Find the absolute value of the jacobian, |j(u,v)|, for the change of variables given by x=2u 7v,y=2u v |j(u,v)|= see the definition of the jacobian on page 722.
Answers
Variables given by x = 2u + 7v and y - 2u + v does not distort the area or volume in the transformation, as the Jacobian determinant is a constant value of 2.
The Jacobian is a mathematical concept used in calculus to describe how a change of variables affects a function. In this case, we are given a change of variables from x and y to u and v. The change of variables is defined as x = 2u + 7v and y - 2u + v.
To find the absolute value of the Jacobian, we need to compute the determinant of the Jacobian matrix. The Jacobian matrix is formed by taking the partial derivatives of the new variables (u and v) with respect to the old variables (x and y).
The Jacobian matrix for this change of variables is:
J = [∂u/∂x ∂u/∂y]
[∂v/∂x ∂v/∂y]
To find the absolute value of the Jacobian, we need to compute the determinant of the Jacobian matrix:
|J| = |∂u/∂x ∂u/∂y|
|∂v/∂x ∂v/∂y|
Using the given change of variables, we can compute the partial derivatives:
∂u/∂x = 2
∂u/∂y = 0
∂v/∂x = 7
∂v/∂y = 1
Substituting these values into the determinant formula, we get:
|J| = |2 0|
|7 1|
Calculating the determinant, we have:
|J| = (2*1) - (0*7) - 2
Therefore, the absolute value of the Jacobian, |j(u,v)|, for the given change of variables is 2.
|j(u,v)| = 2. This means that the change of variables given by x - 2u + 7v and y - 2u + v does not distort the area or volume in the transformation, as the Jacobian determinant is a constant value of 2.
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Related Questions
PLZZ HELP!!!
When a star is undergoing nuclear fusion what type of radiation will be found?
Answers
Answer:
I think the correct answer would be the third option. As the elements around the star begins to emit more and more electromagnetic radiation, the rocky materials are pulled in by the electromagnetic radiation. They are being drawn closer to the star and there would be a very high chance of a nuclear
Explanation:
Mrs. Jones has been selected to join Space X on their next mission. When Mrs. Jones goes to
the moon, will her mass or weight change?*
(1 Point)
Her mass will change, but her weight will remain the same.
Her weight will change, but her mass will remain the same
Her mass and weight will both change.
Neither her mass nor her weight will change.
Answers
Answer:
ms jones is a good song poggers
Explanation:
A man pushes a crate along a factory floor by exerting a force of 55 N. If
the crate moves a distance of 4.0 m, how much work does the man
perform?
Answers
Answer:
it's 220 J
the second one
A substance will take on the shape of an open container if it is a
liquid.
plasma.
gas.
solid.
Answers
Answer:
liquid
Explanation:
for the hydraulic structure shown in figure, (a) calculate the seepage loss in m3/day/m. (b) calculate the pressure heads at a, b, c. (k = 0.003cm/sec)
Answers
To calculate the seepage loss, additional information is required, such as the dimensions of the structure and the hydraulic gradient. With the provided data alone, it is not possible to calculate the seepage loss accurately.
What information is needed to accurately calculate the seepage loss?The given paragraph describes a hydraulic structure and presents two questions:
(a) Calculate the seepage loss in m3/day/m.
To calculate the seepage loss, additional information is required, such as the dimensions of the structure and the hydraulic gradient. With the provided data alone, it is not possible to calculate the seepage loss accurately.
(b) Calculate the pressure heads at points a, b, and c.
To calculate the pressure heads, additional information is required, such as the elevation of the water surface and the reference point for measuring pressure. Without these details, it is not possible to determine the pressure heads accurately.
In summary, the paragraph poses two questions related to seepage loss and pressure heads in a hydraulic structure. However, due to the lack of essential information, accurate calculations cannot be performed.
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If the same elevator accelerates downwards
with an acceleration of 1.2 m/s
2
, what is the
upward force exerted by the elevator floor on
the passenger?
Answers
The upward force exerted by the elevator floor on the passenger is 7.6 times mass of the passenger.
What is force?A force in physics is an effect that has the power to alter an object's motion. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Given in question elevator accelerates downwards with an acceleration of 1.2 m/s². There is acceleration due to gravity working downward which is 9.8 m/s².
So, net acceleration due to gravity is given as 9.8 - 1.2 = 7.6 m/s²
The upward force exerted by the elevator floor on the passenger is mass times acceleration, 7.6 times mass of passenger.
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Convert the Metric measurements below.
76km =
m
Answers
Answer:
47.2242 is what I think
The surface air around a strengthening low pressure area normally ____, while, above the system, the air normally ____.
Answers
The surface air around a strengthening low-pressure area normally converges, while above the system, the air normally diverges.
When a low-pressure system strengthens, it means that the pressure at the center of the system is decreasing. As a result, the surrounding air at the surface tends to converge and move towards the low-pressure center.
This convergence of air at the surface creates a cyclonic circulation pattern, where air spirals inward towards the center of the low-pressure system.
At higher altitudes, above the low-pressure system, the air tends to diverge. This means that the air moves away from the center of the system.
The divergence of air at higher altitudes is a result of the vertical motion associated with the low-pressure system.
As air converges at the surface and moves towards the center of the low-pressure system, it rises vertically. This upward motion leads to the divergence of air at higher altitudes.
The combination of surface air convergence and upper-level air divergence is characteristic of a strengthening low-pressure system and contributes to the intensification and development of weather associated with such systems, such as storms and cyclones.
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two stars have the same inherent brightness (absolute magnitude). star a appears 1/16 as bright as star b. star a is 4 light years away. star b must be
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Star b must be 2 light years away. The apparent brightness of a star decreases with the square of the distance. Since star a appears 1/16 as bright as star b, star b must be √16 = 4 times closer, which is 2 light years away.
The apparent brightness of a star is determined by its intrinsic brightness, also known as its absolute magnitude, and its distance from the observer. In this scenario, star a and star b have the same absolute magnitude, indicating that they have the same inherent brightness. However, star a appears 1/16 as bright as star b. Since apparent brightness is inversely proportional to the square of the distance, we can deduce that star b must be 1/4 times the distance of star a to maintain the same apparent brightness. Given that star a is 4 light years away, star b must be 2 light years away. This ensures that the apparent brightness of star b is 1/16 of star a, as observed.
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Which equation best represents the intensity of light coming out of a secondpolarizing filter is equal to the intensity of polarized light coming out of a firstpolarizing filter multiplied by the cosine, squared, of the angle between thepolarizing axes of the two filters?
Answers
Let the angle between the polarizing axes of the two filters be
\(\theta\)Let the intensity of polarized light coming out of the first polarizing filter be I1.
Then the intensity of the second polarizing filter will be
\(I_2=I_1cos^2\theta\)Thus, the correct option is B.
How should three capacitors and two batteries be connected so that capacitors will store maximum energy?
Answers
To connect three capacitors and two batteries in a way that the capacitors will store maximum energy, they should be arranged in a circuit configuration known as a series-parallel combination.
A battery is an electric power source that consists of one or more electrochemical cells with external connections to power electrical equipment. When a battery is supplying power, the positive terminal is referred to as the cathode, and the negative terminal is referred to as the anode.
Begin by connecting two capacitors in series. Connect the remaining capacitor in parallel with the capacitor series combination.
Connect one battery between the first capacitor's unconnected positive terminal and the third capacitor's disconnected negative terminal.
Connect the second battery to the third capacitor's unconnected positive terminal and the second capacitor's disconnected negative terminal.
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When caring for wounds, doctors need to make sure wounds are not infected by bacteria. Which electromagnetic wave would doctors most likely use for this purpose? gamma rays ultraviolet waves visible light X-rays.
Answers
Ultravoilent rays is an type of an electromegnetic wave with wavelength 10nm .Ultraviolet wave is used by doctors in order to keep the wounds away from bacteria.
What is ultravoilent wave ?Ultravoilent rays is an type of an electromegnetic wave with wavelength 10nm. Ultravoilent wave is directly comes frim the sun. It is classified into the UV(A) , UV(B),UV(B).
Ultravoilet rays also effects the human eyes that s why sun glasses are used. The experiments here are compared and quantified to the effectiveness of the sunscreens with various strengths.
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Answer:
B. Ultraviolet waves
Explanation:
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
a 15.9 kg concrete block is pulled 0.90 m to the right in 2.5 s
what is the average speed to the nearest hundreds
Answers
Answer:
the average speed of the blocks is 0.36 m/s
the volume of a sample of helium in a balloon is 4.5 ml at 20.0°c with constant pressure. if the temperature drops from 20 degrees celsius to 10 degrees celsius, what is the new balloon volume?
Answers
A sample of helium has a volume of 4.5 ml in a balloon at 20.0°C and constant pressure. If the temperature falls from 20 to 10°C then at 10°C, the balloon's new volume is 4.34 ml approximately.
To solve this problem, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature when the pressure remains constant.
The equation for Charles's Law is:
\(\frac{{V_1}}{{T_1}} = \frac{{V_2}}{{T_2}}\)
where V₁ and T₁ are the initial volume and temperature, and V₂ and T₂ are the final volume and temperature.
Given:
V1 = 4.5 ml (initial volume)
T1 = 20.0°C (initial temperature)
T2 = 10.0°C (final temperature)
Substituting the values into the equation:
\(\frac{{4.5 \, \text{ml}}}{{20.0°C + 273.15}} = \frac{{V_2}}{{10.0°C + 273.15}}\)
Simplifying the equation:
\(\frac{{4.5}}{{293.15}} = \frac{{V_2}}{{283.15}}\)
Now, we can solve for V₂:
\(V_2 = \left(\frac{{4.5 \, \text{ml}}}{{293.15}}\right) \times 283.15\)
V2 ≈ 4.34 ml
Therefore, the new volume of the balloon at 10°C is approximately 4.34 ml.
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A bike travels at a constant speed of 4.0 m/s for 5.0s. How far does it go?
Answers
Answer:
20 m
Explanation:
1 s = 4 m
5 s = ?
? = (4 x 5) = 20 meters
Answer:
distance = 0.8 m
Explanation:
given:
A bike travels at a constant speed of 4.0 m/s for 5.0s.
find:
How far does it go?
solution:
distance = speed / time
distance = 4.0 m/s
5 sec.
distance = 0.8 m
3. Explain why the planets orbit the Sun and why the orbits are slower the further
away a planet is from the Sun.
Answers
Answer:
The closer a planet is to the Sun, the stronger the Sun's gravitational pull on it, and the faster the planet moves. The farther it is from the Sun, the weaker the Sun's gravitational pull, and the slower it moves in its orbit.
The parent function `f\left(x\right)=\sqrt[3]{x}` is compressed vertically by a factor of `\frac{1}{3}` and then translated 3 units left and 7 units down. What is the transformed function `g\left(x\right)`?
Answers
Answer:
The answer is below
Explanation:
Given that f(x) = x√3.
A function can be vertically stretched or compressed by multiplying it by a positive constant. If the constant is greater than 1, it is vertically stretched and if the constant is less than 1 it is vertically compressed.
If a function f(x) = x is compressed or stretched by a constant a, then the new function g(x) = a f(x)
If a function f(x) = x is translated a units down, then the new function g(x) = f(x) - a
If a function f(x) = x is translated a units left, then the new function g(x) = f(x-a)
If f(x) = x√3 is compressed vertically by a factor of 1/3. The new function is
\(f(x)'=x\sqrt{3} *\frac{1}{3} \\\\f(x)'=\frac{x}{3} \sqrt{3}\)
If it is then translated 3 units left and 7 units down, the transformed function g(x) is:
\(g(x)=(\frac{x-3}{3}\sqrt{3} )-7\)
which command is capable of creating connecting lines that have a rounded or sharp edge?
a.trim
b.rotate
c.hatch
d.fillet
Answers
Answer:
it is dddd
Explanation:
circular motion of charges: a charged particle of mass 0.0050 kg is subjected to a 7.0 t magnetic field which acts at a right angle to its motion. if the particle moves in a circle of radius 0.10 m at a speed of 3.0 m/s, what is the magnitude of the charge on the particle?
Answers
Charged particles in a circle with a radius of 0.10 m and a speed of 3.0 m/s experience a 7.0 T magnetic field perpendicular to their velocity. The particle has a charge that is roughly 0.0214 Coulombs in size.
To find the magnitude of the charge on the particle, we can use the equation for the centripetal force experienced by a charged particle in a magnetic field:
F = qvB
Where:
F is the centripetal force
q is the charge on the particle
v is the velocity of the particle
B is the magnetic field strength
In circular motion, the centripetal force is given by:
\(F = \frac{{mv^2}}{{r}}\)
Where:
m is the mass of the particle
v is the velocity of the particle
r is the radius of the circle
Since the centripetal force is also equal to qvB, we can equate the two expressions:
\(\frac{{mv^2}}{{r}} = qvB\)
Simplifying the equation:
mv = qrB
Rearranging the equation to solve for the charge (q):
\(q = \frac{{mv}}{{rB}}\)
Given:
m = 0.0050 kg (mass of the particle)
v = 3.0 m/s (velocity of the particle)
r = 0.10 m (radius of the circle)
B = 7.0 T (magnetic field strength)
Substituting the values into the equation:
\(q = \frac{{0.0050 \, \text{{kg}} \cdot 3.0 \, \text{{m/s}}}}{{0.10 \, \text{{m}} \cdot 7.0 \, \text{{T}}}}\)
Calculating the value:
q ≈ 0.0214 C
Therefore, the magnitude of the charge on the particle is approximately 0.0214 Coulombs.
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Give two ways humans can reduce the amount of carbon at the location from #3. Give one example that will reduce carbon entering this location and one example that will increase carbon exiting this location. Explain how this reduces the carbon.
Answers
1. Reducing Carbon Entering: Planting more trees at the location is an effective way to reduce the amount of carbon at this location.
What is Carbon?Carbon is an element found in abundance in the Earth's atmosphere and is one of the most abundant elements in the universe. Carbon is a key component of all living organisms and serves as the backbone of life on Earth. Carbon exists in several different forms, including coal, oil, natural gas, and diamonds, and can be found in many other materials, such as plastics, paper, and fabrics.
Trees absorb carbon dioxide from the atmosphere and use it to produce oxygen through photosynthesis. This process helps to reduce the amount of carbon entering the location.
2. Increasing Carbon Exiting: Installing solar panels at the location is an effective way to increase the amount of carbon exiting the location. Solar panels convert solar energy into electricity, releasing carbon dioxide into the atmosphere during the process. This helps to reduce the amount of carbon at the location by releasing it back into the atmosphere.
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A toy car of mass 2-kg travels along a horizontal surface with negligible friction at a speed of 1.0 m/s. The car then collides with a vertical wall. The wall applies a force of magnitude 20 N for 0.2 s on the toy car. Which of the following predicts the motion of the toy care immediately after the collision?
A: The speed of the car will increase, and the car will travel in the opposite direction.
B: The speed of the car will decrease, and the car will travel in the opposite direction.
C: The speed of the car will remain the same, and the car will travel in the opposite direction.
D: The car will stop and remain motionless.
Please show your work in finding the direction of motion - ie. please don't use common sense but rather show the applicable physics principles along with formulas to find the direction of motion.
Answers
Answer:
An experiment is conducted in which a cart travels across a horizontal surface and collides with a wall. Data collected from the experiment are used to create the graph of the cart's velocity as a function of time. All frictional forces are considered to be negligible. Which data from the graph should the student use to determine the direction of the net force exerted on the cart and the direction of the change in momentum of the cart from the time intervals of A to B?
Explanation:
As we know that
Force=dp/dt(Change in momentum/time)So
20N=dp/2dp=10N/sHence the speed of car will remain the same it won't affect the speedAs momentum from wall is more the ball will travel in opposite directionOption C is correct
how long does it take to accelerate to 60 mph ? your answer, which seems impossibly short, is confirmed by track tests.
Answers
It takes around 5 seconds to accelerate to 60 mph.
1. What is acceleration?
Acceleration is the process of increasing speed or velocity over time. When a car accelerates, it gradually increases its velocity from a standstill to a faster speed.
As a result, acceleration can be measured in units of distance over time, such as meters per second squared (m/s2) or miles per hour per second (mph/s).
Acceleration is an important concept in physics and engineering, as it helps to describe the motion of objects in terms of their speed, direction, and rate of change. In addition, acceleration is often used in the design of cars, aircraft, and other vehicles, as it can affect their performance and fuel efficiency.
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Keesha conducts an experiment by pouring equal amounts of boiling water into four containers. The containers are the same size and shape, but they are made of different materials. The chart lists the containers according to their materials. A 2-column table with 4 rows. The first column labeled Container has entries W, X, Y, Z. The second column labeled Material has entries foam, glass, plastic, stainless steel. Using protective gloves, Keesha carefully touches each container immediately after pouring the water. Which container was likely the hottest? W X Y Z.
Answers
Option Z is correct. The stainless steel container was likely the hottest. Stainless steel is an excellent heat conductor because it quickly warms the substance.
What are the qualities of stainless steel?Stainless steel is an excellent heat conductor because it quickly warms the substance or allows heat to travel through it. Stainless steel is also corrosion-resistant.
Foam, glass, and plastic, on the other hand, are all poor heat and electrical conductors. As a result, they do not allow heat to travel through.
As a result, we may deduce that, among the available possibilities, the stainless steel container was most likely the hottest.
Hence Option Z is correct. The stainless steel container was likely the hottest.
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A box weighing 2.4 x 10^2 Newton's is lifted at a constant speed to a shelf 1.2 meters high in 4.0 seconds. What power is required to lift the box
Answers
Answer:
72Watts
Explanation:
Power = Force * distance/Time
Given the following
Force = 2.4 x 10^2 = 240N
distance = 1.2m
Time = 4.0secs
Substitute
Power = 240*1.2/4
Power = 60 * 1.2
Power = 72watts
Hence the power required to lift the box is 72Watts
what is the approximate distance from earth to the sun?
Answers
The approximate distance from the Earth to the Sun is about 93 million miles
What is the approximate distance from the Earth to the Sun?The average distance from the Earth to the Sun is about 93 million miles (149.6 million kilometers). This distance is known as an astronomical unit (AU) and it is used to measure distances within the solar system. It is important to note that this distance is not a constant and varies slightly over time due to the elliptical shape of Earth's orbit around the Sun.
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How long would it take a car going 25 m/s to travel 1000 meters?
Answers
Answer:
40
Explanation:
1000 divided by 25 is 40
If the vehiche has a speed of 24.0 m/s at point a what is the force of the track on the vehicle at this point?
Answers
Question:
A roller-coaster vehicle has a mass of 500 kg when fully loaded with passengers. If the vehicle has a speed of 20.0 m/s at point A, what is the force exerted by the track on the vehicle at this point?
See attachment
Answer:
33700 Newton
Explanation:
Given
\(m = 500kg\\v = 24.0m/s\\r=10m\)
First, we determine the forces acting on mass m.
They are: the force exerted by the track (Fn) and the weight of the vehicle (W)
So, the net force is:
\(F_{net} = F_n - W\)
\(W=mg\)
So:
\(F_{net} = F_n - mg\)
Make Fn the subject
\(F_n = F_{net} + mg\)
Fnet is calculated as:
\(F_{net} = F_c = \frac{mv^2}{r}\) --- i.e. the centripetal force
So:
\(F_n = F_{net} + mg\)
\(F_n = \frac{mv^2}{r} + mg\)
\(F_n = \frac{500 * 24^2}{10} + 500 * 9.8\)
\(F_n = 28800 + 4900\)
\(F_n = 33700N\)
Which element will donate electrons?
A Sulfur
B aluminum
C nitrogen
D chlorine
Answers
Answer:
B aluminum
Explanation:
Because aluminum loses 3 types of electrons and it donates it to fluorine.
A 264 kg boulder is pulled with a rope across a field by a strong man. If the man uses a force of 2,452 N to cause the boulder to accelerate across the field. The coefficient of friction is 0.53. How fast does the strong man accelerate the boulder?
Answers
The strong man accelerates the boulder of mass 264 kg at 4.1 m / s² if he uses a force of 2452 N.
W = m g
W = Weight
m = Mass
g = Acceleration due to gravity
m = 264 kg
g = 9.8 m / s²
W = 264 * 9.8
W = 2587.2 N
F = 2452 N
W = Normal force, N = 2587.2 N
\(f_{k}\) = μ N
\(f_{k}\) = Kinetic frictional force
μ = Co-efficient of kinetic friction = 0.53
\(f_{k}\) = 0.53 * 2587.2
\(f_{k}\) = 1371.22 N
∑ \(F_{x}\) = m a
F - \(f_{k}\) = m a
2452 - 1371.22 = 264 * a
a = 1080.78 / 264
a = 4.1 m / s²
Therefore, the strong man accelerates the boulder at 4.1 m / s²
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