the radius of a ball is increasing at a rate of 2 mm per second. how fast is the volume of the ball increasing when the diameter is 40 mm

Answers

Answer 1

Step 1: Define an equation that relates the volume of a sphere to its radius.

V = 4/3*π*r3

Step 2: Take the derivative of each side with respect to time (we will define time as "t").

(d/dt)V = (d/dt)(4/3*π*r3)

dV/dt = 4πr2*dr/dt

Step 3: We are told in the problem statement that diameter is 100m, so therefore r = 50mm. We are also told the radius of the sphere is increasing at a rate of 2mm/s, so therefore dr/dt = 2mm/s. We are looking for how fast the volume of the sphere is increasing, or dV/dt.

dV/dt = 4π(50mm)2*(2mm/s)

dV/dt = 62,832 mm3/s


Related Questions

Suppose that a car speaker produces sound waves with a frequency of 4000 Hz. As the car speaker moves away from an observer, which of the
following occurs?

Answers

Frequency is reduced with the sound waves being less heard when the speaker moves away from an observer.

What is Frequency?

This is defined as the number of occurrences of a repeating event per unit of time.

As the speaker is moved away from the observer, the wavelength increases and the frequency decreases thereby resulting in less sound being heard.

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Which of the following is NOT an example of force?
A. gravity
B. mass
C. a push
D. remain at rest

Answers

Answer:

D. remain at rest

Explanation:

D remain at rest because gravity is a force pulling you towards the earth mass is also a force push is also a type of force as you are applying it to an object so D is the answer

Justina dreamed last night that she was warding off villains in a life or death battle outside a fortified castle. In the dream, she attempted to cross the moat but saw that it was filled with grotesque swamp creatures with warty green skin and she recoiled in fear. Knowing there was only one way to reach safety, she flew over the top of the castle and landed among the weeds in the inner courtyard. She was surprised to run into her seventh period Geometry teacher, Ms. Hargroves, but seeing that her teacher had a spear, compass, and workbook with her, Justina knew they would prevail. Ms. Hargroves told Justina that the key to defeating the villains was to write the theorems from the homework on the castle walls as protection against the invaders. Justina scrambled to write the complicated theorems before the menacing villains closed in. Just when the towering castle walls were about to be sieged, Justina awoke from her dream with a start.

As a therapist who specializes in dreams, who would you interpret Justina’s dream using:
17. Freud’s wish-fulfilling theory:
18. The information-processing theory:
19. The physiological function theory:
20. The activation synthesis theory:
21. The cognitive development theory:

Answers

As a therapist who specializes in dreams, I would interpret Justina’s dream by using: 17. Freud’s wish-fulfilling theory.

Who is Sigmund Freud?

Sigmund Freud was an Austrian physiologist, neurologist, medical doctor and the founder of psychoanalysis. Also, Freud was born in Moravia on the 6th of May, 1856 and he was famously known around the world for his works on psychoanalytic theory of personality development.

In 1923, Sigmund Freud developed the personality theory through which he strongly argued that a person’s personality (human psyche) is structured into three (3) key parts and these include:

The Id (instincts).Ego (reality).Superego (morality).

According to Sigmund Freud, wish fulfillment simply means the satisfaction of a human desire through an involuntary thought process such as dreams. Thus, it typically happens to a person when unconscious desires are adequately repressed by both the ego and superego.

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a bulb rated 100 watt 120 volt is connected across a 120 volt source find the current in the bulb and power consumed by it ​

Answers

As it mentioned

100W/120V

So

power is 100W

Now

Current be I

[tex]\\ \rm\rightarrowtail I=\dfrac{P}{V}=\dfrac{100}{120}=\dfrac{5}{6}=0.8A[/tex]

waves disturb a medium by causing the particles to_____.

Answers

Answer:

Oscillate

Explanation:

wave oscillates the particles of the medium around their equilibrium point.

Find out the three methods of energy transfer (conduction, convection and radiation). think about
2 situations of daily life where you know or think you know that each one applies

Answers

Explanation:

conduction- putting a metal spoon in fire

convection- boiling water. In ventilation

Radiation- suns heat reaches us by radiation. heat from fire place reaches us by radiation.

Three-Dimensional Thinking
2. Aiden collected canned goods for a neighborhood service project. He
pulled a plastic wagon behind him to put the items in. From the time
Aiden began until he finished collecting, the mass of the wagon tripled.
The walk back to Aiden's house was downhill and the speed of the
wagon tripled. What happened to the kinetic energy when the mass
tripled? What happened to the kinetic energy when the speed tripled?
A
When the speed tripled, the kinetic energy increased by a factor of 3.
B
When the mass tripled, the kinetic energy increased by a factor of 3.
When the mass tripled, the kinetic energy increased by a factor of 3.
When the speed tripled, the kinetic energy increased by a factor of 9.
When the mass tripled, the kinetic energy increased by a factor of 9
When the speed tripled, the kinetic energy increased by a factor of 3.
When the mass tripled, the kinetic energy increased by a factor of 9.
When the speed tripled, the kinetic energy increased by a factor of 9.
с
D

Answers

Answer:

A.

Explanation: both triple by 3

Answer: B

Explanation: It is because the formula for this eq is KE=V^2. In the eq, it says that the mass is triple meaning the KE also must have tripled. For the speed, since it has a formula then you just have 3^2 which is 9.

A bar of soap when weighed in air has a weight of 5,2N . When completely immersed in water , however it has a weight of 3,7N . What is the volume of the bar of soap

Answers

Answer:

A bar of soap when weighed in air has a weight of 5,2N . When completely immersed in water , however it has a weight of 3,7N . What is the volume of the bar of soap

If the force generated by the car to push it forward is 8,000 N, what can be said about the force opposing the car’s motion?

Answers

According to Newton's third law

Ever action has a equal and opposite reaction.

So

[tex]\\ \rm\dashrightarrow F_{A}=-F_A[/tex]

Hence if applied force is 8000N opposing force is also 8000N

As car is pushed forward so the opposing force is less than 8000N

Answer:It is less than 8,000 N and greater than zero.

Explanation:

1. (30 pts) Let x(t) = cos(πt/2) be a continuous-time signal,
a. Sketch the signal for -4 b. Find the fundamental period of the signal (if it is periodic).
c. Determine if the signal is odd / even or neither.
d. Compute the energy of the signal for all time.
e. Compute the power of the signal for all time.

Answers

Given that the function of the wave is f(x) = cos(π•t/2), we have;

a. The graph of the function is attached

b. 4 units of time

c. Even

d. 4.935 J/kg

e. 1.234 W/kg

How can the factors of the wave be found?

a. Please find attached the graph of the signal created with GeoGebra

b. The period of the signal, T = 2•π/(π/2) = 4

c. The signal is even, given that it is symmetrical about the y-axis

d. The energy of the signal is given by the formula;

[tex] \frac{1}{2} \cdot \mu^{2} \cdot \omega ^{2} \cdot \: {a}^{2} \times \lambda[/tex]

Which gives;

E = 0.5 × 1.571² × 1² × 4 = 4.935 J/kg

e. The power of the wave is given by the formula;

E = 0.5 × 1.571² × 1² × 4 × 0.25 = 1.234 W/kg

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The force of an object is equal to its mass times its ______.
A. inertia
B. friction
C. acceleration
D. faster
E. slower

Answers

Answer:

C. acceleration

Explanation:

The connection between an object's mass and the amount of force required to accelerate it is described by Newton's second law of motion. F=ma is a common expression for Newton's second law, which states that the force (F) exerted on an object is equal to the mass (m) of the object times its acceleration (a). This indicates that the greater the mass of an item, the more force is required to accelerate it. And the more force there is, the faster the item accelerates.

When people are interested in changing their personalities, they are usually most interested in
a.more turbulent less feeling
b.more judging less extroverted
c.more neurotic less assertive
d. More extroverted less neaurotic

Answers

When people are interested in changing their personalities, they are usually most interested in more neurotic less assertive.

What is personality?

Personality makes up an individual, they are the features or characteristics that forms an individual.

Each individual is made of distinctive character which makes one of different from other.

Therefore, when people are interested in changing their personalities, they are usually most interested in more neurotic less assertive

Learn more on personality here,

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A wheel rotates with a constant angular acceleration of 6.0 rad/s2. During a certain time interval its angular displacement is 8.0 rad. At the end of the interval its angular velocity is 14.0 rad/s. What is its angular velocity at the beginning of the interval

Answers

The angular velocity at the beginning of the interval of the wheel rotating  at a constant angular acceleration is determined as 10 rad/s.

Initial angular velocity of the wheel

The initial angular velocity of the wheel is determined by applying the kinematic equation as shown below;

ωf² = ωi² + 2αθ

where;

ωf is the final angular velocityωi is the initial angular velocityα is angular accelerationθ is angular displacement

Substitute the given parameters and solve for the initial angular velocity.

14² = ωi² + 2(6)(8)

196 = ωi² + 96

ωi² = 196 - 96

ωi² = 100

ωi = √100

ωi = 10 rad/s

Thus, the initial angular velocity of the wheel is 10 rad/s.

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An unbalanced force acting on an object will cause it to? A. Increase in mass. B. Decrease in mass. C. Accelerate. D. Remain at rest.

Answers

Answer:

I think the object would accelerate.

Explanation:

When the unbalanced force hits the object, it transfers some of its force to the object, making it accelerate

Calculations a technician performs for the CSP should be located on the O a) standard operating procedure (SOP). b) master formulation record (MFR). O) compounding record (CR). d) quality assurance

Answers

The calculations a technician performs for the CSP should be located on the master formulation record (MFR).

What is Master formulation record?

This is a master document which contains all information about the manufacturing process for the product.

This document contains all the calculations required to make the CSP thereby making option B the most appropriate choice.

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The ________ of an object is the same on the earth as it is on the moon.
A. mass
B. kilogram
C. newton
D. acceleration of gravity
E. weight

Answers

Answer:

mass

Explanation:

The mass of an object is the same on the earth as it is on the moon.

Mass always remains constant, it never changes with respect to place.

Which statements accurately describe mechanical waves? Check all that apply.

A. Energy is transferred through vibrating particles.
B. A mechanical wave does not carry energy through matter.
C. A longitudinal wave is a type of mechanical wave.
D. A transverse wave is a type of mechanical wave.
E. An ocean wave moving through water is an example of a mechanical wave.

Answers:
A.
C.
D.
E.

I already did this
Edge 2022​

Answers

Answer:

A

Explanation:

E. An ocean wave moving through water is an example of a mechanical wave

e.g sound waves wave on a rope or string

and Ans a is also correct

In mechanical waves, the energy is transferred through the vibration of the particles.

Mechanical waves are the type of waves that transfers energy through the vibration of particles. Since, mechanical waves require a medium to transfer energy, they carry energy through matter.

Both longitudinal and transverse waves are two types of mechanical waves.

It is known that mechanical waves propagate through medium like matter, water, etc. Therefore, an ocean wave moving through water is an example of a mechanical wave.

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Find the temperature

Answers

Answer:

-------1

Explanation:

beacuse that is what i know

On a dusty day clean polished shoes attrack alot of dust.Explain this?​

Answers

Answer:

Because when we polish the shoes, they gain charges or the shoes become charged, the small non-charged particles are attracted to them.

Environment A is warm and gets lots of rain. Environment B is warmer and gets more rain year round. Identify Environment A.(2 points)

Tundra

Rainforest

Desert

Swamp

Answers

The Swamp
There are many websites that say the rainforest but the rainforest is warmer and gets rain year round and swamps are warm and gets lots of rain but not year round.

Answer:

Swamp

Explanation:

there were answers that said rainforest, but i got it wrong, so its swamp.

1. Greek scientist called Archimedes was asked to check the purity of the gold in a crown. He did this by comparing the density of the crown with the density of pure gold.
a) Describe how he could have measured the density of an irregular shaped object as a crown.

Answers

Answer:

Suppose Archimedes weighed the crown (we'll say 2700 grams)

Then he put the crown on a string and weighed the crown in water and found its weight to be 2560 g.

That means that an equivalent volume of water weighed

2700 - 2560 = 140 grams

Then the density of the crown is 2700 / 140 = 19.3

So this is the density of pure gold and the crown could be considered to be made of pure gold with no other metals in its composition.

Archimedes weighed the crown, then suspended it on a rope and measured the volume of water it displaced in order to determine its weight, then he calculated the density of the crown and compared it with the density of the pure gold.

What is density?

It can be defined as the mass of any object or body per unit volume of the particular object or body. Generally, it is expressed as in gram per cm³ or kilogram per meter³.

As given in the problem statement Greek scientist called Archimedes was asked to check the purity of the gold in a crown. He did this by comparing the density of the crown with the density of pure gold.

Archimedes weighed the crown, then suspended it on a rope and measured the volume of water it displaced in order to determine its weight.

Thus, he could have measured the density of an irregularly shaped object as a crown.

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she incorrect? Select all that apply.
because electromagnetic waves can only travel in gases
А
B
because electromagnetic waves can only travel through solids
С
because electromagnetic waves only come from the Sun
D
because electromagnetic waves are not created using force on a medium
m
because electromagnetic waves are created using accelerating charges
F
because electromagnetic waves require a medium to travel

Answers

electromagnetic waves can travel not only through air and solid materials, but also through the vacuum of space.

hope it helps...!!!

Why did the chicken cross the road

Answers

Answer:

to get to the other side.

Explanation:

bada bam, bop, BOOM

To get to the other side

2. What value did you calculate for the index of refraction of the acrylic block in Part 2? How does your value compare to the accepted value of 1.50? Calculate the percentage error. Different materials have distinct indexes of refraction. Explain how you might identify a material based on experiments like this one. Mention at least one of the difficulties in identifying materials based on their indexes of refraction.

Answers

The percentage error in calculated value of the refractive index of acrylic block is calculated using the formula: (true value - calculated value/true value) × 100%.

What is refractive index of a refracting medium?

The refractive index of a medium is the ratio of the sine of the angle of incidence on the medium and the sine of the angle of refraction.

Refractive index = sin i/sin r

where;

i is the angle of incidencer is angle of refraction.

The refractive index of a medium increases with density of the medium.

To determine the percentage error in determining the refractive index of a medium, the following formula is used:

Percent error = error/true value × 100%

Therefore, the percentage error in calculated value of the refractive index of acrylic block is the ratio of the error and true value multiplied by 100%.

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An athlete lifts a 330 N set of weights from ground level to a position over her head, a vertical distance of 2.05 m. Assume the weights are moved at constant speed. a) How much work does the athlete do? b) What is the mass of the weights?​

Answers

Force=330NDistance=2.05m

Work done:-

Force×Displacement330(2.05)676.5J

Now

Apply Newtons second law

F=ma

m is mass

a is acceleration due to gravity (10)

330=10mm=33kg

Which material is a good heat conductor ?​

Answers

Answer:

wood lighters gasoline hope it helps

Explanation:

If a 40 N block is resting on a rough horizontal table with a
coefficient of static friction p=0.60, then what is the force of
static friction acting on the block?

Answers

Based in the relationship between static frictional force and coefficient of static friction, the force of static friction is 24 N.

What is friction?

Friction is a force that opposes the relative motion of an object moving over another at their surafce of contact.

Frictional force is constant for each type of material. This constant is known as coefficient of friction.

The coefficient of friction is given as follows:

Coefficient of friction = Frictional force/normal reaction

From the data given:

coefficient of static friction p = 0.60Weight of block = 40 N

Force of static friction = 0.60 × 40

Force of static friction = 24 N.

Therefore, the force of static friction is 24 N.

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The weight of an object on the moon is less because the _______ on the moon is less.
A. mass
B. kilogram
C. newton
D. acceleration of gravity
E. weight

Answers

Answer:

acceleration of the gravity

Explanation:

The weight of an object on the moon is less because the acceleration of the gravity on the moon is less.

How does the gravitational force between two objects change if the distance between the objects doubles?
a)
The force decreases by a factor of 4.
b)
The force decreases by a factor of 2.
c)
The force increases by a factor of 4.
d)
The force increases by a factor of 2.

Answers

if the distance between the objects is doubled the force is reduced by a factor of 4

Whats is gravitational force?

Gravitational force is the force of attraction between objects in the universe.

f = G * m1 * m2 / r^2

f = gravitational force

G = gravitational constant

m1 = mass of object 1

m2 = mass of object 2

r = distance between the objects

From the formular, the gravitational force and the distance is an inverse relationship so increasing the distance by a factor results to reduction of the force by the square of the factor. hence doubling the distance which is distance mutiplied by 2 will lead to reduction of the force by 2^2 = 4

Therefore: The force decreases by a factor of 4.

hope it helps

a 2.99 kg sphere makes a perfectly inelastic collision with a second sphere that is intially at rest. the composite moves with a speed equal to one third the original speed of the 2.99kg. what is the mass of the second sphere?​

Answers

Answer:

5.98 kg

Explanation:

To solve this problem, let use the Linear Momentum Conservation Law:

Before collision: [tex]\sum p=p_{1}+p_{2}=m_{1}v_{1}+m_{2}v_{2}=(2.99v_{1})+0=2.99v_{1}[/tex]

After collision: [tex]\sum p'=p_{1}'+p_{2}'=(2.99+m_{2})(v_{1}/3)[/tex]

So, we obtain:

[tex]\sum p =\sum p' \rightarrow 2.99v_{1}=(2.99+m_{2})(v_{1}/3) \rightarrow 8.97 = 2.99 + m_{2}[/tex]

[tex]m_{2}=8.97-2.99=5.98 kg[/tex]

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