find three consecutive even integers such that two times the second equals the sum of the first and third

Answers

Answer 1

We are asked to determine three consecutive even integers. Let those integers be:

\(n_1,n_2,n_3\)

Since the integers are consecutive we have the following relationships:

\(\begin{gathered} n_2=n_1+2 \\ n_3=n_1+4 \end{gathered}\)

We are also given that two times the second equals the sum of the first and third. This can be expressed mathematically as:

\(2n_2=n_1+n_3\)

Now we can substitute the value of n3 from the previous relationship:

\(2n_2=n_1+n_1+4\)

Adding like terms:

\(2n_2=2n_1+4\)

We can also substitute the value of n3:

\(2(n_1+2)=2n_1+4\)

We get:

\(2n_1+4=2n_1+4\)

This is valid for any "n". Therefore any three consecutive integers are a solution.


Related Questions

physics
Consider a
man of mass sokg
standing lom from a woman with
a mass of skg. The attractive
grauitional force between them
would be?

Answers

The attractive gravitational force between the man and the woman can be calculated using the formula for the gravitational force:

F = G * (m1 * m2) / r^2

where F is the gravitational force, G is the gravitational constant (6.6743 × 10^-11 N·m^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass.

Substituting the given values, we get:

F = (6.6743 × 10^-11 N·m^2/kg^2) * [(50 kg) * (60 kg)] / (1 m)^2

F = 2.00329 × 10^-7 N

Therefore, the attractive gravitational force between the man and the woman is approximately 2.00329 × 10^-7 N.

Anatomy and physiology can be classified as ____ science

A. behavioral
B. life
C. physical
D. formal

Answers

B is your answer, hope it helps.

A grasshopper is an insect that goes through three distinct stages during its life cycle. The life cycle of a grasshopper is an example of which one of the following?

A. Quick metamorphosis
B. Slow metamorphosis
C. Complete metamorphosis
D. Incomplete metamorphosis

Answers

Answer:

B is the answer bc it's no way c an a and d can maybe c

From t=10.0 seconds to t=15.0 seconds, a space shuttle increased speed from 57 m/s to 99 m/s. What was the average acceleration of the shuttle

Answers

Answer:

   a = 8.4 m / s²

Explanation:

The mean acceleration is defined by

          a = (v_f- v₀) / (t_f - t₀)

where v are the final and initial velocities, respectively and t is the time interval

Let's apply this equation to our case

the final velocity is 99 m / s and the initial velocity is 57 m / s

         a = (99 - 57) / (15 - 10)

         a = 8.4 m / s²

3.
How much force does the atmosphere exert on one side of a vertical wall 4.00-m high and
10.0-m long? The atmospheric pressure is standard atmospheric pressure.
4.05 x 105 N
E)
C)
4.05 x 106N
A)
2.53 x 103 N
D)
zero N
101 x 105N

Answers

Answer:

4.05×10⁶ N.

Explanation:

The following data were obtained from the question:

Breadth (B) = 4 m

Length (L) = 10 m

Standard pressure (P) = 101325 Nm¯²

Force (F) =..?

Next, we shall determine the area of the wall. This can be obtained as follow:

Area (A) = length (L) × breadth (B)

A = 10 × 4

A = 40 m²

Finally, we shall determine the force exerted on one side of the wall as follow:

Standard pressure (P) = 101325 Nm¯²

Area (A) = 40 m²

Force (F) =.?

Pressure (P) = Force (F) /Area (A)

101325 = F/40

Cross multiply

F = 101325 × 40

F = 4.05×10⁶ N.

Therefore, a force of 4.05×10⁶ N was exerted on one side of the wall.

How are magnetic fields like vectors?

Answers

Answer:Magnetic fields from two sources add up as vectors at each point, so the strength of the field is not necessarily the sum of the strengths1. Magnetic fields are vectors, which means they have direction as well as size. Therefore, the sum of two magnetic fields is not simply the sum of their magnitudes2.

Explanation:

HELP PLEASE
What is the correct definition of amplitude?

A. the height of a wave

B. the distance between two crests or troughs

C. the number of complete waves that pass a point in a second

D. the time it takes for one complete wave to pass a given point

Answers

Answer:

correct answer is A) the height of a wave

Explanation:

i just did the test:)

The amplitude is used represent the height of the wave.

What is wave?

A wave is a disturbance in a medium that carries energy without a net movement of particles. In general, waves are classified into two types as Longitudinal and Transverse

Given is the amplitude of a wave.

Amplitude of a wave is equal to measure of the length of crest or trough. Crest and trough are the points that represents the maximum and minimum displacement of the wave with respect to the reference axis. The crest and the trough points are both at a equal straight line distance from the reference axis. This distance is also called height of the wave. The amplitude is the distance between the centerline and the Crest or trough. The general equation representing the amplitude of wave is x = A sin (ωt + ϕ) or x = A cos (ωt + ϕ) is the formula.

Therefore, the amplitude represents the height of the wave.

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Hey guys can you help me with this problem it's giving me a headache. "If 2500 kg roller coaster car begins its descent from 500m above above the first hill. What is its kinetic energy at the bottom of the hill."

Answers

The kinetic energy of the roller coaster at the bottom of the hill is 12250000 J

To answer this question, we must understand that the energy of a system is always conserved as explained by the law of conservation of energy.

The kinetic energy of the roller coaster will be equivalent to the potential energy of the roller coaster.

The kinetic energy of the roller coaster can be obtained as follow:

Mass (m) = 2500 KgHeight (h) = 500 mAcceleration due to gravity (g) = 9.8 m/s²Kinetic energy (KE) =?

Kinetic energy = Potential energy

KE = mgh

KE = 2500 × 9.8 × 500

KE = 12250000 J

Therefore, the kinetic energy of the roller coaster is 12250000 J

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An Eagar resident is driving down the road late at night at a velocity of 14 m/s. Suddenly an elk runs out in front of the car and the driver slams on the brakes. If the car comes to a stop (velocity final = 0 m/s) in 32 m, what is the acceleration of the car?

Answers

The acceleration of the car is approximately -3.06 m/s^2.

To find the acceleration of the car, we can use the kinematic equation:

v^2 = u^2 + 2as

Where:

v = final velocity = 0 m/s

u = initial velocity = 14 m/s

a = acceleration (to be determined)

s = displacement = 32 m

Plugging in the values into the equation, we can solve for acceleration:

0^2 = 14^2 + 2a(32)

Simplifying:

0 = 196 + 64a

Rearranging the equation:

64a = -196

Dividing both sides by 64:

a = -196/64

a ≈ -3.06 m/s^2

This means that every second, the car's velocity decreases by 3.06 meters per second. The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, opposing the car's motion and bringing it to a stop.

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Suppose the water at the top of Niagara Falls has a horizontal speed of 2.73 m/s just before it cascades over the edge of the falls. At what vertical distance below the edge does the velocity vector of the water point downward at a 52.9 ° angle below the horizontal?

Answers

Answer:

required vertical distance below the edge is 0.6648 m

Explanation:

Given the data in the question;

Horizontal speed of water falls v = 2.73 m/s

direction of water falls 52.9° below the horizontal

The vertical velocity must be such that;

tanθ = v\(_y\) / v\(_x\)

Now, vertical speed of water falls;

v\(_y\) = v\(_x\) × tanθ

we substitute

v\(_y\) = 2.73 × tan(52.9°)

v\(_y\) = 2.73 × 1.322237

v\(_y\) = 3.6097

Now, at the top of falls, initial speed u = 0

v² - u² = 2as

s = ( v² - u² ) / 2as

we substitute

s = ( 0² - (3.6097)² ) / (2 × 9.8)

s = 13.029934 / 19.6

s = 0.6648 m

Therefore, required vertical distance below the edge is 0.6648 m


For a circuit find the total potential differences if two resistors
of resistance R1 and R2 respectively kept series wise for a
current I passing through it.

Answers

-- If the two resistors are connected in series, then they behave like a single resistor whose resistance is (R₁ + R₂) ohms.

-- For any resistance, the potential difference (volts) across the resistance is   V = (current) x (resistance) .

-- So in THIS circuit,  V = I x (R₁ + R₂) .


What arguments can you think of for staying single

Answers

Answer:

Staying single makes it a whole lot easier to focus on yourself, gain self love, and work on yourself!

Explanation:

At its highest temperature, a space heater has a resistance of 17.5 Ω when it is plugged into a wall outlet that supplies a peak voltage of 176.8 V sinusoidally at 60 Hz . What is the average power output ⎯⎯⎯⎯ of the space heater?

Answers

At its highest temperature, a space heater has a resistance of 17.5 Ω when it is plugged into a wall outlet that supplies a peak voltage of 176.8 V sinusoidally at 60 Hz . the average power output of the space heater is 888 watts.

The average power output of the space heater can be calculated using the root mean square (RMS) values of the voltage and current. The RMS voltage and current are related to the peak voltage and the resistance of the space heater as follows:

V_RMS = V_peak / sqrt(2)

I_RMS = V_RMS / R

where V_RMS is the RMS voltage, I_RMS is the RMS current, V_peak is the peak voltage, and R is the resistance of the space heater.

Substituting the given values, we get:

V_RMS = 176.8 V / sqrt(2) = 124.8 V

I_RMS = 124.8 V / 17.5 Ω = 7.12 A

The average power output of the space heater is given by:

P_avg = V_RMS * I_RMS * cos(θ)

where cos(θ) is the power factor, which we will assume to be 1 for a resistive load like the space heater.

Substituting the values for V_RMS and I_RMS, we get:

P_avg = 124.8 V * 7.12 A * 1 = 888 W.

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Two billiard balls, each with a mass of 0.21 kg, collide with each other on a pool table. Before the collision, one ball is moving north at 1.7 m/s and the other ball is moving south at 2.6 m/s. What is the momentum of this system after the collision? A. 0.19 kg-m/s north OB. 0.19 kg m/s south C. 0.90 kg-m/s north D. 0.90 kg-m/s south​

Answers

Answer:

Explanation:

Ok I am an expert in this class. two balls which is 32 weighted for both. 21+21=41+1.7=42.7/4=10.7  

Both would=10.7

g A projectile of mass 3 kg is launched horizontally from an initial height 3 m with an initial velocity 10 m/s. This velocity in the x direction is preserved when you ignore air resistance. The projectile still accelerates in the vertical y direction toward the ground, but this is exactly the energy lost from potential energy. Energy is conserved as long as you use the total mechanical energy equation. What is the final kinetic energy as the projectile just reaches the ground

Answers

Answer:

The kinetic energy at ground will be "238.2 J".

Explanation:

The given values are:

mass,

m = 3 kg

Initial height,

h = 3 m

Initial velocity,

v = 10 m/s

By using the conservation of energy at points A and B,

⇒  \(E_A=E_B\)

⇒  \(mgh+\frac{1}{2}mv^2=k_B\)

On substituting the values, we get

⇒  \(3\times 9.8\times 3+\frac{1}{2}\times 3\times (10)^2=k_B\)

⇒             \(88.2+0.5\times 3\times 100=k_B\)

⇒                            \(88.2+150=k_B\)

⇒                                    \(238.2 =k_B\)

what is the Vector product of A=2.00i+3.00j+1.00k and B= 1.00i -3.00j -2,00k

Answers

The vector product of A=2.00i+3.00j+1.00k and B=1.00i-3.00j-2.00k is C=9.00i+4.00j-9.00k.

To find the vector product (also known as the cross product) of two vectors, A and B, we can use the following formula:

C = A × B

Where C is the resultant vector, A and B are the given vectors, and × denotes the cross product.

Given A = 2.00i + 3.00j + 1.00k and B = 1.00i - 3.00j - 2.00k, we can substitute these values into the formula to find the vector product:

C = (2.00i + 3.00j + 1.00k) × (1.00i - 3.00j - 2.00k)

Now, let's expand the cross product using the properties of vector products:

C = (2.00i × 1.00i) + (2.00i × -3.00j) + (2.00i × -2.00k) +

   (3.00j × 1.00i) + (3.00j × -3.00j) + (3.00j × -2.00k) +

   (1.00k × 1.00i) + (1.00k × -3.00j) + (1.00k × -2.00k)

Now, let's calculate each of these cross products:

C = (2.00 × 1.00) \(i^2\) + (2.00 × -3.00) i × j + (2.00 × -2.00) i × k +

   (3.00 × 1.00) j × i + (3.00 × -3.00) \(j^2\) + (3.00 × -2.00) j × k +

   (1.00 × 1.00) k × i + (1.00 × -3.00) k × j + (1.00 × -2.00) \(k^2\)

Since i × j = k, j × k = i, and k × i = j, we can simplify the expression further:

C = 2.00k - 6.00i + 4.00i - 9.00j + k - 3.00j - 2.00j - 2.00k

Combining like terms, we get:

C = (2.00i + 4.00i) + (-6.00i - 9.00j - 3.00j) + (2.00k + k - 2.00k)

Simplifying further:

C = 6.00i - 12.00j + k

Therefore, the vector product of A and B is C = 6.00i - 12.00j + k, which can be written as C = 9.00i + 4.00j - 9.00k in terms of i, j, and k.

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Final answer:

The vector product of A and B is -3i - 5j - 9k.

Explanation:

The vector product, also known as the cross product, of two vectors A and B is denoted as A x B. It is a vector that is perpendicular to both A and B. To calculate the vector product, you can use the formula A x B = (Ay * Bz - Az * By)i + (Az * Bx - Ax * Bz)j + (Ax * By - Ay * Bx)k.

In this case, we have A = 2.00i + 3.00j + 1.00k and B = 1.00i - 3.00j - 2.00k. Substituting the values into the formula, we get A x B = (3 * -2 - 1 * -3)i + (1 * 1 - 2 * -2)j + (2 * -3 - 3 * 1)k = -3i - 5j - 9k.

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An electron has a mass of 9.1x10^-31 kg and a charge
of -1.6x10^-19 C. Suppose you could isolate one electron in
a perfect vacuum and then create an electric field to pull
and edi 107. upward on the electron. How strong would the field have to
be to counteract the electron's weight? (In other words,
di Delfine bu how strong would the field have to be to put the electron in
a state of force equilibrium?)

Answers

is one of these the question

An electron has a mass of 9.1x10^-31 kg and a chargeof -1.6x10^-19 C. Suppose you could isolate one electron
An electron has a mass of 9.1x10^-31 kg and a chargeof -1.6x10^-19 C. Suppose you could isolate one electron

why fur coats would keep their owners warmer if they were worn inside out?​

Answers

Answer:

The reason why this is, is because:

Explanation:

According to Jones, fur serves as an insulator for the body during cold weather and regulates the process of heat absorption during warm weather. It acts as a thermal regulator, preventing the body from taking on excessive heat. Dogs and cats shed their fur in hot weather to make their coats more appropriate for heat protection rather than warmth.

Answer:

Insulation

Explanation:

The reason for this is insulation, which describes the process of an object absorbing heat and harboring heat. It works as such: Fur protects you from the cold by forming what’s called a “boundary layer.” This happens as cold air hits the surface of your coat and the molecules cause friction.

a ball is thrown straight up into the air with an initial speed of 3.1 m/s. a. After 0.24 seconds what is the ball's velocity and b. what is it's acceleration?

Answers

a. The ball's velocity after 0.24 s is 0.75 m/s

b. The acceleration of the ball is given by the acceleration due to gravity

a. The ball's velocity can be calculated with the following equation:

\( v_{f} = v_{0} - gt \)

Where:

\( v_{f} \): is the final speed =?

\(v_{0}\): is the initial speed = 3.1 m/s

g: is the acceleration due to gravity = 9.81 m/s²

t: is the time = 0.24 s

The minus sign is because the acceleration is in the opposite direction (downward) of the motion of the ball (upward).

The final speed is:

\( v_{f} = v_{0} - gt = 3.1 m/s - 9.81 m/s^{2}*0.24 s = 0.75 m/s \)

Hence, the ball's velocity after 0.24 s is 0.75 m/s.

b. The acceleration of the ball is given by the acceleration due to gravity because the ball is thrown straight up (the motion of the ball is in the y-direction). The velocity of the ball in the x-direction is zero so the acceleration in the same direction is also zero.  

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The number of hours
of daylight tat a location receives varies depending on how far north or south it is from the

Answers

Answer:

equator

Explanation:

in south & north pole you could have 20+ hours daylight or night, everyday!

true or false:The potential energy of an object is affected by its speed

Answers

True because the speed of a mass can change it's gravitational potential energy in the gravitational field of another massive object.

45.678 g to 4 digits

Answers

Answer:

45.68 g

Explanation:

Given 45.678 g, converting the value to 4 digits is similar to converting the decimal number to 4 significant figure. We can see that the decimal number initially contains 5 numbers. To covert to a 4 digits number we will convert the last digit which is 8 to 0 because 0 is insignificant.

If the number we are converting to zero is more than 4 then the preceding number (7) will be rounded up by adding 1 to it

The decimal number will become 45.68.

Note that the value of 7 was rounded up to 8 since the value we are converting to zero is more than 4.

Hence the decimal value in 4 digits is 45.68 g

Cart A with a mass of 28kg is moving to the RIGHT at 11m/s and Cart B with a mass of 17kg is moving LEFT at negative 9m/s. The carts collide and STICK TOGETHER. What is the velocity of the carts after they collide?

Answers

Answer:

Should be 17.8m/s

Explanation:

Initial momentum = Final momentum

(m1×v1)+(m2×v2)=(m1+m2)v since its an inelastic collision.

7. A football is kicked into the air vertically upwards. What is its a) Velocity at the highest point? b) Acceleration at the highest point?

Answers

Given that a football is kicked into the air vertically upwards, let's determine the following:

(a) Velocity at the highest point.

As the ball is kicked vertically up, it has an initial velocity.

As the ball moves up, the velocity decreases because of the force of gravity acting on it.

When the ball reaches the highest point, the velocity of the ball will be zero.

Therefore, the velocity of the ball at the highest point is zero.

(b) Acceleration at the highest point.

The acceleration of the ball as it is kicked up is equal to the acceleration due to gravity.

Where:

Acceleration due to gravity, g = 9.8 m/s².

Since the ball is moving upwards, the acceleration due to gravity is acting vertically downwards which makes the acceleration of the ball constant.

The acceleration of the football at the highest point is the opposite of acceleration due to gravity = -9.8 m/s².

ANSWER:

• a) Velocity at the highest point is 0.

,

• b) Acceleration at the highest point is -9.8 m/s².

How much heat must be added to a gas that does 10 J of work in an isothermal process?

How much heat must be added to a gas that does 10 J of work in an isothermal process?

Answers

Answer:

10 J

Explanation:

Using the idea of the first law of thermodynamics to answer this question.

The first law of thermodynamics simply restates energy conservation: Energy is not created nor is it destroyed it is simply transformed into other forms of energy. It can be stated in the following formula,

\(\boxed{\left\begin{array}{ccc}\text{\underline{The First Law of Thermodynamics:}}\\\\\Delta E_{int.}=Q-W_{by}\end{array}\right}\)

In a isothermal process the change in internal energy is equal to zero. So plug in what we know.

\(\Longrightarrow \Delta E_{int.}=Q-W_{by}\\\\\Longrightarrow 0=Q-10\\\\\Longrightarrow \boxed{Q=10 \ J}\)

Thus, 10 J of heat must be added to the gas.

Please solve this, I’ll give brainliest if it’s correct but
AI answers will be reported!

Q6. Saul (30 kg) is tobogganing down a hill on a toboggan that has a mass of 10 kg. Part way down, when he is still 20 m (measured vertically) above the bottom of the hill, he passes his sister Nadia at a velocity of 15 m/s. [9 marks]

(a) What is the total energy of Saul and the toboggan?

(b) What is the height of the hill?

(c) What will Saul’s velocity at the bottom of the hill be?

(d) What will Saul’s height be when he is moving at a velocity of 9.5 m/s?

Answers

part a.

the total energy of Saul and the toboggan  is 70530 J

part b.

The height of the hill is  235.1 m.

part c.

Saul's velocity at the bottom of the hill will be  22.3 m/s.

part d.

Saul's height when he is moving at a velocity of 9.5 m/s is 10.5 m

How do we calculate?

The total energy of Saul and the toboggan is the addition all of potential energy and kinetic energy.

we know that the initial total energy = potential energy at top of hill

Therefore total energy is gien as

initia total energy  = mass of Saul + mass of toboggan x gravity x height

initia total energy  = (30 kg + 10 kg) x (9.81) x (20 m)

initia total energy  = 5886 J

Total energy  = potential energy + kinetic energy

Total energy = (30 kg + 10 kg) (9.81 ^2) x (20) + (30 kg + 10 kg) x (15)^2/2

= 70530 J

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does the stirling engine follow the law of conservation energy

Answers

Answer:

Conservation of Energy: Like all things, Stirling Engines follow the conservation of energy principle (all the energy input is accounted for in the output in one form or another). ... The hot one supplies all of the energy QH, while the cold one removes energy QC (a necessary part of the cycle).

Explanation:

Answer: Yes

Explanation: All the energy input is accounted for in the output in one form or another

Suppose you have a 115 kg wooden crate resting on a wood floor, with coefficient of static friction 0.500 between these wood surfaces. (Enter the magnitudes.) (a) What maximum force (in N) can you exert horizontally on the crate without moving it

Answers

Answer:

maximum force (in N) can you exert horizontally on the crate without moving it = 564.075 N

Explanation:

Given data:

mass m= 115 kg

coefficient of friction μ =0.5

according to newton law of motion the net force acted on body is given by

\(F_{net}=ma=F_{max}- F_{f}\)

here the body is in rest ,

\(F_{net}=0\\\Rightarrow F_{max}=F_{f}\\\text{frriction force}  F_{f} = \mu\times N\\\)

N= it is the normal reaction force

N= mg = 115×9.81

therefore,

\(F_{f} = 0.5\times115\times9.81 = 564.075 N = F_{max}\)

A certain car traveling 33.0mph skids to a stop in 39m from the point where the brakes were applied. In approximately what distance would the car stop had it been going 66.0mph

Answers

Answer: 156.02 metre.

Explanation:

Give that a certain car traveling 33.0mph skids to a stop in 39m from the point where the brakes were applied.

Let us use third equation of motion,

V^2 = U^2 + 2as

Since the car is decelerating, V = 0

And acceleration a will be negative.

U = 33 mph

S = 39 m

Substitute both into the formula

0 = 33^2 - 2 × a × 39

0 = 1089 - 78a

78a = 1089

a = 1089 / 78

a = 13.96 m/h^2

If we assume that the car decelerate at the same rate.

the distance the car will stop had it been going 66.0mph will be achieved by using the same formula

V^2 = U^2 + 2as

0 = 66^2 - 2 × 13.96 × S

4356 = 27.92S

S = 4356 / 27.92

S = 156.02 m

Therefore, the car would stop at

156.02 m

An experiment invilves three charges objects: A, B, and C. Object A repels object B and attracts onject C. object C ir repelled by ebonite charged with fur. What is the charge on the object?

Answers

Answer:

A and B is positive charge

C_negative

Explanation:

because when an ebonite is rubbed with fur produce negative charge due to law of electrostatic like charge repel and unlike attract

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