Why is the combination of two protons and two neutrons stable, but two protons and one neutron is not?

Answers

Answer 1
Because it's unbalanced.
Answer 2

Answer:

There are not enough neutrons to overcome the electrical repulsion of the protons.

Explanation:

Neutrons help stabilize a nucleus by attracting other nucleons (protons and neutrons). Although protons also attract other nucleons using the strong nuclear force, they repel other protons with the electrical force.

Hope this helps!


Related Questions

A container of gas is at a pressure of 1.3x10^5 Pa and a volume of 6 m^3. How much work is done by the gas if it expands at a constant pressure to twice its initial volume.

Answers

Final answer:

The work done by the gas is 7.8x10^5 J.

Explanation:

To determine the work done by the gas as it expands at a constant pressure, we can use the formula:

Work = Pressure x Change in Volume

Given that the initial volume is 6 m^3 and the gas expands to twice its initial volume (12 m^3), the change in volume is 12 m^3 - 6 m^3 = 6 m^3. The given pressure is 1.3x10^5 Pa. Plugging these values into the formula:

Work = (1.3x10^5 Pa) x (6 m^3) = 7.8x10^5 J

PLEASE HELP The rotating light on a lighthouse is 400 feet from a cliff. It completes one rotation every 10 seconds. The equation representing the distance, d, in feet that the center of the circle of light is from the lighthouse is d(t) = 400sec (πt/5). What is the period of d(t)? (Enter only the number.) ...?

Answers

The period is [2(pi)] / |b| 

so, it would be 2pi / pi/5 = 10 

for the second part, just plug in 10 where the "t" is. 

400sec(10pi/5) or 400sec(2pi) 

Sec = 1 / cos 

SO, you get 400*(1/cos(2pi)) = 400* 1/1 = 400. since cos(2pi) = 1 
so you get 400 as your answer 


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

This part of the electromagnetic spectrum can be used to generate power.
a. gamma rays
b. radio waves
c. microwaves
d. infrared rays

Answers

A.) Gamma Rays are your answer.

Hope this helps!

Answer

a. gamma rays


Explanation

Gamma rays are the electromagnetic waves with the highest frequency. They are the waves with the smallest wavelength.

Due to their high frequency they can produce more energy. They are the most energetic waves or the most powerful.

A 1.4 kg block slides across a rough surface such that it slows down with an acceleration of 1.25 m/s(squared). What is the coefficient of kinetic friction between the block and the surface?
Help please. Show steps. ...?

Answers

The coefficient of kinetic friction for the block k slides across a rough surface is 0.128.

What is Newtons second law of motion?

Newtons second law of motion shows the relation between the force mass and acceleration of a body.

It says, that the force applied on the body is equal to the product of mass of the body and the acceleration of it.

It can be given as,

[tex]F=ma[/tex]

Here, (m) is the mass of the body and (a) is the acceleration.

Step 1) Find the friction force-

As the mass of the block is 1.4 kg and the acceleration of it is 1.25 m/s (squared). Therefore the friction force can be given as using the above formula as,

[tex]F_f=1.4\times1.25\\F_f=1.75\rm N[/tex]

Step 2) Find the normal force-

The normal force acting on it due to gravity force is,

[tex]F_n=1.4\times9.8\\F_n=13.72\rm N[/tex].

Step 3) Find the coefficient of kinetic friction[tex](\mu)[/tex]-

Now the friction force acting on a moving body is equal to the product of normal force acting on it and the coefficient of kinetic friction.

Thus, the coefficient of kinetic friction[tex](\mu)[/tex] can be given as,

[tex]F_f=F_N\times\mu\\1.75=13.72\times \mu\\\mu=0.128[/tex]

Hence, the coefficient of kinetic friction for the block k slides across a rough surface is 0.128.

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What is depth perception?

Answers

Depth perception is the way in which some animals, such as humans, can tell if a object is close or far away from them.

Explanation:

Depth perception is the ability that humans have to perceive depth. With depth perception animals are able to see something in three dimensions. The configuration of the eyes allows animals to see depth.

Having two eyes that is having binocular vision gives animals an accurate sense of depth. Animals have evolved in such a way that gives us depth perception. In order for animals to survive in a three dimensional world depth perception is vital.

Which statement is true concerning the evidence for black holes?

Scientists can see black holes with powerful telescopes.

Scientists can see the effect of black holes on nearby stars.

Scientists can see trails left in space by black holes.

There is no evidence for black holes.

Answers

Scientists can see the effect of black holes on nearby stars is true concerning the evidence for black holes.

what social science involves studying legal policies?

political science

history

economics

law

Answers

I believe it's political science.

Answer: law

Explanation:

Social science can be define as the scientific study of human society and their  relationship among themselves.

A law can be define as rules which is enforced over the society to regulate it's functioning, restricting the ill-legitimate activities like crime, and safeguarding the rights of the human beings, and animals.

On the basis of the above description, the law is the social science which involves the studying of the legal policies.

Please help!
Find the tension in each cord in the figure if the weight of the suspended object is w = 210N

A) Find the tension in the cord A for system (b).
B) Find the tension in the cord B for system (b).

Answers

We have to solve the system of equations:
- T a * cos 60° + T b * sin 45° - 210 N = 0
- T a * sin 60° + Tb cos 45° =  0
------------------------------------------------------
- 1/2 T a + √2 / 2 T b = 210 N
- √3 / 2 T a + √ 2 / 2 T b = 0     / * ( - 1 )
---------------------------------------------------
- 1/2 T a + √2 / 2 T b = 210 N
√ 3 / 2 T a - √2 / 2 T b = 0
----------------------------------------
T a ( √3 / 2 - 1 / 2 ) = 210 N
0.366 T a = 210 N
T a = 210 N : 0.366
1 ) T a = 573.77 N
Ta * √3 / 2 = T b * √ 2 / 2
T b = ( 573.77 * 1.732 ) : 1.4142
2 ) T b = 702.7 N 

A) Tension in the cord A ≈ 570 Newton

B) Tension in the cord B ≈ 700 Newton

[tex]\texttt{ }[/tex]

Further explanation

Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.

[tex]\large {\boxed {F = ma }[/tex]

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

[tex]\texttt{ }[/tex]

Given:

weight of the suspended object = w = 210 N

Asked:

tension in the cord A = T_A = ?

tension in the cord B = T_B = ?

Solution:

Let:

γ = 360° - 60° - 45° - 90° = 165°

α = 90° + 45° = 135°

β = 60°

[tex]\texttt{ }[/tex]

We will use Lami's Theorem in this question.

If the system is in equilibrium , then:

[tex]\large {\boxed{\frac{T_A}{\sin \alpha} = \frac{w}{\sin \gamma}}}[/tex]

[tex]T_A = w \times \frac{\sin \alpha}{sin \gamma}[/tex]

[tex]T_A = 210 \times \frac{\sin 135^o}{sin 165^o}[/tex]

[tex]T_A = 210 \times ( 1 + \sqrt{3} )[/tex]

[tex]T_A \approx 570 \texttt{ Newton}[/tex]

[tex]\texttt{ }[/tex]

[tex]\large {\boxed {\frac{T_B}{\sin \beta} = \frac{w}{\sin \gamma}}}[/tex]

[tex]T_B = w \times \frac{\sin \beta}{sin \gamma}[/tex]

[tex]T_B = 210 \times \frac{\sin 60^o}{sin 165^o}[/tex]

[tex]T_B = 210 \times \frac{1}{2}( 6 + 3\sqrt{2} )[/tex]

[tex]T_B \approx 700 \texttt{ Newton}[/tex]

[tex]\texttt{ }[/tex]

Learn moreImpacts of Gravity : https://brainly.com/question/5330244Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454The Acceleration Due To Gravity : https://brainly.com/question/4189441Newton's Law of Motion: https://brainly.com/question/10431582Example of Newton's Law: https://brainly.com/question/498822

[tex]\texttt{ }[/tex]

Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

[tex]\texttt{ }[/tex]

Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant

10 kg cart and a 5 kg cart are placed on identical surfaces. The 10 kg cart experiences a net force of 12 N to the left, while the 5 kg cart experiences a net force of 8 N to the left. Compare and contrast the motion of the two carts.

Answers

F=ma

For the first (10kg) cart,
12=10a
a=6/5 m/s^2 to the left

For the second (5kg) cart,
8=5a
a=8/5 m/s^2 to the left

Therefore, the lighter (5kg) cart experiences a greater acceleration.
Final answer:

The 10 kg cart and 5 kg cart under different net forces will move to the left but with different accelerations. Despite the larger force acting on the 10 kg cart, the lighter 5 kg cart will actually accelerate at a greater rate.

Explanation:

Comparing the motion of a 10 kg cart experiencing a net force of 12 N to the left and a 5 kg cart experiencing a net force of 8 N to the left involves the principles of Newton's second law of motion, F=ma. For the 10 kg cart, the acceleration is found by dividing the force by mass(12 N / 10 kg), which equals 1.2 m/s² to the left. For the 5 kg cart, the acceleration is (8 N / 5 kg), which equals 1.6 m/s² to the left.

Therefore, despite the 10 kg cart experiencing a larger force, the 5 kg cart actually accelerates at a greater rate due to its lighter mass. This illustrates the principle that net force not only depends on the magnitude of the force but also on the mass of the object it is acting on.

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The temperature of water in a beaker is 45°C. What does this measurement represent?

Answers

Temperature represents the degree of "Hotness" or "Coldness" of the body so, 45 C represents that it's neither a cold nor very hot.

Hope this helps!

Answer:

the average kinetic energy of water particles

Explanation:

A bird flies from the South Pole to the North Pole. Part of the journey is 1000 miles that takes 2 weeks. What is the bird’s velocity in that time?

Answers

We Know, Velocity = Distance / Time
Here, Distance = 1000 miles
Time = 2 weeks = 14*24 Hours  [ 1 week = 7 days & 1 day = 24 hours ] 
Time = 336 Hours

Now, substitute the values,
Velocity = 1000/336 = 2.976 miles/hour

So, your final answer is 2.976 miles/hour 

Hope this helps! Happy studying :)

W
Which statement best describes how the period and frequency of electromagnetic waves change between gamma rays and microwaves?
A) The period and the frequency stay the same.
B) The period increases and the frequency decreases.
C) The period decreases and the frequency increases.
D) The period increases and the frequency increases.

Answers

B) The period increases and the frequency decreases.

Hope this helps!

Answer:

B) The period increases and the frequency decreases.

Explanation:

Gamma rays are high energy rays which means these rays have high frequency. Microwaves have low energy and low frequency. For electromagnetic wave change between gamma rays to microwaves, the frequency decreases and period increases.

[tex]T= \frac{1}{f}[/tex]

Thus, option B is correct.

You have 9 stones that are identical in appearance. One of these stones weighs just a bit more than the other 8. These other 8 stones are exactly the same in weight. Using a balance scale only TWICE, how can you determine exactly which stone is the heavier?

Answers

i think you can weigh it 3 and 3.
If they balance, choose set not used.

If not balanced, take the heavier side

then weigh 1 and 1
if balanced, stone not used, if not balanced, take the heavier side

hope this helps

A 50.0-kg wolf is running at 10.0 m/sec. What is the wolfs kinetic energy

Answers

kinetic energy = mass time squared speed divided by 2 
W=mv^2/2 = 50*10*10/2 = 2500 J

Final answer:

The kinetic energy of the wolf is 2500J.

Explanation:

The kinetic energy of the wolf can be calculated using the formula: Kinetic Energy = 0.5 x mass x velocity^2. Plugging in the given values, we have: Kinetic Energy = 0.5 x 50.0 kg x (10.0 m/sec)^2. Solving this equation will give us the wolf's kinetic energy.

Given values:

- Mass (m) = 50.0 kg

- Velocity (v) = 10.0 m/s

Using the formula for kinetic energy:

Kinetic Energy (KE) = 0.5 x mass x velocity^2

Plugging in the values:

KE = 0.5 x 50.0 kg x (10.0 m/s)^2

Calculating the square of the velocity:

KE = 0.5 x 50.0 kg x 100.0 m^2/s^2

Now, calculate the product:

KE = 2500.0 kg m^2/s^2

The unit of kinetic energy is joules (J), so we can rewrite it as:

KE = 2500.0 J

Therefore, the wolf's kinetic energy is 2500.0 joules (J).

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what connects neurons and what chemicals help neurons communicate

Answers

The neurons are connected, with a tiny gap between them called the synapse, by dendrites. Neurotransmitters are chemical compounds that carry signals across the synapse.

Answer:

synapses

The chemical that helps them to communicate is neurotransmitters

Explanation: synapses have a receiving end and a sending end that helps them receive signal transmitted through the neurotransmitters

What is the magnitude of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 35 cm?

Answers

The magnitude of the acceleration of a speack of clay on the edge of potter's wheel turning at 45 rpm if the wheels diameter is 35cm ?

4.66 is your answer. 

OK.  We can do this !  Fasten your seat belt.

The formula we need is:  A = V²/R
                           Centripetal acceleration = (speed)² / (radius) .

Also        V  =  D / T           Speed = (distance) / (time).

with everything in meters, kilograms, and seconds.

Circumference of the wheel = (π · diameter) = 0.35 π  meters.

Speed = (0.35π m) x (45 / minute) x (1 minute / 60 sec)

           = (0.35π · 45 / 60) m/sec

           =     0.2625π m/sec

Acceleration  =  (speed²) / (radius)

                    =  (0.2625π m/s)² / (0.175 m)

                    =  (0.06890625π² / 0.175)  m² / s²·m

                    =     3.89  m / s²

Which of the following is true about melting and freezing points?

Choices:

A. The melting point is always the same as the freezing point.
B. The melting point is achieved at a higher temperature than the freezing point.
C. The freezing point is applied to liquids, whereas the melting point is applied only to gases.
Which of the following is true about melting and freezing points?

Choices:

A. The melting point is always the same as the freezing point.
B. The melting point is achieved at a higher temperature than the freezing point.
C. The freezing point is applied to liquids, whereas the melting point is applied only to gases.

Answers

Answer:

Explanation:

I agree with what the first person said

Final answer:

The correct answer is that the melting point and freezing point of a substance are always the same, illustrating the equilibrium between the solid and liquid states of that substance at a specific temperature, such as 0°C for water.

Explanation:

The correct answer to which of the following is true about melting and freezing points is: The melting point is always the same as the freezing point. This principle is crucial in understanding the thermal properties of substances. The temperature at which a substance changes from solid to liquid (melting point) is the same temperature at which it changes from liquid to solid (freezing point) when the process is reversible and under the same pressure conditions. For instance, with water (H₂O), this equilibrium occurs at 0°C, illustrating that at this temperature, the solid and liquid states of H₂O are in equilibrium (H₂O (s) = H₂O (l)).

It's essential to refute common misconceptions like the melting point being higher than the freezing point or that these concepts apply differently to liquids and gases. All materials, whether solid, liquid, or gas at room temperature, have characteristic melting/freezing points that do not depend on their state at room temperature but rather on their inherent thermal properties.

t (sec) 0.0 - 0.5 - 1.0 - 1.5 - 2.0 - 2.5 - 3.0 - 3.5 - 4.0
s (ft) 12.5 - 26 - 36.5 - 44 - 48.5 - 50 - 48.5 - 44 - 36.5
Assuming that this smooth curve represents the motion of the body, estimate the velocity at t = 1.0, t = 2.5, and t = 3.5.

Answers

 Well let me help you here. My suggestion is that you use your favorite technique to find a smooth curve that fits the data points 
reasonably well. Lets remember that  the t values are equally spaced, I'd use Newton's forward difference formula 
It tells you that s(t) = 12.5 + 30t - 6t², and this fits the data perfectly. 
So s'(t) = 30 - 12t,
Apply what im telling you and yu will get to the result

How long is a pendulum with a period of 1.0 S on the moon which has 1/6 of the earths gravity

Answers

Final answer:

To find the length of a pendulum with 1.0 seconds on the Moon, we use the formula for a pendulum's period, adjust the acceleration due to gravity to the Moon's 1.63 m/s², and solve for the pendulum's length.

Explanation:

The subject question inquires about the length of a pendulum on the Moon that has a period of 1.0 seconds, taking into consideration that the Moon's gravity is 1/6th that of Earth's. The formula for the period of a simple pendulum is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

On Earth, assuming the acceleration due to gravity (g) is approximately 9.81 m/s², the length (L) for a pendulum with a period (T) of 1.0 seconds can be calculated using this formula. However, since we are interested in the situation on the Moon where g is 1/6th that of Earth's, we would have to adjust the acceleration due to gravity in our formula to be 1.63 m/s² (since 9.81 m/s² divided by 6 equals approximately 1.63 m/s²).

Accordingly, by rearranging the formula to L = T²g/(4π²), and substituting T with 1.0 second, and g with 1.63 m/s², one can compute the appropriate length of the pendulum on the Moon that would have a period of 1.0 second.

Final answer:

The length of a pendulum with a period of 1.0 second on the Moon can be calculated by rearranging the period formula for a simple pendulum, T = 2π√(L/g), and substituting in the Moon's gravity of 1.63 m/s².

Explanation:

The length of a pendulum that has a period of 1.0 second on the Moon, where gravity is 1/6th of Earth's gravity, can be found using the formula for the period of a simple pendulum, T = 2π√(L/g). On Earth, where the standard acceleration due to gravity, g, is approximately 9.81 m/s², a 1.0-second period requires a certain pendulum length. However, on the Moon, the acceleration due to gravity is only 1.63 m/s².

We can rearrange this formula to solve for the length (L) of the pendulum on the Moon: L = (T² * g) / (4π²). By substituting T for 1.0 second and g for 1.63 m/s², the length of the pendulum on the Moon can be calculated.

Using the provided formula, we get L = (1.0² seconds² * 1.63 m/s²) / (4π²) which gives us the length of the pendulum on the Moon. You would then perform the calculation to find the exact value for L.

Which three statements about electromagnetic radiation are true?
1)Light is a kind of electromagnetic radiation.
2)Electromagnetic radiation can travel only short distances.
3)Electromagnetic radiation has no mass.
4)Electromagnetic radiation can travel through a vacuum.
5)All kinds of electromagnetic radiation are invisible.

Answers

Answers

1)Light is a kind of electromagnetic radiation.

3)Electromagnetic radiation has no mass.

4)Electromagnetic radiation can travel through a vacuum.

Explanations

Electromagnetic waves are waves that can travel through vacuum. that is they do not require material medium for propagation.

Light is in the electromagnetic spectrum.

Electromagnetic waves can travel through a long distance. For instance, radio waves are electromagnetic radiations that travel long distances.

Electromagnetic radiations carry energy with it but no mass.

Some of the electromagnetic radiations are visible such as visible light.

I'LL GIVE ONE OF YOU BRAINLIEST ANSWER. PLEASE HELP ME
a) The electric field between two equally but oppositely charged parallel plates is 2.35 N/C [south]. If a charge of –2.00 C was placed at the midway point between the plates, what force (magnitude and direction) would act on the charge?
Give the direction as acting north or south. b) For another set of parallel plates, a charge of –4.00 C experiences a force of 6.00 x 10–3 N [east]. Determine the magnitude and direction of the electric field between these plates. Give the direction as east or west. (continued) 58 G r a d e 1 2 P h y s i c s Assignment 7.4: Electric Field between the Plates of a Parallel Plate Capacitor (continued) d) Label each plate in the diagram below with the appropriate polarity according to the information from part (c) above

Answers

a) The magnitude of the electric field = (electric force)/(charge of particle)

Electric force = (charge of particle) (electric field magnitude)
= (2 C)(2.35 N/C) = 4.7 N

(electric force and electric field are always in the same direction)
so, force = 4.7 N south

b) Electric field magnitude = (electric force)/(particle charge)
= (6*10^-3 N)/(-4 C) = -0.0015 N/C = -1.5*10^-3 N/C east

For part d, I think I'll need to see part c first. 

The height of a sinusoidal wave is called its
a. phase.
b. amplitude.
c. period.
d. frequency.

Answers

The height of a sinusoidal wave is called its "Amplitude"

So, option B is your answer.

Hope this helps!

Answer:

The height of a sinusoidal wave is called its amplitude.

Explanation:

The height of a sinusoidal wave is called its amplitude. It is also defined as the maximum displacement of the particles of the waves. It the distance between the rest position to the crest or the rest position to the trough of the wave. The amplitude of a wave measures its intensity.

The intensity of a wave is directly proportional to the square of its amplitude.

So, the height of a sinusoidal wave is called wave's amplitude. So, the correct option is (b) "amplitude".

What is the mass of an object with a density of 13.5 g/cm3 and a volume of 5cm3?

Answers

density d=m/V

mass m=d.V=13.5×5=67.5g

m=67.5g

hope this helps you

How much force is needed to stop a 90-kg soccer player if he decelerates at 15 m/s²? A. 6 N B. 15 N C. 135 N D. 1350 N

Answers

The answer is: D. 1350 N

The answer is 1350 N

The pull of the moon on Earth's tidal bulge is causing

Answers

The pull of the moon on Earth's tidal bulge is causing The moon to slowly move farther away from the Earth. Hope that helps.
The gravitational attraction of the moon causes the oceans to bulge out in the direction of the moon. Another bulge occurs on the opposite side, since the Earth is also being pulled toward the moon (and away from the water on the far side). Ocean levels fluctuate daily as the sun, moon and earth interact.

What do telescopes detect that assists astronomers making discoveries in space

Answers

Telescopes help astronomers to view the stars in a closer view than the naked eye can see.
Final answer:

Telescopes assist astronomers by detecting and analyzing light from celestial objects in great detail, enabling scientists to view distant objects and investigate their properties, including the chemistry of their atmospheres. They provide insight into the deep time and space of the universe.

Explanation:

Telescopes play an integral role in astronomical discoveries as they allow us to detect and analyze light and other forms of electromagnetic radiation from celestial objects. The key components in telescopes that make this possible are their light-gathering power and high-resolution imaging capabilities.

Telescopes gather more light than the human eye, allowing them to observe dim and distant objects in more detail. They can detect images and spectra of planets and galaxies, some of which are so distant that their light has traveled for billions of years to reach us. This provides profound insight into the structure of the universe and the life cycles of celestial bodies.

Moreover, by observing the chemistry of these planets' atmospheres, telescopes enable astronomers to search for signs of extraterrestrial life. Advanced telescopes such as the Hubble Space Telescope and the Very Large Telescope in Chile provide views of deep space and deep time – periods of time deep in the past – at an unrivaled resolution.

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When baking soda and vineager react, the surface bubbles. what does this most likely indicate?

Answers

A chemical change because a gas is being formed

Answer:

Chemical

Explanation:

its bubbling

Describe the circumstances for which the output work would equal the input work in a machine

Answers

The output work circumstances would be the fact that the machine could do a good amount of time at a good pace, and distance. where the machine doesn't need any help to be controlled. the input work would be you being able to use the machine with no difficulty. you are the client the machine is your server, you command, and the machine obeys.

During an investigation, a student determines that a copper sample has a density of 8.10 g/ml. What is the students percent error of the accepted density for copper is 8.96 g/ml

Answers

During an investigation, a student determines that a copper sample has a density of 8.10 g/ml. What is the students percent error of the accepted density for copper is 8.96 g/ml

a particle moving along the x axis has the position x(t) at time t with the velocity of the particle given by v(t)=5sin(t^2). At time t=6, the particles position is (4,0). Find the position of the particle when t=7...

please and thank you :) ...?

Answers

Final answer:

To find the position of the particle when t=7, integrate the velocity function to obtain the position function. Substitute a given position value to determine the constant of integration. Finally, plug in t=7 into the position function and evaluate to find the position of the particle.

Explanation:

To find the position of the particle when t=7, we need to integrate the velocity function from t=6 to t=7. The velocity function v(t) = 5sin(t^2) represents the rate of change of position with respect to time. Integrating this function gives us the position function x(t) = -5cos(t^2) + C, where C is a constant of integration.

We can find the value of C by substituting the given position x(6) = 4.0 into the position function. Plugging in t=6 and x=4.0, we get 4.0 = -5cos(6^2) + C. Solving for C, we find C = 4.0 + 5cos(6^2).

Now we can find the position of the particle when t=7 by plugging in t=7 into the position function x(t) = -5cos(t^2) + C, where C is the value we obtained earlier. Evaluating the expression, we find x(7) = -5cos(7^2) + (4.0 + 5cos(6^2)). Therefore, the position of the particle when t=7 is approximately (0.609, 0).

Final answer:

The position of the particle at t=7 can be determined by integrating the given velocity function v(t) = 5sin(t^2) from t=6 to t=7 and adding the result to the known position at t=6. The integral does not have an elementary antiderivative, so numerical methods are needed for evaluation.

Explanation:

The position of the particle, while it moves along the x-axis, can be found by integrating the velocity function. Since the velocity is given by v(t) = 5sin([tex]t^2[/tex]), we will integrate this with respect to time to find the position function x(t). Given that the particle's position at time t=6 is (4,0), we can use this information to find the constant of integration after integrating the velocity function.

To find the position x(t) at any time t after t=6, we would calculate the integral of the velocity function from 6 to t, and add this to the initial position at t=6:

∫6t 5sin(τ2)dτ + 4

To find the position at t=7, we would evaluate this integral from 6 to 7, which requires a numerical method since the integral of sin(t2) is not an elementary function. Once the integral is evaluated, this value is added to 4 (the position at t=6) to determine the final position of the particle at t=7.

Other Questions
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