinct stars. What is the difference between the two photos?.

Answers

Explanation:

i think the second picture is smaller and has a better angular resolution

In second photo, there has more resolution than that of first photo.

What is resolving power?

The ability of an optical equipment to discern between two things that are close to one another and produce distinct images of the two items is known as its resolving power.

To put it simply, when viewed through an optical instrument, resolving power varies inversely with the distance between the two objects to be resolved. As a result, when viewed from the device, the images of two things that are close to one another should appear distinct and separate.

Consider using a telescope to observe two stars that are close to one another; the telescope's resolving power depends on its capacity to distinguish between the pictures of the two stars.

According to the question, second telescope can detect two stars separately but first one can't because the resolving power of the second telescope is greater than that of first one. That's way, the difference between the two photos is that second photo is with greater resolution.

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You use your working memory when you:A) store knowledgeB) remember a phone number C)long enough to dial itD) retrieve informationE) none of these Which quadratic equation has solutions x=8 and x=1? clear submit 8x2 7x1=0 x2 7x8=0 x2x 8=0 x27x8=0 The body mass index (bmi) is a measure of body fat, and an indicator tool for obesity, based on height and weight. the formula for calculating bmi using kilograms and meters is? While doing research for a paper, the first article you found is one you think is trustworthy. According to sift, after investigating the article, what should you do next?. The measure of one angle on a right triangle is 16 more than the measure of the smallest angle. find the measures of all three angles 80 percent of 42 is what percent of 16 ?a. 240b. 210c. 150d. 50 e. 30 Which igneous rock has an amorphus texture? Use summation notation to write each arithmetic series for the specified number of terms. Then evaluate the sum. 6+7.4+8.8+ . . . ; n=11 You have a drawer with 7 different pencils. Each pencil is a different color (red, blue, white, green, pink, black, and yellow). If you take a pencil out of the drawer, it is green, and do not put it back, what is the probability that the next pencil is pink? Use the given rule to write the 4th, 5th, 6th, and 7th terms of each sequence. an = n/{n+1} What mass in grams of tin would be required to completely react with1.50 L of 0.750 M HBr in the following chemical reaction?Sn(s) + 4 HBr(aq) - SnBr (aq) + 2 H (g) someone help me for 100 points and brainliest pls Which lines are parallel to the graph of 4x y = 6? cindy was able to earn $275 in two weeks . at the same rate , how much will he earn in 6 weeks A decrease in the price of ice cream is likely to cause a(n) _____ in the demand for ice cream cones, due to a change in _____. All people in tribes of the northcoast region were treated as equals. question 6 options: true false How to write four hundred seven million six thousand nine hundred and sixty two? What is the labeling theory? The measure of one angle is 3 degrees more than 1/2 the measure of its supplement. Identify and solve an algebraic equation. Consider the sequence of real numbers[tex] \rm a_1 = \frac{ log_{2}( {3}^{2} ) }{ log_{3}(2) } ,a_2 = \frac{ log_{ {3}^{3} }( {4}^{4} ) }{ log_{ {4}^3}( {3}^{4} ) } ,a_3 = \frac{ log_{ {4}^5 }( {5}^{6} ) }{ log_{ {5}^{5} }( {4}^{9} ) }, \dots[/tex]In general, [tex] \rm a_k = \frac{ log_{(k + 1) ^{(2k - 1)} } ((k + 2 {)}^{2k}) }{log_{(k + 2) ^{(2k - 1)} } ((k + 1 {)}^{ {k}^{2} })} [/tex] Let [tex] \rm P_n = \frac{ log_{ {(n + 1)}^{(2n - 1)} }( {2}^{2n} ) }{ log_{ {2}^{(2n - 1)} }((n + 1) {}^{ {n}^{2} } )} \cdot \prod \limits_{k = 1}^{n - 1} a_k[/tex] for integer n [tex]\geq [/tex] 2.[tex] \rm Find \sum \limits_{n = 2}^{ \infty } P_n[/tex]