itisarainyday/ml_classifier_bert_training · Datasets at Hugging Face

0 stringlengths 10 969	label int64 0 1
*If you are unsure, look at 1M Thermo.	0
The wind velocity is latex2 towards the shoreline.	0
Consider the interval latex0 and develop a series of polynomials of successively higher order that form an orthonormal set.	1
Inertial frame of reference 4.	0
If latex0 , verify that latex1	1
Assume that contaminant concentration and mean velocity across the pipe are uniform.	0
Would it be possible to obtain upstream migration (against the flow) of an antidune system if the total sediment transport is downstream?	1
Evaluate the limits: latex0 latex1 latex2	1
Sketch the parabola.	1
Transform the following time domain equations into Laplace domain (assume that all the variables are at rest at latex0 ): latex1 latex2 where latex3 latex4 where latex5 is defined in the same way as in part (b).	1
In cartesian co-ordinates, what is the latex1 -component of the pressure?	1
Next, we will prove an important property of the Michalis-Menten equation.	1
A piston of diameter latex0 is fitted inside a U-shaped tube filled with liquid mercury (with density in latex1 ), as shown by the sketch below.	0
The chain pitch is 12mm The final stage in this task is to determine the torque and resultant acceleration you can expect from your go-kart.	1
Establish if by choosing a capacitor latex0 , the circuit below is underdamped or overdamped: The other component values are as follows: latex1 \ latex2 \ latex3 \ latex4 \ latex5	1
Find: The final pressure of the contents.	1
Sketch the solution for a concentration latex5 which satisfies the reflector boundary condition as a superposition of the concentration profiles in a and b.	1
A torus is described in spherical polar coordinates by latex0 (independent of latex1 ).	0
If a matrix element does not exist, input 'n'.	1
As you push the cart at constant speed the mass will be displaced by a length latex1 .	0
Find the downstream height latex3 .	1
Write the following numbers in polar form latex0 , where latex1 .	1
Now suppose that there are three non-zero vectors latex5 , latex6 , and latex7 in latex8 that obey: latex9 Can you conclude that latex10 ?	1
The mercury rises by latex2 under the weight of the piston.	0
For the approximate solution (in part (c)) near to latex7 , comparing to the Taylor series in part (d) the find the relative error when: latex14 Notice how the approximate equation produced a solution latex7 .	1
(1) and (2), derive the other three SUVAT equations: latex6	1
If latex0 , calculate latex1 and latex2 and show that latex3	1
Give the solution to this problem in symbolic form.	1
You are supplied with a motor providing operating at an output shaft speed of 2900 rpm at a torque of 4Nm.	0
The function latex0 never vanishes (goes to zero).	0
It took latex17 for the absorbance of the assay to increase from latex18 to latex19 .	0
How far below point B should point D be placed?	1
Sketch the output waveform at “P”, showing peak values and time intervals	1
Calculate the Reynolds number in this vein assuming the dynamic viscosity of blood to be 0.003 Pa s, and the density is 1060 kg/m latex0 .	1
A truck travels through shallow water at some speed latex7 .	0
The release occurs at the water surface, which is modelled as a perfect reflector.	0
You should have found that latex24 and latex25 were not the same so the above method is wrong in the moving frame.	0
Hence find the angular momentum latex13 and torque latex14 about the origin at latex10 .	1
There is no superheat.	0
Explain whether, at latex11 m, the Blasius solution is applicable for speeds, latex1 , of: (i) latex13 m/s; (ii) latex14 m/s; (iii) latex15 m/s.	1
Kinetic energies at entry and exit are negligible and nitrogen can be modelled as a perfect gas under these conditions.	0
You can assume the full load operating speed for this motor is 1000rpm and that the maximum torque it can provide is 0.045Nm.	0
Solve Problem 10.4 by considering a cylindrical frame of reference attached to the ground, with origin in the centre of the tank and with axial direction latex0 .Determine an expression for the velocity field Determine the deformation tensor.	1
Sketch a graph of latex12 and indicate on it any points of equilibrium.	1
Consider the rate law: latex0 Where latex1 is the concentration of reactant, latex2 is time, and latex3 is a rate constant.	0
What is its final velocity?	1
Comment on the gradient at the wall.	1
Steam enters a turbine with a pressure of 30 bar and a temperature of latex0 with a velocity of latex1 .	0
What is the mass, latex3 , of the piston?	1
Find the deflection at the quarter span of the loaded beam.	1
Explain what is meant by the by the expressions that follow.	1
Using the symbols above: latex7 Which can be re-arranged as: latex8 The solution for this equation for latex3 would allow you to calculate the latex10 of a solution of a weak acid.	0
* Note:** In the response area, type the same answer twice for repeated solutions.	1
We count symbols from the list, going from latex14 to latex23 .	0
The transport of contaminant when diffusion is negligible.	0
In two or more dimensions, for most (but not all) force fields latex7 , the work done, latex8 depends on the route taken from latex9 to latex10 .	0
The natural frequency of the oscillator is latex3 .	0
You are encouraged to individually work through several possible solutions and then discuss as a group.	0
Negligible effects of gravity In Section A In Section B In Section C In Section D In Section E	0
Write down the general solution to **eq.	1
What are the efficiencies of the engine based on GCV and NCV respectively?	1
Once a flow has been started by sufficient suction, the syphon will run continuously as long as there is fluid available in the reservoir.	0
latex2 latex3 latex4 latex5 latex6	0
The wind is now blowing and exerts a constant (time-independent) force latex1 in the forward direction.	0
What, thermodynamically, distinguishes the situations in (a) and (b)?	1
The rate at which entropy is generated within the turbine per latex8 of steam flowing in units of latex9 .	0
Derive an expression for the acceleration of the particle.	1
Make use of Taylor series and start from the compressible flow relation for the ratio of stagnation to static pressure.	1
*** The triangular function below is periodic on the interval latex0 a_0=0 latex1 a_n=0 latex2 b_n latex3 b_n latex4 n latex1 \int_{-\pi}^{\pi}f(x)\sin(n x)dx=2\int_{0}^{\pi}f(x)\sin(n x)dx \;.	0
He thinks she might be joking.	0
Diffusion only and in both latex0 and z-directions.	0
What will be: (i) the energy utilisation factor of the CHP plant?	1
The temperature of steam with a pressure of latex12 bar and specific enthalpy of latex13 .	0
What is the angle (in degrees), anti-clockwise relative to horizontal, of lines of constant pressure within the water in the accelerating tank?	1
Give the exact length.	1
Once you know how to count, then you can define operations such as addition and subtraction, which are nothing but the ability to count in the forward or backward directions by increments of any lengths.	0
Draw a sketch of the imaginary part of latex2 up to latex4 , latex8 , latex9 and latex10 terms in the Fourier series.	1
(Assume that the steam is wet at the turbine exhaust).	0
(Based on P3.139, White) The horizontal pump shown below discharges water at latex0 C at a volume flux of latex1 .	0
A boundary layer develops along the walls of the working section, but the velocity profile outside the boundary layer remains uniform and steady.	0
Find the magnitudes and directions of the maximum shear stresses at the point.	1
Determine the values of latex6 and latex3 .	1
* You may wish to use .	0
latex0 latex1 latex2 latex3	0
Using the Tables in the Data & Formulae book for the properties of water and steam, write down the magnitude and units for the following: The specific volume of saturated water at latex0 bar.	1
Flywheel latex0 is driven by a torque latex16 , given by: latex17 where latex18 is the time and latex19 is a constant equal to latex20 .	0
Show that an area element of the surface of the torus is given by: latex3 *** Let all the formal machinery developed in lectures work for you and you should easily reach the expression for latex4 .	1
This question relates to combined cycle plants and combined heat and power plants.	0
On a latex6 diagram, sketch three Joule cycles with different pressure ratios (one very low, one medium and one very high) but the same maximum temperature.	1
Hence, find the maximum solar energy (with no solar panel tilting) that can be obtained in London ( latex10 ) as compared to the equator.	1
What is happening, physically, in the water?	1
As the disc rotates in the direction shown, four optical sensors with switching outputs, arranged along the line “ab”, generate a 4-bit natural binary signal which represents its angular position.	1
How much did the density change relative to latex17 if the drone is flying latex19 above the ground?	1
Repeat part c) using linear theory.	1
*** The pendulum consists of a mass suspended from a cord of length latex0 suspended vertically (the latex1 direction) at latitude latex2 , with the rotation plane being free to move in the latex3 - latex4 plane (see the Figure below).	0
I leave it to you to learn how to play with these four operators in base- latex16 (Wikipedia is your friend), and we proceed with solving our logistic-map conversion problem.	0
Calculate the values of the amplitude latex1 , the angular frequency latex2 , the frequency latex3 , the period latex4 , the spring constant, latex5 .	1
Write down an expression for the total head at surface 1, latex0 , if gravitational effects can be neglected.	1
* *** Consider an infinitely long rod where the temperature is evolving according to the heat flow equation: latex0 where latex1 represents the temperature at the point latex2 and time latex3 .	0
A planet circles a star (in the latex0 - latex1 plane) with a motion described as a function of time latex2 by the position vector: latex3 (you may assume that quantities are normalised and so dimensionless).	0

*If you are unsure, look at 1M Thermo.

0

The wind velocity is latex2 towards the shoreline.

0

Consider the interval latex0 and develop a series of polynomials of successively higher order that form an orthonormal set.

1

Inertial frame of reference 4.

0

If latex0 , verify that latex1

1

Assume that contaminant concentration and mean velocity across the pipe are uniform.

0

Would it be possible to obtain upstream migration (against the flow) of an antidune system if the total sediment transport is downstream?

1

Evaluate the limits: latex0 latex1 latex2

1

Sketch the parabola.

1

Transform the following time domain equations into Laplace domain (assume that all the variables are at rest at latex0 ): latex1 latex2 where latex3 latex4 where latex5 is defined in the same way as in part (b).

1

In cartesian co-ordinates, what is the latex1 -component of the pressure?

1

Next, we will prove an important property of the Michalis-Menten equation.

1

A piston of diameter latex0 is fitted inside a U-shaped tube filled with liquid mercury (with density in latex1 ), as shown by the sketch below.

0

The chain pitch is 12mm The final stage in this task is to determine the torque and resultant acceleration you can expect from your go-kart.

1

Establish if by choosing a capacitor latex0 , the circuit below is underdamped or overdamped: The other component values are as follows: latex1 \ latex2 \ latex3 \ latex4 \ latex5

1

Find: The final pressure of the contents.

1

Sketch the solution for a concentration latex5 which satisfies the reflector boundary condition as a superposition of the concentration profiles in a and b.

1

A torus is described in spherical polar coordinates by latex0 (independent of latex1 ).

0

If a matrix element does not exist, input 'n'.

1

As you push the cart at constant speed the mass will be displaced by a length latex1 .

0

Find the downstream height latex3 .

1

Write the following numbers in polar form latex0 , where latex1 .

1

Now suppose that there are three non-zero vectors latex5 , latex6 , and latex7 in latex8 that obey: latex9 Can you conclude that latex10 ?

1

The mercury rises by latex2 under the weight of the piston.

0

For the approximate solution (in part (c)) near to latex7 , comparing to the Taylor series in part (d) the find the relative error when: latex14 Notice how the approximate equation produced a solution latex7 .

1

(1) and (2), derive the other three SUVAT equations: latex6

1

If latex0 , calculate latex1 and latex2 and show that latex3

1

Give the solution to this problem in symbolic form.

1

You are supplied with a motor providing operating at an output shaft speed of 2900 rpm at a torque of 4Nm.

0

The function latex0 never vanishes (goes to zero).

0

It took latex17 for the absorbance of the assay to increase from latex18 to latex19 .

0

How far below point B should point D be placed?

1

Sketch the output waveform at “P”, showing peak values and time intervals

1

Calculate the Reynolds number in this vein assuming the dynamic viscosity of blood to be 0.003 Pa s, and the density is 1060 kg/m latex0 .

1

A truck travels through shallow water at some speed latex7 .

0

The release occurs at the water surface, which is modelled as a perfect reflector.

0

You should have found that latex24 and latex25 were not the same so the above method is wrong in the moving frame.

0

Hence find the angular momentum latex13 and torque latex14 about the origin at latex10 .

1

There is no superheat.

0

Explain whether, at latex11 m, the Blasius solution is applicable for speeds, latex1 , of: (i) latex13 m/s; (ii) latex14 m/s; (iii) latex15 m/s.

1

Kinetic energies at entry and exit are negligible and nitrogen can be modelled as a perfect gas under these conditions.

0

You can assume the full load operating speed for this motor is 1000rpm and that the maximum torque it can provide is 0.045Nm.

0

Solve Problem 10.4 by considering a cylindrical frame of reference attached to the ground, with origin in the centre of the tank and with axial direction latex0 .Determine an expression for the velocity field Determine the deformation tensor.

1

Sketch a graph of latex12 and indicate on it any points of equilibrium.

1

Consider the rate law: latex0 Where latex1 is the concentration of reactant, latex2 is time, and latex3 is a rate constant.

0

What is its final velocity?

1

Comment on the gradient at the wall.

1

Steam enters a turbine with a pressure of 30 bar and a temperature of latex0 with a velocity of latex1 .

0

What is the mass, latex3 , of the piston?

1

Find the deflection at the quarter span of the loaded beam.

1

Explain what is meant by the by the expressions that follow.

1

Using the symbols above: latex7 Which can be re-arranged as: latex8 The solution for this equation for latex3 would allow you to calculate the latex10 of a solution of a weak acid.

0

*** **Note:** In the response area, type the same answer twice for repeated solutions.

1

We *count* symbols from the list, going from latex14 to latex23 .

0

The transport of contaminant when diffusion is negligible.

0

In two or more dimensions, for most (but not all) force fields latex7 , the work done, latex8 depends on the route taken from latex9 to latex10 .

0

The natural frequency of the oscillator is latex3 .

0

You are encouraged to individually work through several possible solutions and then discuss as a group.

0

Negligible effects of gravity In Section A In Section B In Section C In Section D In Section E

0

Write down the general solution to **eq.

1

What are the efficiencies of the engine based on GCV and NCV respectively?

1

Once a flow has been started by sufficient suction, the syphon will run continuously as long as there is fluid available in the reservoir.

0

latex2 latex3 latex4 latex5 latex6

0

The wind is now blowing and exerts a constant (time-independent) force latex1 in the forward direction.

0

What, thermodynamically, distinguishes the situations in (a) and (b)?

1

The rate at which entropy is generated within the turbine per latex8 of steam flowing in units of latex9 .

0

Derive an expression for the acceleration of the particle.

1

Make use of Taylor series and start from the compressible flow relation for the ratio of stagnation to static pressure.

1

*** The triangular function below is periodic on the interval latex0 a_0=0 latex1 a_n=0 latex2 b_n latex3 b_n latex4 n latex1 \int_{-\pi}^{\pi}f(x)\sin(n x)dx=2\int_{0}^{\pi}f(x)\sin(n x)dx \;.

0

He thinks she might be joking.

0

Diffusion only and in both latex0 and z-directions.

0

What will be: (i) the energy utilisation factor of the CHP plant?

1

The temperature of steam with a pressure of latex12 bar and specific enthalpy of latex13 .

0

What is the angle (in degrees), anti-clockwise relative to horizontal, of lines of constant pressure within the water in the accelerating tank?

1

Give the exact length.

1

Once you know how to count, then you can define operations such as *addition* and *subtraction*, which are nothing but the ability to count in the forward or backward directions by increments of any lengths.

0

Draw a sketch of the imaginary part of latex2 up to latex4 , latex8 , latex9 and latex10 terms in the Fourier series.

1

(Assume that the steam is wet at the turbine exhaust).

0

(Based on P3.139, White) The horizontal pump shown below discharges water at latex0 C at a volume flux of latex1 .

0

A boundary layer develops along the walls of the working section, but the velocity profile outside the boundary layer remains uniform and steady.

0

Find the magnitudes and directions of the maximum shear stresses at the point.

1

Determine the values of latex6 and latex3 .

1

* You may wish to use .

0

latex0 latex1 latex2 latex3

0

Using the Tables in the Data & Formulae book for the properties of water and steam, write down the magnitude and units for the following: The specific volume of saturated water at latex0 bar.

1

Flywheel latex0 is driven by a torque latex16 , given by: latex17 where latex18 is the time and latex19 is a constant equal to latex20 .

0

Show that an area element of the surface of the torus is given by: latex3 *** Let all the formal machinery developed in lectures work for you and you should easily reach the expression for latex4 .

1

This question relates to combined cycle plants and combined heat and power plants.

0

On a latex6 diagram, sketch three Joule cycles with different pressure ratios (one very low, one medium and one very high) but the same maximum temperature.

1

Hence, find the maximum solar energy (with no solar panel tilting) that can be obtained in London ( latex10 ) as compared to the equator.

1

What is happening, physically, in the water?

1

As the disc rotates in the direction shown, four optical sensors with switching outputs, arranged along the line “ab”, generate a 4-bit natural binary signal which represents its angular position.

1

How much did the density change relative to latex17 if the drone is flying latex19 above the ground?

1

Repeat part c) using linear theory.

1

*** The pendulum consists of a mass suspended from a cord of length latex0 suspended vertically (the latex1 direction) at latitude latex2 , with the rotation plane being free to move in the latex3 - latex4 plane (see the Figure below).

0

I leave it to you to learn how to play with these four operators in base- latex16 (Wikipedia is your friend), and we proceed with solving our logistic-map conversion problem.

0

Calculate the values of the amplitude latex1 , the angular frequency latex2 , the frequency latex3 , the period latex4 , the spring constant, latex5 .

1

Write down an expression for the total head at surface 1, latex0 , if gravitational effects can be neglected.

1

* *** Consider an infinitely long rod where the temperature is evolving according to the heat flow equation: latex0 where latex1 represents the temperature at the point latex2 and time latex3 .

0

A planet circles a star (in the latex0 - latex1 plane) with a motion described as a function of time latex2 by the position vector: latex3 (you may assume that quantities are normalised and so dimensionless).

0