use spherical coordinates. find the volume of the part of the ball ≤ 7 that lies between the cones = /6 and = /3.
Answers
To determine the volume of the part of the ball ≤ 7 that lies between the cones = π/6 and = π/3 in spherical coordinates, we first need to determine the limits of integration.
Limits of integration: 0 ≤ ρ ≤ 7, π/6 ≤ φ ≤ π/3, 0 ≤ θ ≤ 2πVolume of the part of the ball ≤ 7 that lies between the cones = π/6 and = π/3 in spherical coordinates
:∫∫∫ Vρ²sin φ dρ dφ dθ= ∫₀²π ∫π/6π/3 ∫₀⁷ρ²sin φ dρ dφ dθ
= ∫₀²π ∫π/6π/3 [ρ³/3]
₌⁷sin φ dφ dθ
= ∫₀²π [7³/3 − 1³/3]∫π/6π/3 sin φ dθ dφ= 2π [7³/3 − 1³/3] [−cos θ]π/6π/3
= 2π [7³/3 − 1³/3] [cos π/3 − cos π/6]
= 2π [7³/3 − 1³/3] [(1/2) − (√3/2)]= π [343 − 1] (√3 − 1)/3≈ 947.779
cm³Therefore, the volume of the part of the ball ≤ 7 that lies between the cones = π/6 and = π/3 in spherical coordinates is approximately 947.779 cm³.
Learn more about coordinates here:
https://brainly.com/question/16634867
#SPJ11
Related Questions
Determine the mass of fuel required for the expected energy consumption in the United States for the next 10 years:
Provide the energy use per person per year in the United States = 3.5 × 1011 joules.
Base your calculations on a current population of 310,000,000.
Answers
Answer:
(This will depend on the type of fuel, I will assume that the fuel is petrol)
First, let's find the expected energy consumption in the US for the next 10 years.
We know that in one year, a person consumes 3.5*10^11 joules.
There are 310,000,00 people on the US
Then the total consumption in one year is:
310,000,000*3.5*10^11 joules = 1.085*10^20 J
In 10 years the consumption is 10 times the consumption of a single year, then the expected energy consumption in the US for the next 10 years is:
10*1.085*10^20 J = 1.085*10^21 J
Now let's find the mass of fuel required.
We know that a liter of petrol has 31,536,000 joules of energy,
And a liter of petrol weights 0.75 kg
To find the number of liters of petrol that we need, we need to find the quotient between the expected energy consumption in the next 10 years and the energy of a single liter of petrol, this is:
N = (1.085*10^20 J)/(31,536,000 j) = 3.44*10^13
We will need 3.44*10^13 liters of petrol.
And the total mass of petrol will be:
M = 3.44*10^13*0.75 kg = 2.58*10^13 kg of fuel.
A hydraulic jack is used to lift a car by applying a force of 120N at the pump piston,if the area of the ram and pump piston are 100cm squared and 1m squared respectively
Answers
Complete question:
A hydraulic jack is used to lift a car by applying a force of 120N at the pump piston, if the area of the ram and pump piston are 100cm squared and 1m squared respectively. What is the weight of the car?
Answer:
the weight of the car is 1.2 N
Explanation:
Given;
applied force, F₁ = 120 N
area of the effort (pump), A₁ = 1 m²
area of the load (ram), A₂ = 100 cm² = 1 x 10⁻² m²
let the weight of the car = F₂
The applied pressure is constant and the following equations can be used to calculate the weight of the car.
\(P = \frac{F_1}{A_1} = \frac{F_2}{A_2} \\\\F_2 = \frac{F_1 \times A_2}{A_1} \\\\F_2 = \frac{120 \times (1\times 10^{-2})}{1} \\\\F_2 = 1.2 \ N\)
Therefore, the weight of the car is 1.2 N
a heavy crate rests on the bed of a flatbed truck. when the truck accelerates, the crate remains where it is on the truck so it too accelerates. what force(s) is/are responsible for the acceleration of the crate? be specific as to the root causes (on, by) of this force.
Answers
The force responsible for the acceleration of the crate is the frictional force between the crate and the bed of the truck.
When the truck accelerates, the crate tends to remain at rest due to inertia. However, the frictional force between the crate and the bed of the truck acts in the forward direction, allowing the crate to accelerate along with the truck.
This frictional force is a result of the interaction between the surfaces of the crate and the truck bed. Without this frictional force, the crate would slide or move independently from the truck's acceleration.
The frictional force arises due to the microscopically rough surfaces of the crate and the truck bed. As the two surfaces are pressed against each other, intermolecular forces come into play, resulting in the generation of the frictional force
To learn more about acceleration here
https://brainly.com/question/30660316
#SPJ4
A basketball rolls down a hill until it comes to a stop in a ditch
A. 1st Law of motion
B. 2nd Law of motion
C. 3rd Law of motion
Answers
The first law of motion states that a object will be at motion or rest until a unbalanced force is applied on it.
Answer:
1st law.
Explanation:
explain; water wets glass surface but does not wet the waxed glass surface pliz answer and will follow
Answers
Answer:
Recycled answer from jaskhanna07343
Explanation:
Water does not wet waxed surfaces because the cohesive forces within the drops are stronger than the adhesive forces between the drops and the wax. Water wets glass and spreads out on it because the adhesive forces between the liquid and the glass are stronger than the cohesive forces within the water
The gravitational pull of the Moon is much less than the
gravitational pull of Earth. An object with a mass of 50
kilograms weighs about 18 pounds on the Moon.
Which statement describes the object on Earth?
A. It would have less mass.
B. It would weigh more.
C. It would have the same weight.
D. It would have more mass.
Answers
Answer:
than what is it
Explanation:
A book containing the ________ of every incarcerated person has been put on display in los angeles.
Answers
With more than six million books in its collection and 19 million people living in the Greater Los Angeles Area, the system serves the biggest population of any public library system in the country.
The Los Angeles Public Library's size is what?The structure has eight stores with a total area of 538,000 square feet, approximately 89 miles of shelves, and more than 1,400 seats. There are 255 public computers with free access scattered around the building and the Computer Center. Wi-fi enables access to the internet as well.
The largest and most varied population in the country is served by the Los Angeles Public Library. There are four million people living within the library's huge 468 square mile service area, who speak more than 220 different languages.
Residents of 49 of the 88 incorporated cities in Los Angeles County, California, are served by LA County Library, one of the country's biggest public library systems.
To learn more about 'los angeles' refer to
https://brainly.com/question/25305703
#SPJ4
solve for x: |2x + 6| − 4 = 20 Group of answer choicesx = 9 and x = 11x = −9 and x = 15x = 9 and x = −15No solution
Answers
Given,
\(|2x+6|-4=20\)On simplifying,
\(\begin{gathered} |2x+6|=20+4 \\ \Rightarrow|2x+6|=24 \\ 2x+6=\pm24 \end{gathered}\)Thus,
\(\begin{gathered} 2x=+24-6 \\ \Rightarrow x=\frac{18}{2} \\ =9 \end{gathered}\)Or
\(\begin{gathered} 2x=-24-6 \\ x=\frac{-30}{2} \\ =-15 \end{gathered}\)Thus, x=9 and x=-15
Therefore the correct answer is the third option
Which of the following is TRUE about the stages of grieving?A.Each stage should be experienced only once for each loss.B.Everyone must move through the stages in the same order.C.Progressing through these stages will help to deal with loss in a healthy manner.D.none of the abovePlease select the best answer from the choices provided.ABCD
Answers
Grief can be defined as a natural response to loss. Some of the most common states of grieving are denial, isolation, anger, depression, and acceptance.
The statement 'Progressing through these stages will help to deal with loss in a healthy manner' about the stages of grieving is TRUE (Option C).Grief refers to the emotional suffering that has come when someone close has died.Actions such as avoid, ignoring, or escaping are not good feelings to deal with grief effectively (they are unhealthy).Learn more in:
https://brainly.com/question/16528722?referrer=searchResults
Which two subfields of psychology are similar and involve diagnosing and treating mental disorders?
A). Counseling psychology and social psychology
B). Clinical psychology and developmental psychology
C). Clinical psychology and counseling psychology
D). Developmental psychology and counseling psychology
Answers
The two subfields of psychology that are similar and involve diagnosing and treating mental disorders are Clinical psychology and the Counseling psychology. Therefore, the correct answer is: C).
Clinical psychology and Counseling psychology. Both of these subfields involve the assessment, diagnosis, and treatment of mental health disorders, although they may differ in their focus and approach. Clinical psychology tends to the focus on more severe mental health issues, such as schizophrenia and the bipolar disorder, while Counseling psychology tends to focus on a wider range of issues, such as stress management, relationship problems, and career counseling. Hence correct answer is : C) .
To know more about Clinical psychology, here
brainly.com/question/15401191
#SPJ4
Small blocks, each with mass m , are clamped at the ends and at the center of a rod of length L and negligible mass.
A.Compute the moment of inertia of the system about an axis perpendicular to the rod and passing through the center of the rod.
Express your answer in terms of the given quantities.
B.Compute the moment of inertia of the system about an axis perpendicular to the rod and passing through a point one-fourth of the length from one end.
Express your answer in terms of the given quantities.
Answers
a) To find the moment of inertia of the system about an axis perpendicular to the rod and passing through the center of the rod, we can use the parallel axis theorem. The moment of inertia of the rod about an axis perpendicular to it and passing through its center is (1/12)ML^2, and the moment of inertia of each small block about an axis passing through its center and perpendicular to it is (1/12)ma^2, where a is the length of each block.
Using the parallel axis theorem, the moment of inertia of each block about an axis passing through one end of the rod is (1/12)ma^2 + (1/4)m(L/2)^2 = (1/12)m(a^2 + L^2/16), since the distance between the axis passing through the center of the rod and the axis passing through one end of the rod is L/4.
There are two blocks, one at each end of the rod, so their combined moment of inertia about an axis passing through one end of the rod is (2/12)m(a^2 + L^2/16) = (1/6)m(a^2 + L^2/16).
The moment of inertia of the rod about an axis passing through one end of the rod is (1/3)ML^2. Therefore, the moment of inertia of the entire system about an axis passing through one end of the rod is:
I = (1/6)m(a^2 + L^2/16) + (1/3)ML^2
b) To find the moment of inertia of the system about an axis perpendicular to the rod and passing through a point one-fourth of the length from one end, we can again use the parallel axis theorem.
The distance between the new axis and the axis passing through the center of the rod is L/4, and the distance between the new axis and the axis passing through one end of the rod is L/2 - L/4 = L/4.
The moment of inertia of the rod about the new axis is (1/12)ML^2 + (1/4)M(L/4)^2 = (7/192)ML^2.
The moment of inertia of each block about the new axis is (1/12)ma^2 + (1/4)m(L/4)^2 = (1/12)m(a^2 + L^2/16).
Again, there are two blocks, so their combined moment of inertia about the new axis is (2/12)m(a^2 + L^2/16) = (1/6)m(a^2 + L^2/16).
Therefore, the moment of inertia of the entire system about the new axis is:
I = (1/6)m(a^2 + L^2/16) + (7/192)ML^2
/brainly.com/question/31183071
SPJ11
three devices that control the speed and direction of your vehicle are the
Answers
Three devices that control the speed and direction of a vehicle are the accelerator pedal, brake pedal, and steering wheel.
The accelerator pedal is used to control the speed of the vehicle. By pressing the accelerator pedal, the driver can increase the engine's power and accelerate the vehicle. Releasing or easing off the pedal reduces the engine power and slows down the vehicle.
The brake pedal is used to control the deceleration and stopping of the vehicle. When the driver presses the brake pedal, it activates the braking system, which applies friction to the wheels, slowing down the vehicle or bringing it to a complete stop.
The steering wheel is used to control the direction of the vehicle. By turning the steering wheel left or right, the driver can steer the vehicle and change its course. The steering wheel is connected to the vehicle's steering system, which allows for precise control of the front wheels and, consequently, the vehicle's direction.
These three devices are essential for manoeuvring and controlling a vehicle's speed and direction, providing the driver with the means to navigate safely and effectively on the road.
To know more about speed, visit:
https://brainly.com/question/13263542
#SPJ11
What is your(human) role in energy transition? Write 5 points
with arguments
Answers
Human roles in energy transition are:
Consumer choicesAdvocacy and awarenessEnergy efficiencySupport for innovation:Community engagement: Consumer choices: The conscious choice of sources creates a market need for clean energy sources and signals to energy providers the need for sustainable solutions. This can stimulate investment in renewable energy infrastructure and technologies.Advocacy and awareness: By actively disseminating information about renewable energy sources and the advantages associated with them, you can influence public opinion in favor of clean energy policy. This can be done through social media posts, participation in community activities, or involvement in advocacy groups that advocate for renewable energy solutions.Energy efficiency: Reducing energy consumption leads to a decrease in overall energy consumption and a decrease in the requirement for additional energy production. This contributes to the reduction of greenhouse gas emissions, as well as the conservation of natural resources. Additionally, it results in cost savings for both individuals and businesses.Support for innovation: By choosing products and services from companies that prioritize renewable energy and sustainable practices, you send a message to the market that there is a demand for clean technologies. This encourages further innovation and investment in renewable energy research and development.Community engagement: Active involvement in local energy initiatives allows you to contribute to the energy transition at the grassroots level. By joining community energy projects, attending meetings, and collaborating with others, you can work towards implementing renewable energy solutions within your community and driving positive change.By taking these steps, you can actively contribute to the energy transition and be a part of the movement toward a more sustainable and clean energy future.
To know the main sources of renewable energy: https://brainly.com/question/79953
PLEASE HELP WILL MARK AND 5 STARS I AM TIMED!!!!!!!!1
Answers
Answer:
is there a better picture
Signals that are broken up into binary code are characterized as
.
Answers
Answer:
AM/FM radio is a perfect type of technology.
A smart phone is also a great presentation of technology.
Explanation:
have great day
state law of movement
Answers
Answer:
Explanation:
In the first law, an object will not change its motion unless a force acts on it. In the second law, the force on an object is equal to its mass times its acceleration. In the third law, when two objects interact, they apply forces to each other of equal magnitude and opposite direction.
What is the strength of an electric field that will balance the weight of a 1.7 g plastic sphere that has been charged to -9.2 nc ?
Answers
The strength of the electric field required to balance the weight of the charged plastic sphere is approximately -1.823 x 10^6 N/C (newtons per coulomb).
To find the strength of the electric field required to balance the weight of a charged plastic sphere, we need to consider the force due to gravity acting on the sphere and the electric force acting on it.
The force due to gravity can be calculated using the equation:
Force_gravity = mass * acceleration due to gravity
Given that the mass of the plastic sphere is 1.7 g (0.0017 kg) and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the force due to gravity:
Force_gravity = 0.0017 kg * 9.8 m/s²
Next, we calculate the electric force using the equation:
Force_electric = charge * electric field strength
The charge on the plastic sphere is -9.2 nC (negative because it is negatively charged).
Now, we equate the forces to find the electric field strength:
Force_electric = Force_gravity
charge * electric field strength = mass * acceleration due to gravity
electric field strength = (mass * acceleration due to gravity) / charge
Plugging in the values, we get:
electric field strength = (0.0017 kg * 9.8 m/s²) / (-9.2 x 10^(-9) C)
Calculating this, the strength of the electric field required to balance the weight of the charged plastic sphere is approximately -1.823 x 10^6 N/C (newtons per coulomb).
Note: The negative sign indicates that the electric field is directed opposite to the force of gravity, as the sphere has a negative charge.
For more such questions on electric field
https://brainly.com/question/19878202
#SPJ4
You might have noticed that a feather falls slowly toward the ground, while a ball falls rapidly. Which statement correctly explains the motion of these objects?
1. The ball does not experience fluid friction as it falls.
2. Gravity is the only force acting on the feather and the ball.
3.The acceleration of the ball and feather are the same.
4. The feather experiences more fluid friction than the ball.
Answers
Answer:
4. the feather experiences more fluid friction than the ball
The solar winds blow outward from: a. the entire photosphere. b. sunspots. c. flares. d. the sun's poles only. e. coronal holes.
Answers
The solar winds blow outward from: e. coronal holes.
Solar winds are streams of charged particles that are emitted by the Sun. They originate from the Sun's corona, which is the outermost layer of the Sun's atmosphere. Coronal holes are regions on the Sun's surface where the corona appears darker and cooler. These regions have lower density and temperature compared to the surrounding areas.
Due to the lower magnetic field strength in coronal holes, the solar winds can escape more easily, resulting in higher speed and greater flow of particles. Therefore, the solar winds primarily blow outward from coronal holes.
Know more about Solar winds here,
https://brainly.com/question/16524443
#SPJ11
All of the following choices are examples of commonly used assessment methods for body
composition EXCEPT
A. waist to hip ratio
B. bioelectrical impedance analysis
C. the spongy bob technique
D. skinfold measurements this is PE please help mee
Answers
Answer:
letter D
Explanation:
sana po makatulong po sa inyo
Which of the following is true of the structures labeled A in the cell membrane?
Choose 1 answer:
(Choice A) A They are membrane proteins.
(Choice B) B They are entirely hydrophobic.
(Choice C) C They are phospholipids.
(Choice D) D They are carbohydrates. Report a problem
Answers
Answer:
they are membrane proteins
They are membrane proteins
Explanation:
what is the point value for scoring in handball
Answers
Answer:
one point
Explanation: trust me :)
hange the horizontal axis of your graph to cross-sectional area. what relationship appears to exist between resistance and the cross-sectional area of the rods?
Answers
Based on the graph and the change of the horizontal axis to cross-sectional area, it appears that there is an inverse relationship between resistance and cross-sectional area of the rods. This means that as the cross-sectional area increases, the resistance decreases.
The change in the horizontal axis to cross-sectional area allows us to observe how resistance changes as the area of the rod changes. The graph shows that as the cross-sectional area increases, the resistance decreases. This is because a larger cross-sectional area allows for more space for electrons to flow, resulting in less resistance to the flow of current. On the other hand, a smaller cross-sectional area creates more resistance because there is less space for electrons to flow. Therefore, based on the data and graph presented, it appears that resistance and cross-sectional area have an inverse relationship.
To know more about resistance, visit here :
brainly.com/question/30799966
#SPJ11
the uniform probability distribution's standard deviation is proportional to the distribution's range.
Answers
Uniform probability distribution is a type of probability distribution in which each value in a given interval has an equal chance of occurring. The uniform probability distribution's standard deviation is proportional to the distribution's range.
The formula for finding the standard deviation of a uniform distribution is:σ= b−a√12Where σ is the standard deviation, a is the lower bound, and b is the upper bound of the interval. In the uniform distribution, the range is equal to the difference between the upper bound and the lower bound of the interval.
Therefore, we can rewrite the formula as:σ= Range√12We can see that the standard deviation of the uniform distribution is proportional to the square root of the range. This means that as the range of the distribution increases, the standard deviation will also increase, and vice versa.
In conclusion, the standard deviation of a uniform probability distribution is proportional to the distribution's range, as demonstrated by the formula σ= Range√12. This relationship is important to understand when analyzing data with a uniform distribution, as it can affect the interpretation of the data.
To know more about Uniform probability visit -
brainly.com/question/3422367
#SPJ11
NH3 → N2 + H2 Balance and classify it
Answers
Answer:
2NH3 --> N2 + 3H2 decomposition
Which type of satellite has the shortest orbital life?.
Answers
Answer:
The answer is Low earth orbit
You are riding a bicycle you apply forward force of 50 n, and you and the bicycle have a combined mass of 100kg. What is the acceleration of the bicycle?
Answers
Answer:
a = 0.5m.s²
Explanation:
Fnet = m×a
50 = 100×a
a = 0.5
If € ₁ 4. 0 V. & 2 = 12. 0 V, R₁ = 40, R₂ = 1202, C-3 μF, Q = 18 μC, and I = 2. 5 A, what is the potential difference V, - V? b- 5. 0 V O-5. 0 V 30 V O-30 V & - 1. ³ 30
Answers
According to the given statement , the potential difference V across the resistor R is 3105 V.
To find the potential difference V, we can use Ohm's Law and the formula for the potential difference across a capacitor.
First, let's calculate the current flowing through the circuit. We are given that I = 2.5 A.
Next, we can calculate the total resistance in the circuit using the formula R = R₁ + R₂. Given that R₁ = 40 Ω and R₂ = 1202 Ω, we can calculate the total resistance:
R = 40 Ω + 1202 Ω = 1242 Ω
Now, we can calculate the charge stored in the capacitor using the formula Q = C * V, where Q is the charge, C is the capacitance, and V is the potential difference across the capacitor. We are given that Q = 18 μC and C = 3 μF. Plugging these values into the formula, we can solve for V:
18 μC = 3 μF * V
V = 18 μC / 3 μF
V = 6 V
Finally, we can calculate the potential difference V across the resistor R. Using Ohm's Law, we can use the formula V = I * R:
V = 2.5 A * 1242 Ω
V = 3105 V
So, the potential difference V across the resistor R is 3105 V.
In conclusion, the potential difference V across the resistor R is 3105 V.
To more about capacitor visit:
https://brainly.com/question/31627158
#SPJ11
A CO4
B CO
C CH4
D CO3
Answers
Answer:
B Co is the chemical formula for carbon monoxide
which treatment uses magnetic pulses of various frequencies to stimulate certain regions of the brain?
Answers
The treatment that uses magnetic pulses of various frequencies to stimulate certain regions of the brain is called transcranial magnetic stimulation (TMS).
TMS is a non-invasive procedure that involves placing a coil near the scalp, which delivers magnetic pulses to specific areas of the brain. These pulses generate small electrical currents that can modulate the activity of targeted brain regions.
TMS is primarily used as a therapeutic intervention for various psychiatric and neurological conditions, including depression, anxiety disorders, obsessive-compulsive disorder (OCD), and certain types of chronic pain.
The exact mechanisms by which TMS exerts its effects are still being studied, but it is believed to influence the neural circuits involved in mood regulation and cognition. TMS is typically conducted in multiple sessions over a period of weeks, under the guidance of a trained healthcare professional.
To know more about the TMS refer here :
https://brainly.com/question/31948902#
#SPJ11