Answers
Answer:
138
Explanation:
(since there's a blank next to "9x y j", I'm assuming the y of F(x, y) is 9x[tex]\sqrt{y}[/tex] j)
1) find the partial derivative of each:
[tex](6y^{\frac{3}{2} })i + (9x\sqrt{y} )j[/tex]
[tex]f_{x} =(6y^{\frac{3}{2} })_{x} = \int\limits{6y^{\frac{3}{2} }} \, dx = 6xy^{\frac{3}{2} } +c \\\\f_{y} = (9x\sqrt{y} )_{y} = \int\limits{9xy^{\frac{1}{2} } } \, dy = 9x(\frac{2}{3} )y^{\frac{3}{2} } +c = 6xy^{\frac{3}{2} } +c[/tex]
2) use partial integrals to make gradient of f:
take whatever you got from partial integral and add them together (if they repeat, just use it once)
[tex]F =[/tex] Vf (V = gradient of)
[tex]F(x, y) = 6xy^{\frac{3}{2} }[/tex]
3) Evaluate the integrals with given points:
Integral of F dotted with dr = F(point B) - F(point A) = F(3, 4) - F(1, 1)
[tex]F(point B) = 6(3)(4)^{\frac{3}{2} }\\F(Point A) = 6(1)(1)^{\frac{3}{2}}\\F(point B) - F(pointA) = 6(3)(4)^{\frac{3}{2} }-(6(1)(1)^{\frac{3}{2}})[/tex]
= 144 - 6 = 138 units of work
Work done by the force field F in moving an object from A to B = 138 J
Given data :
Force field F(x,y) = [tex]6y^{\frac{3}{2} }i + (9x\sqrt{y} ) j[/tex]
Step 1 : determine the partial derivatives of the vector quantity
Fx = ∫ [tex]6y^{\frac{3}{2} }i = 6xy^{\frac{3}{2} } + c[/tex]
Fy = ∫ [tex](9x \sqrt{y})_{y} = 9x(\frac{2}{3})y^{\frac{3}{2} } + c[/tex]
Equating the partial derivatives :
[tex]9x(\frac{2}{3})y^{\frac{3}{2} } + c[/tex] = [tex]6xy^{\frac{3}{2} } + c[/tex]
therefore the gradient of F i.e. F = vF = F( x,y ) = [tex]6xy^{\frac{3}{2} }[/tex]
Next step : Determine the work done
Work done ( F.dr ) = [ F(point b ) = F( 3,4 ) ] - [ F(point A) = F( 1,1 ) ]
F(3,4 ) = 6(3)(4)[tex]^{\frac{3}{2} }[/tex] = 144
F( 1,1 ) = 6(1)(1)[tex]^{\frac{3}{2} }[/tex] = 6
Therefore the work done by the force field = 144 - 6 = 138 J
Hence we can conclude that the work done by the force field F is = 138 J
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Related Questions
A 5 kg bowling ball travelling at 2 m/s hits a motionless 10 kg bowling ball. If the smaller ball bounces back at a speed of -1 m/s, what will be the speed of larger ball after the collision? Hint: Use the conservation of momentum equation to solve this problem.
Answers
Answer:
1.5 m/s
Explanation:
Conservation of momentum means the momentum of the system before the collision is the same as after.
The before, after momentum of each ball is ...
5 kg ball: (5 kg)(2 m/s), (5 kg)(-1 m/s)
10 kg ball: (10 kg)(0 m/s), (10 kg)(v)
The sum of the "before" products is the same as the sum of the "after" products:
(5 kg)(2 m/s) +0 = (5 kg)(-1 m/s) +(10 kg)v
(10 +5) kg·m/s = (10 kg)·v . . . . . add (5 kg)(1 m/s) to both sides
v = (15 kg·m/s)/(10 kg) = 1.5 m/s
The speed of the larger ball will be 1.5 m/s. Its direction of motion will be the opposite of that of the 5 kg ball after the collision.
The less dense areas created as a sound wave propagates are called
A. rarefactions✅
B. troughs
C. crests
D. compressions
Answers
Answer:
C. crests
don't trust me though
Answer:
The less dense areas created as a sound wave propagates are called rarefactions.
Explanation:
Hoped this helped.
the push up is dynamic or static
Answers
Answer:
Dynamic exercises
Explanation:
The Greek root astro means "stars." Use the context clues to choose the correct definition of the word astronomer. According to the astronomer, the bigger the telescope, the more detail we can see in the images. O A. a person who studies astronauts O B. a person who studies the stars O C. a person who tells the future O D. a person who studies other people
Answers
Answer:
b, it's a pretty easy explanation
E5. A ball is thrown downward with an initial velocity of 12 m/s.
Using the approximate value of g 10 m/s2, what is the
velocity of the ball 1.0 seconds after it is released?
Answers
Hi there!
We know the following kinematic equation:
vf = vi + at
Where:
vf = final velocity
vi = initial velocity
a = acceleration
t = time
In this instance, the ball is experiencing a constant acceleration of that of gravity, thus:
vf = 12 + 10(1) = 22 m/s (if downward is considered positive in this instance)
What is the maximum height above ground a projectile of mass 0.79 kg, launched from ground level, can achieve if you are able to give it an initial speed of 80.3 m/s?
Answers
From kinematic, the maximum height above ground a projectile of mass 0.79 kg, launched from ground level can achieve is 329 meters approximately.
The parameters given from the question are
mass m = 0.79kg
initial speed U = 80.3 m/s
Maximum height H = ?
The object will be going up under the influence of gravity. Acceleration due to gravity g = -9.8m/[tex]s^{2}[/tex]
At maximum height, final velocity V = 0
From kinematic formula, the best formula to use is
[tex]V^{2} = U^{2} - 2gH[/tex]
Substitute all the parameters into the equation
0 = [tex]80.3^{2}[/tex] - 2 x 9.8 x H
19.6H = 6448.09
H = 6448.09 / 19.6
H = 328.98 m
Therefore, the maximum height above ground a projectile of mass 0.79 kg, launched from ground level can achieve is 329 meters approximately.
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A plastic bag is massed. It is then filled with a gas which is insoluble in water and massed again. The apparent weight of the gas is the difference between these two masses. The gas is squeezed out of the bag to determine its volume by the displacement of water. What is the actual weight of the gas
Answers
The actual weight of the gas = apparent weight + weight.
The actual weight = [tex]W_{A}[/tex] + W
Given that a plastic bag is massed. It is then filled with a gas which is insoluble in water and massed again.
If the apparent weight of the gas is the difference between these two masses, then let the apparent weight = [tex]W_{A}[/tex]
The gas is squeezed out of the bag to determine its volume by the displacement of water. Since
density = mass / volume
The density of water is 1000 kg/[tex]m^{2}[/tex]
we can get the mass of the gas by making m the subject of the formula.
W = mg
The actual weight of the gas = apparent weight + weight
That is,
The actual weight = [tex]W_{A}[/tex] + W
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URGENTLY NEED HELP!!!!!!
the stretch of a spring and the force it exerts are inversely proportional.
Select one:
O True
O False
Answers
Answer:
False.
Explanation:
HELP ASAP!!!!! Choose all the answers that apply. Technology A)influences science
B)helps scientists observe fast phenomena
C)is the same as science
D) influences history
E)helps scientists observe slow phenomena
Answers
We have seen in earlier readings how to determine the speed of a wave on a string. What will happen to the wavelength of a sinusoidal wave on a string if the tension in the string is increased (assuming we keep the frequency of the wave the same)
Answers
This question involves the concepts of tension in a string and the wavelength of the wave in a string.
The wavelength of a sinusoidal wave will "increase by square power" on a string if the tension in the string is increased when the frequency is kept constant.
The speed of a wave on a string is given by the following formula:
[tex]v=\sqrt{\frac{T}{\mu}}[/tex]
where,
v = speed of wave = fλ
f = frequency of the wave
λ = wavelength of the wave
T = tension force
μ = linear mass density of the string
Therefore,
[tex]f\lambda=\sqrt{\frac{T}{\mu}}\\\\T = f^2\lambda^2\mu[/tex]
It is given that the frequency is kept constant. The linear mass density is also constant for a string. Therefore,
[tex]T=(constant)\lambda^2\\T\ \alpha\ \lambda^2[/tex]
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If you were told an atom was an ion, you would know the atom must have a?
A neutral charge
B charge
C negative charge
D positive charge
Answers
Answer:
its b it must be charge
Explanation:
3. What can you infer about the position of the galaxies 100 million years before this telescope photo was taken
Answers
The galaxies are in constant motion so it can be inferred that their position will not be the same as a hundred million years ago.
A galaxy is a term to refer to the set of stars, gas clouds, planets, cosmic dust, dark matter, and energy gravitationally united in a more or less defined structure in the universe.
Galaxies are in constant motion because the elements that make them up are not static at any time; The galaxies rotate around the center of the galaxy. If they were still, the gravitational attraction would cause them to immediately fall towards the center of the galaxy: it is the same that would happen to the Earth and the other planets if they stopped rotating around the Sun, they would fall towards the Sun.
According to the above, it can be inferred that the galaxies after a while have moved from the place where they were last seen.
Note: This question is incomplete because there is some missing information. However, I can answer based on my general prior knowledge.
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Over half the global population faces a shortage of clean water. Which example is a point source water pollutant? pesticide run-off from farmers’ fields a sewer pipe draining directly into a river road oil washing into sewer drains, and eventually reaching waterways erosion from a denuded slope after a heavy rainfall
Answers
An example of a point source water pollutant is a sewer pipe draining directly into a river.
According to the United States Environmental Protection Agency, a point source pollution is defined as; “any single identifiable source of pollution from which pollutants are discharged, such as a pipe, ditch, ship or factory smokestack.”
Hence, an example of a point source water pollutant is a sewer pipe draining directly into a river. The pollution is coming from an easily identifiable source which is a sewer pipe connected to a river directly.
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6. A 15.53 kg bag of soil falls 5.50 m at a construction site. If all the energy is retained by the soil in the bag, how much will its temperature increase
Answers
The increase in the temperature of the soil when bag fall from the given height is 0.065 ⁰C.
The given parameters:
mass of the bag, m = 15.53 kgheight of fall, h = 5.5 mspecific heat capacity of soil, C = 0.200 kcal/kg ⁰CApply the principle of conservation of energy as follows;
[tex]mgh = mC \Delta T\\\\gh = C \Delta T\\\\\Delta T= \frac{gh}{C}[/tex]
Convert the value of C in kcal/kg ⁰C to J/kg ⁰C
1 kcal = 4180 J
[tex]0.200 \ kcal/kg ^0 C= 0.2 \times 4180 (J/kg ^0C) = 836 \ J/kg^0 C[/tex]
The increase in the temperature of the soil is calculated as follows;
[tex]\Delta T= \frac{gh}{C}\\\\\Delta T= \frac{9.8 \times 5.5}{836} \\\\\Delta T= 0.065 \ ^0C[/tex]
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How do mechanical waves compare with electromagnetic waves?
Answers
Answer:
Main Difference Between Mechanical and Electromagnetic waves
A wave is composed of some kind of disturbance that propagates. We can classify waves into many different types based on their properties. One of the properties of the waves depends on whether they need a medium to propagate or not. The primary difference between electromagnetic and mechanical waves is also based on this property. Mechanical waves need a medium, while electromagnetic waves do not need a medium to propagate. Electromagnetic waves can travel through a vacuum. The other differences between mechanical and electromagnetic waves are given below:
Electromagnetic waves can travel through a vacuum, that is an empty space, whereas mechanical waves cannot. They need a medium to travel such as water or air. Ripples in a pond are an example of mechanical waves whereas electromagnetic waves include light and radio signals, which can travel through the vacuum of space.
Mechanical waves can be classed as elastic waves because their transmission depends on the medium's (water, air etc.) elastic properties.
Electromagnetic waves are caused because of the varying magnetic and electric fields. They are produced by the vibration of the charged particles.
Because of these differences, the speed of each type of wave varies significantly. Electromagnetic waves travel at the speed of light but mechanical waves are far slower.
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49. A particle starts from rest at time t=0 and movies along the x axis. if the net force on is proportional to t its kinetic energy is proportional to?
Answers
Answer:
F net ∞ [tex]\frac{1}{\sqrt{t} }[/tex]
Explanation:
In pic
_________________
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help meee please please please
Answers
On clear day, sunlight delivers approximately 1000 J each second to a 1 m2 surface; smaller areas receive proportionally less--half the area receives half the energy. A 12% efficient solar cell, a square 12 cm on a side, is in bright sunlight.
How much electric power does it produce?
Answers
The direct proportions rule allows to find the result for the energy produced by a solar cell is:
E = 1,728 J
The efficiency of a solar cell is the percentage of incident energy that transforms into electricity.
The direct proportions rule or three rule stable that if two quantities are proportional the product remains constant.
They indicate that the length of the solar cell is l = 12 cm = 0.12m. Let's find the area of the solar cell.
A = l²
A = 0.12²
A = 1.44 10⁻² m²
Let's use a direct proportion rule. If 1 m² receives 1000J of energy, how much does an area of 1.44 10⁻² m² receive?
Energy_cell = 1000 J ( [tex]\frac{1.44 \ 10^{-2}}{1}[/tex] )
Energy_ cell = 14.4 J
Let's use another direct ratio rule for efficiency.
[tex]Energy_{produced} = Energy_{cell} \frac{12}{100} \\Energy_{produced} = 14.4 0.12 \\Energy_{produced} = 1.728 J[/tex]
In conclusion using the direct proportions rule we can find the result for the energy produced by a solar cell is:
E = 1,728 J
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To become a healthy individual, a person must have a properly executed routine to achieve his/her fitness goals. On the contrary, in what instance does a person become unhealthy
Answers
A mass is placed at the end of a spring. It has starting velocity of V & allowed to oscillate freely. If the mass has a starting velocity of 2V, what would the period be? Half as long, remains constant, 1/4 as long , 4 times as long, or 2 times as long?
Answers
Answer:
Equation for SHM can be written
V = w A cos w t where w is the angular frequency and the velocity is a maximum at t = 0
V1 = w1 A cos w1 t
V2 = w2 A cos w2 t
V2 / V1 = w2 / w1 since cos X t = 1 if t = zero
V2 / V1 = 2 pi f2 / (2 pi f1) = f2 / f1 = T1 / T2
If the velocity is twice as large the period will be 1/2 long
A rod of length 0.82 m, rotating with an angular speed, 4.2 rad/s, about axes that pass perpendicularly through one end, has a mass of 0.63 kg, which is distributed uniformly along its length. Find the kinetic energies of the rod.
Answers
Answer:
Explanation:
KE = ½Iω²
ΚΕ = ½(mL²/3)ω²
ΚΕ = ½(0.63(0.82²)/3)4.2²
ΚΕ = 1.24541928
KE = 1.2 J
PLEASE HELP I NEED TO PASS THIS CLASS
Answers
Answer:
I think that the answer is 4.318 as a=f/p
Over a period of 3 seconds, a speedboat accelerates uniformly from 20 m/s
to 50 m/s. What is the acceleration of the speedboat relative to the shore?
Answers
The acceleration of the speedboat relative to the shore is 10m/s²
Acceleration is the change in velocity of an object with respect to time. Mathematically;
Acceleration = change in velocity/Time
Change in velocity = 50 - 20
Change in velocity = 30m/s
Time = 3secs
Substitute into the formula to have:
acceleration = 30/3
acceleration = 10m/s²
Hence the acceleration of the speedboat relative to the shore is 10m/s²
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7.2
8
How is kinetic
molecular
model of matter helpful in
differentiating various states
of matter?
V
Answers
Answer:
The kinetic molecular theory of matter asserts that: Matter is made up of particles that are continually moving. All particles contain energy, however the energy fluctuates depending on the temperature the sample of matter is in. This in turn decides whether the material exists in the solid, liquid, or gaseous form.
Explanation:
Hope it helps:)
A baseball is hit with a speed of 30.0 m/s at an angle of 47.0 ∘ . It lands on the flat roof of a 11.0 m -tall nearby building. If the ball was hit when it was 1.4 m above the ground, what horizontal distance does it travel before it lands on the building?
Answers
Answer:
500m/s
Explanation:
ma thii nay pathe me thuda dase dangur ni puthar
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a wave travels at a constant speed. how does the wavelength change if the frequency is reduced by a factor of 3? assume the speed of the wave remains unchanged.
A. the wavelength decreases by a factor of 3
B. the wavelength does not change
C. the wavelength increases by a factor of 3
D. the wavelength increases by a factor of 9
Answers
Answer:
b
Explanation:
when the wavelength increase it doesnt affect the frequency of a wave.
Answer: The wavelength increases by a factor of 3
Explanation:
Look up the specs on a c6 rocket engine. How many C6 engines would it take to launch Mr. Blazey (90kg)
from the elevation of Boulder to the elevation of longs peak? (3 points) What would the max power be? (3
points) The max acceleration? (3 points) For all 12 points, you'll need to account for the mass of the added
rockets (you can assume their mass declines linearly over their burn and is O after they finish burning).
Answers
Answer:
The Estes C6-0 engine is a booster stage engine designed for model rocket flight and has to be used with a standard engine. This engine is for flights in rockets weighing less than 4 ounces, including the engines. Each package includes 3 engines, 4 starters and 4 plugs.
2. Jason rode his bike 10 miles and only rode for 2 hours how fast was he going?
Answers
Answer:
5 miles per hour.
Explanation:
10miles / 2hours = 5 mph
13. Which of the following lines (of latitude or longitude) would be represented by 0° Latitude?
14. Which of the following lines (of latitude or longitude) would be represented by 90° North
Latitude?
15. Which of the following lines (of latitude or longitude) would be represented by 90° South
Latitude?
16. Which of the following lines (of latitude or longitude) would be represented by 0° Longitude?
a. south pole b. equator c. prime meridian d. north pole
Answers
Answer:
14. Which of the following lines (of latitude or longitude) would be represented by 90° North Latitude?
ANSWER: D. North Pole
15. Which of the following lines (of latitude or longitude) would be represented by 90° South Latitude?
ANSWER: A. South Pole
16. Which of the following lines (of latitude or longitude) would be represented by 0° Longitude?
ANSWER: C. Prime Meridian
Answer:
A
Explanation:
i mark u brainliest answer please answer me
Answers
Answer:
bathing and wear clean clothes 2 pollute 3throwing waste in land air water pollution