Assuming the earth is a uniform sphere of mass M and radius R, show that the acceleration of fall at the earth's surface is given by g = Gm/R2 . What is the acceleration of a satellite moving in a circular orbit round the earth of radius 2R​

Answers

Answer 1

Explanation:

The weight of an object on the surface of the earth is equal to the gravitational force exerted by the earth on the object.

[tex]W=F_G[/tex]

[tex]mg = G \dfrac{mM}{R^2}[/tex]

which gives us an expression for the acceleration due to gravity g as

[tex]g = G\dfrac{M}{R^2}[/tex]

At a height h = R, the radius of a satellite's orbit is 2R. Then the acceleration due to gravity [tex]g_h[/tex] at this height is

[tex]mg_h = G \dfrac{mM}{(2R)^2}= G \dfrac{mM}{4R^2}[/tex]

Simplifying this, we get

[tex]g_h= G \dfrac{M}{4R^2} = \dfrac{1}{4} \left(G \dfrac{M}{R^2} \right) = \dfrac{1}{4}g[/tex]


Related Questions

A(n) 60.9 kg astronaut becomes separated
from the shuttle, while on a space walk. She
finds herself 36.5 m away from the shuttle
and moving with zero speed relative to the
shuttle. She has a(n) 0.928 kg camera in her
hand and decides to get back to the shuttle
by throwing the camera at a speed of 12 m/s
in the direction away from the shuttle.
How long will it take for her to reach the
shuttle? Answer in minutes.
Answer in units of min.

Answers

Answer:

m v = M V  conservation of momentum after  throwing camera

V = m * v / M =   .928 * 12 / 60.9 = .183 m/s

t = S / V = 36.5 / .183 = 199 sec = 3.32 min

The red light from a helium-neon laser has a wavelength of 644.6 nm in air. Find the speed, wavelength, and frequency of helium-neon laser light in air, water, and glass. (The glass has an index of refraction equal to 1.50.)speed (m/s)wavelength (nm)frequency (Hz)airwaterglass

Answers

Answer:

air  f = 4.6527 10¹⁴ Hz

water f = 3.4914 10¹⁴ Hz

glass f = 3.1027 10¹⁴ Hz

Explanation:

The refractive index of a material is given by

         n = c / v

where c is the speed of light in a vacuum c = 3 108 m / s and v is the speed of light in the material medium.

the speed of the wave is

         v = λ f

we substitute

         c / n = λ f

          f = [tex]\frac{c}{n \ \lambda}[/tex]

 

The refractive indices are

air 1,00029

water 1.3330

glass 1.5

let's calculate the frequencies

vaccum

         f = 3 10⁸ / 1 644.6 10⁻⁹

         f = 4.6540 10¹⁴ Hz

air

         f = 3 10⁸ / 1,00029 644.6 10⁻⁹

         f = 4.6527 10¹⁴ Hz

Water

         f = 3 10⁸ / 1.333 644.6 10⁻⁹

         f = 3.4914 10¹⁴ Hz

glass

        f = 3 10 ^ 8 / 1.5 644.6 10⁻⁹

        f = 3.1027 10¹⁴ Hz

2. When you increase your speed from 35 mph to 70 mph, the force of impact you experience will be increased: A. 2 times B. 4 times C. 5 times D. 7 times​

Answers

you just have to divide 35 and 70, the answer is A. 2 times

When you increase your speed from 35 mph to 70 mph, the force of impact you experience will be increased 4 times.

Hence, the correct option is B.

The force of impact in a collision is directly proportional to the square of the velocity. When the speed is doubled (increased from 35 mph to 70 mph), the force of impact will increase by a factor of four ([tex]2^2[/tex]). This is a fundamental concept in physics known as the kinetic energy formula, which is given by:

Kinetic Energy = (1/2) * mass * [tex]velocity^2[/tex]

Since kinetic energy is directly proportional to the square of velocity, doubling the speed results in four times the kinetic energy and, consequently, four times the force of impact.

Therefore, When you increase your speed from 35 mph to 70 mph, the force of impact you experience will be increased 4 times.

Hence, the correct option is B.

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You take your pulse and observe 80 heartbeats in a minute. What is the period of your heartbeat? What is the frequency of your heartbeat?

Answers

Answer:

120 beats per minute.

Explanation:

If I take your pulse and observe 80 heartbeats in a minute. Then the period of your heartbeat is 0.8 s and frequency is 1.3Hz.

What is Heartbeat ?

A pulse is the term used in medicine to describe the tactile arterial palpation of the cardiac cycle (heartbeat) by skilled fingertips. Any location where an artery can be compressed close to the surface of the body, such as the carotid artery in the neck, the radial artery in the wrist, the femoral artery in the groyne, the popliteal artery behind the knee, the posterior tibial artery near the ankle joint, and on the foot, can be used to palpate the pulse (dorsalis pedis artery). Heart rate may be determined by monitoring pulse, or the number of arterial pulses per minute. Auscultation, which is the process of counting the heartbeats while listening to the heart using a stethoscope, is another way to determine the heart rate. Typically, three fingers are used to gauge the radial pulse.

Given,

heart beat = 80 beats/min = 1.3 beats/s

Frequency is nothing but how much beats is heart having in one second and that is 1.3 beats/s. Hence frequency of heart is 1.3Hz.

The Period is reciprocal of frequency,

T = 1/f = 0.8 s

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CR Physical Science B (GP) 20-21 / 1 Motion
1. A distance-time graph indicates that an object travels 2 m in 2 s and then travels another 80 m during the next 40 s.
What is the average speed of the object?
O 4 m/s
O
2 m/s
O 8 m/s
10 m/s

Answers

Answer:

Average speed = total distance traveled / total time traveled

V = (2 + 80) / (2 + 40) = 82 / 42 = 2 m / s

A uniform electric field is oriented in the −x direction. The magnitude of the electric field is 6500 N/C. How will the equipotential surfaces associated with this electric field be oriented?

Answers

A uniform electric field is an electric field having all of it's lines parallel to each other and of constant magnitude.

A temperature of 200 degrees Fahrenheit is equivalent to approximately A.93.3 degrees Celsius B. 232 degrees Celsius C. 37.8 degrees Celsius D. 840 degrees Celsius

Answers

Answer:

you can use G.oogle for this question.

Answer:

93.3 degrees Celsius.

Explanation:

Which best describes velocity?

A. 15 miles an hour
B. 15 miles an hour going west.
C. Speeding up from 10 to 15 miles an hour.
D. Going 15 miles an hour for 2 hours.

Answers

Answer:

B. 15 miles an hour going west

A 2.5-kg rock is dropped off a 32-m cliff and hits a spring, compressing it 57 cm. What is the spring constant? Round your answer to two significant figures.

The spring constant, k, is
StartFraction N over m EndFraction.

Answers

Answer: 4800 N/m

Explanation:

Given

mass of rock [tex]m=2.5\ kg[/tex]

Height of cliff [tex]h=32\ m[/tex]

compression in the spring [tex]x=57\ cm[/tex]

Here, potential energy is converted into kinetic energy which in turn converts to elastic potential energy of the spring

[tex]\Rightarrow mgh=\dfrac{1}{2}kx^2\\\\\Rightarrow k=\dfrac{2mgh}{x^2}\\\\\Rightarrow k=\dfrac{1568}{0.3249}\\\\\Rightarrow k=4826.100\approx 4800\ N/m[/tex]

Answer:

480

Explanation:

2021

Một mol khí đang ở điều kiện tiêu chuẩn thì bị nén váo một bình 5 lít. Nhiệt độ khí trong bình là 770 C. Tính áp suất khí?

Answers

Đáp án:

 p=5,74atm

Giải thích các bước giải:

áp suất khí là:

pV=nRT⇒p=nRTV=1.0,082.(77+273)5=5,74atmpV=nRT⇒p=nRTV=1.0,082.(77+273)5=5,74atm

p=5,74atm

Giải thích các bước giải:

áp suất khí là:

pV=nRT⇒p=nRTV=1.0,082.(77+273)5=5,74atmpV=nRT⇒p=nRTV=1.0,082.(77+273)5=5,74atm

How high can water be theoretically lifted by a vacuum pump at sea level?

A) less than 10.3 m
B) 10.3 m
C) more than 10.3 m

Answers

Explanation:

everything can be found in the picture

Consider a point on a bicycle wheel as the wheel turns about a fixed axis, neither speeding up nor slowing down. Compare the linear and angular accelerations of the point.

a. Both are zero.
b. Only the angular acceleration is zero.
c. Only the linear acceleration is zero.
d. Neither is zero

Explain your choice

Answers

Answer:

c. Only the linear acceleration is zero.

Explanation:

The linear acceleration is defined as the rate of change of linear velocity. Since the bicycle is moving in the same direction, with the same speed, without speeding up or slowing down. Therefore, there will be no change in linear velocity and as a result, linear acceleration will be zero.

The angular acceleration is the rate of change of angular velocity. Since the angular velocity is changing its direction constantly. Therefore, it has a certain component of acceleration at all times called centripetal acceleration.

Therefore, the correct option is:

c. Only the linear acceleration is zero.

A person rolls a 7 kg bowling ball down a lane in a bowling alley. The lane is
18 m long. The ball is traveling at 7 m/s when it leaves the person's hand.
What is the ball's kinetic energy at this point?

Answers

Answer:

171.5J

Explanation:

K=1/2 *m *U²

K=1/2 *7 *7²

K=171.5 J

The spring in the figure has a spring constant of 1400 N/m . It is compressed 17.0 cm , then launches a 200 g block. The horizontal surface is frictionless, but the block's coefficient of kinetic friction on the incline is 0.210.
What distance d does the block sail through the air?

Answers

Use the work-energy theorem to find the velocity of the block when it's released by the spring. The work done by the spring on the block as it's restored to equilibrium is

W = 1/2 kx ²

where k is the spring constant and x is the compression of the spring. So

W = 1/2 (1400 N/m) (0.170 m)² = 20.23 J

This is equal to the block's change in kinetic energy ∆K,

W = ∆K

and since it starts from rest, the initial K is zero, leaving us with

W = 1/2 mv ²

where m is the mass of the block and v is its speed, so that

20.23 J = 1/2 (0.200 kg) v ²

==>   v ≈ 14.2 m/s

The block slides at this speed across the frictionless surface until it hits the incline which introduces friction.

First, you need to find the length of the incline. It forms a 45° angle, and the underlying 45°-45°-90° triangle has a hypotenuse of length √2 (2.0 m) ≈ 2.83 m.

Next, you need to find the total work done on the block as it slides up the incline. Use Newton's second law to examine the forces acting on the block during this phase:

• the net force acting on the block in the direction perpendicular to the incline is

F = n - mg cos(45°) = 0

where n = mg cos(45°) ≈ 1.39 N is the magnitude of the normal force and mg cos(45°) ≈ 1.39 N is the perpendicular component of the block's weight;

• the net force acting on the block parallel to the surface is

F = -f - mg sin(45°) = ma

where f = µn = 0.210n ≈ 0.291 N is the magnitude of kinetic friction, mg sin(45°) ≈ 1.39 N is the parallel component of the weight, and a is the acceleration of the block.

Only the parallel forces do work on the block, and this work is negative because friction and weight oppose the block's sliding up the incline. The total work done on the block is then

W = (-0.291 N - 1.39 N) (2.83 m) ≈ -4.74 J

Use the work-energy theorem again to find the block's new speed v at the top of the incline:

W = ∆K

==>   -4.74 J = 1/2 (0.200 kg) v ² - 1/2 (0.200 kg) (14.2 m/s)²

==>   v ≈ 12.4 m/s

And now this becomes a projectile problem. The block travels a horizontal distance x after being launched at an angle of 45° with initial speed 12.4 m/s after time t according to

x = (12.4 m/s) cos(45°) t

Its height y from the 2.0 m-high surface at time t is given by

y = (12.4 m/s) sin(45°) t - 1/2 gt ²

The block lands on the surface when y = 0, which occurs after t ≈ 1.79 s, at which point the block has covered a distance d15.7 m.

The block sail through the air at the distance of "15.8 m"

Given:

Spring constant,

1400 N/m

Mass,

200 g

Block's coefficient,

0.210

By using Work energy theorem, we get

→ [tex]W_{spring}+W_g+W_f = KE_f-KE_i[/tex]

By substituting the values, we get

→ [tex]\frac{1}{2}\times 1400\times (0.17)^2- (0.2\times 9.8\times 2)-(0.21\times 0.2\times \frac{9.8}{\sqrt{2} }\times \sqrt{2}\times 2 )= \frac{1}{2}\times 0.2\times V_f^2[/tex]

here,

[tex]V_f = 12.44 \ m/s[/tex]

→ [tex]d = \frac{V_f^2 Sin 2 \Theta}{g}[/tex]

     [tex]= \frac{(12.44)^2 Sin 90^{\circ}}{9.8}[/tex]

     [tex]= 15.8 \ m[/tex]

Thus the answer above is right.  

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A jet is circling an airport control tower at a distance of 15.8 km. An observer in the tower watches the jet cross in front of the moon. As seen from the tower, the moon subtends an angle of 9.21x10-3 radians. Find the distance traveled (in meters) by the jet as the observer watches the nose of the jet cross from one side of the moon to the other.

Answers

Answer:

The Distance traveled (in meters) by the jet as the observer watches the nose of the jet cross from one side of the moon to the other.

=145.5m

Explanation:

The radius of the circling jet r = 15.8km = 15.8*10^3 m

the angle subtended by moon

θ = 9.21*10^-3 rad

Therefore, the distance traveled by jet is

s = rθ

= (15.8*10^3 m)(9.21*10^-3 )

= (15,800)(0.00921)

=145.5m

Which of these hazmat products are allowed in your FC?
Please choose all that apply.
A GPS unit (lithium batteries)
A subwoofer (magnetized materials)
A can of hairspray (flammable/aerosols)
Fireworks (explosives)

Answers

Answer: Hazmat products are allowed in your FC are:

A GPS unit (lithium batteries) A subwoofer (magnetized materials)

Explanation:

Hazmat products consist of flammable, corrosive and harmful substances which are actually very hazardous to human health and environment.  

Hazardous material allowed in FC are as follows.

Magnetized material products like as speakers.Non-spillable battery products like toy cars.Lithium-ion battery containing products like laptops, mobile phones etc.Non-flammable aerosol.

So, hazmat allowed products are GPS unit (lithium batteries) and subwoofer (magnetized materials).

Thus, we can conclude that hazmat products are allowed in your FC are:

A GPS unit (lithium batteries) A subwoofer (magnetized materials)

concave mirror daily application​

Answers

Answer:

concave mirror use in headlights and torches

Explanation:

Concave mirrors are used in headlights and torches. The shaving mirrors are also concave in nature since these mirrors can produce enlarged clear images. Doctors use concave mirrors as head mirrors to have a clearer view of eyes, noses, and ears. The dental mirrors used by dentists are also concave.

How bullet train and a circuit breaker work on the magnet effect of current

Answers

Mark Brainliest please

Bullet trains

Bullet trains are also called Maglev trains, as they work with the help of powerful electromagnets which make them high speed trains, electromagnets are attached to the metal lining of track,large magnets are present inside the train they work on the principal that like poles repel and unlike poles attract. Circuit breakers it is a device which cuts the power when when there is too much current flowing through the circuits,they are also called fuses, they work with the help of electromagnet to cut the circuit and rejoin.

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kinetic energy of an object is quadrupled, momentum will change by what factor?

Answers

Answer:

So as KE becomes 4times , Momentum will increase by 2 times.

The brachialis attaches to the forearm .035 m from the elbow at an angle of 32 deg. If the brachialis produces 750 N of force, what is the magnitude of the stabilizing component of the brachialis force

Answers

Answer:

[tex]XY=636N[/tex]

Explanation:

From the question we are told that:

Distance [tex]d=0.35m[/tex]

Angle [tex]\theta=32\textdegree[/tex]

Force [tex]F=750N[/tex]

Generally the equation for magnitude of the stabilizing component of the brachialis force is mathematically given by

 [tex]XY=Fcos\theta[/tex]

 [tex]XY=750cos 32\textdegree[/tex]

 [tex]XY=636N[/tex]

44. Water from a fire hose knocks over a wooden shed. Compared with the pressure within the water, the pressure exerted against the shed is

a) less.
b) the same.
c) more.
d) nonexistent.

Answers

b i think sorry if it’s wrong

What is air

A. A Buchner substance
B. A compound
C. An element
D. A mixture

Answers

D. A mixture (mark brainliest)

Air is classified as a mixture. Option D is the correct answer.

Air is a combination of different gases, primarily nitrogen (about 78%), oxygen (about 21%), and small amounts of other gases such as carbon dioxide, argon, and trace elements. These gases are not chemically bonded to each other, but rather exist together in the same space. Option D is the correct answer.

In a mixture, the substances involved retain their individual properties and can be separated by physical means. This is true for air as well. The gases in air can be separated through processes like fractional distillation or filtration. It's important to note that air also contains other components such as water vapor, dust particles, and pollutants, which can vary in concentration depending on the location and environmental conditions. These components further contribute to the complex nature of air as a mixture.

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The extension produced on the wire by the application of 300 N force is 2 mm. The elastic energy stored on the wire is​

Answers

Answer:

150000 is the answer to the question

If you wanted to know how much the temperature of a particular piece of material would rise when a known amount of heat was added to it, which of the following quantities would be most helpful to know?

a. coefficient of linear expansion
b. specific heat
c. initial temperature
d. thermal conductivity
e. density

Answers

Answer:

Option (b) is correct.

Explanation:

The amount of heat required to raise the temperature of substance of mass 1 kg by 1 degree C, is called specific heat of the substance.

The formula of the specific heat is

H = m c (T' - T)

where, m is the mass, c is the specific heat and T' - T is the change in temperature.

So, to know the rise in temperature, by adding the known amount of heat, the specific heat is required.

So, option (b) is correct.

For the following questions, assume the wavelengths of visible light range from 380 nm to 760 nm in a vacuum. (a) What is the smallest separation (in nm) between two slits that will produce a ninth-order maximum for any visible light

Answers

Answer:

Explanation:

This is an interference exercise, which the case of constructive interference is described by the expression

          d sin θ  = m λ

in this case they indicate that we are in the ninth order (m = 9).

To be able to observe the pattern, the dispersion angle must be less than 90º

         

we substitute

           sin 90 = 1

           d = m  lang

           

let's calculate

           d = 9 λ

           d = 9 380 10⁻⁰

            d = 3.42 10⁻⁶  

           d2 = 9 760 10⁻⁹

           d2 = 6.84 10₋⁶

planet smaller than earth but larger than mercury​

Answers

Answer:

venus......................

A kettle operates from a 120 V outlet. It has a heating element with a resistance of 8.0 Ω . Calculate the current going through the element.

Answers

Answer:

I = 15A

Explanation:

V = I*R

120V = I*8.0ohms

I = 120V/8.0ohms

I = 15A

Answer:

I=15A

Explanation:

you know what to do.

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⠄⠄⠄⠄⠄⠛⠁⠄⠄⠄⢀⣿⣿⣧⡀⠄⠹⣿⣿⣿⣿⣿⡿⣿⣻⣿

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⠄⠄⠄⠄⠄⠄⠄⠄⠄⣰⣿⣛⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠄⠄

⠄⠄⠄⠄⠄⠄⠄⠄⠄⣬⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠄⠄

⠄⠄⠄⠄⠄⠄⠄⠄⠄⢘⣿⣿⣻⣛⣿⡿⣟⣻⣿⣿⣿⣿⡟⠄⠄⠄

⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠛⢛⢿⣿⣿⣿⣿⣿⣿⣷⡿⠁⠄⠄⠄

⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠉⠉⠉⠉⠈⠄⠄⠄⠄⠄⠄

Give them the brain list.

The first and second coils have the same length, and the third and fourth coils have the same length. They differ only in the cross-sectional area. According to theory, what should be the ratio of the resistance of the second coil to the first coil and the fourth coil to the third

Answers

Answer:

The ratio of the resistances of second coil to the first coil is the ratio of square of radius of the first coil to the square of radius of  second coil.

And

The ratio of the resistances of fourth coil to the third coil is the ratio of square of radius of the third coil to the square of radius of  fourth coil.

Explanation:

The resistance of the coil is directly proportional to the length of the coil and inversely proportional to the area of coil and hence inversely proportional to the square of radius of the coil.

So, the ratio of the resistances of second coil to the first coil is the ratio of square of radius of the first coil to the square of radius of  second coil.

And

The ratio of the resistances of fourth coil to the third coil is the ratio of square of radius of the third coil to the square of radius of  fourth coil.

An object produces a sound wave with a wavelength 75.0cm. if the speed of sound is 350.0m/s, the frequency of the sound is

Answers

Answer:

wavelength=75.0

speed of sound(v)=350 .0m/s

frequency(f)=?

we know,

v=f*wavelengh

350.0 =f*750

f. =350/75

=4.667

pls mark me brainlest

What is the change in internal energy if 70 J of heat is added to a system and
the system does 30 J of work on the surroundings. Uze al-Q-W.
O A. 40 J
O B. -40.3
O C. 100.
D. -1003

Answers

Answer:

A. 40 J

Explanation:

Given;

heat added to the system, Q = 70 J

work done by the system, W = 30 J

The change in the internal energy of the system is calculated using the first law of thermodynamic as shown below;

ΔU = Q - W

ΔU = 70 J - 30 J

ΔU = 40 J

Therefore, the  change in the internal energy of the system is 40J

Other Questions
What is the value of x?O x = 32O x = 36O x = 37O x = 40 A couple owned a home with a large backyard in which they hosted raucous parties, with extremely loud music and bright lights. These parties often occurred during weekdays and went until dawn. Despite multiple complaints, the couple continued to host these parties. The couple had the following three neighbors: an elderly woman who was abnormally sensitive to loud noises; a teacher who thought the parties were hilarious, as they reminded him of his fraternity days; and a mother who found the parties highly annoying and disruptive to her and her family but never addressed the issue with the couple. Who would be barred from recovering from the couple in a nuisance action Need help!!! Please Alex and Jill share 100 in the ratio of 1 : 7 work out how much money Alex gets? Read the sentence from the passage.The suggestion that we might find a measure of solace in the very machines responsible for our battered minds will seemImplausible to some.What is the best meaning of the word solace as it is used in the passage?OA inspirationOB. Sympathy.encouragementOD. relief Quadrilateral MNQP has vertices as shown. If the figure is translated 4 units left and 3 units down, what are the coordinates of N'? * what was the name of the island where cabeza de vaca's barge landed An electrician needs 4 7/10 rolls of electrical wire to wire each room in a house. How many rooms can he wire with 9 2/5 rolls of wire? mrdunami ate kenkey and fried fish and pepper describe digestion in processn For #4 - 5, the two polygons are similar. Find thevalues of x and y.60181222x + 44. which information could he have used to determine this? In a box there are n red marbles and three times as many black marbles. There are 36marbles in the box. How many red marbles are in the box? Back to the cute little pigs. What are the possible parents of the following groups of guinea pigs. Give all possibilities. You do not need to show Punnett Squares, just the possible parents. There may be more than I answer for each. Case 1: 50 % of the offspring are black Case 2: 75 % of the offspring are black Case 3: 50 % of the offspring are hybrid black Case 4: 100 % of the offspring are black Case 5: 100 % of the offspring are white Case 6: 50 % of the offspring are white Case 7: 25 % of the offspring are white PLEASE HELP! Will give BRAINLIESTList two possible steps where copper yield may be lost (why you may not get all the copper back at the end). Be specific about the steps and how they might lose the copper. You receive $1,000 to put in the bank. You place it in an account that pays 6% annual interest compounded continuously. How much will you have in 12 years? Round the answer to the nearest dollar. SHOW WORK PLZ Based on the following book synopsis, which two purposes could the author have for writing the book? An explorer writes a nonfiction book about an ancient city that he has discovered, including many details and anecdotes.to argueto persuadeto informto entertain y = x2 + 5x - 14 in factored form need answe asap please Prove that if a and b are positive integers,then there exists a unique integers q and r such that a=bq+r where 0r I need help help help Which of the following is themost complete definition ofelectromagnetic radiation?A. energy that can travel through space in theform of wavesB. the energy formed in the sun's coreC. heat waves that travel through planetsD. light that has a higher frequency than visiblelight