itisarainyday/ml_classifier_bert_training · Datasets at Hugging Face

0 stringlengths 10 969	label int64 0 1
Show that: latex9 Find latex1 for any positive value of latex3 .	1
Figures 1 and 2 are two views of a Formula 1 race.	0
Air, supplied by a reservoir at latex0 flows through a converging-diverging nozzle whose throat area is latex1 .	0
Figure 1 Figure 2 Figure 1 is consistent with: Figure 2 is consistent with:	0
Using experimental data given in the table, find the thrust generated by a geometrically similar propeller of diameter latex4 , spinning at latex5 at a forward velocity of latex6 , while operating at an altitude where the density is half that at sea level.	1
The following statements are true at both plates (1) and (2): o Plate area is latex0 .	0
Note that latex24 is the relative speed experienced by the cups, assumed constant for each half rotation of the anemometer.	0
Challenge yourself to answer this question with no further information.	0
Draw a circuit diagram of the system and select a suitable resistor value.	1
A square plate fixed along all four edges has a set of normal modes characterized by two integers latex0 and latex1 .	0
the latex5 component of latex23 .	0
By how much must the fracture toughness of the material be improved in order to tolerate a longer crack latex11 at the same fracture load?	1
In the lectures we looked at the interference pattern due to a pair of point sources with separation latex0 .	0
In this part of the question you will begin to find the latex22 component, latex11 , of the flow Given that the flow does not depend on latex12 or latex13 , simplify the continuity equation and solve it to find the dependency of latex11 upon latex12 , latex13 , latex29 and latex30 .	1
Use the cross product to find the angle between latex5 and latex6 .	1
The card can sample at latex3 .	0
Use a frame of reference fixed to the tank and assume no relative motion between the fluid particles in that frame of reference.	1
Find the values of latex2 and latex3 at latex4 .	1
Make use of Green's Theorem.	1
Consider the function latex0 , where latex1 , is analytic.	0
Using this figure, estimate the maximum operating temperature of a gas turbine blade made out of this material which is to withstand a stress of latex0 for a duration of latex1 hours.	1
The mass flow rate latex4 is the same on each side, so that the temperature difference latex5 between the hot and cold sides is constant throughout the heat exchanger.	0
The ratio of latex7 with latex1 is known as the Froude number (noted latex10 ).	0
It is often easier to understand where they come from and rederive them when needed.	0
Is the discrepancy in air-speed computations significant in this case?	1
There is damping in the system because the accelerating electron dissipates energy by radiation.	0
Show that the maximum value of latex2 is latex3 , and that latex4 The half-power frequencies are defined as the values of latex5 at which latex2 is half the maximum value.	1
Draw an element of material at the point of interest, and indicate the stresses acting on its faces.	1
In the channel flow pictured below, with water entering from the left, in which region (labelled A to F) is the flow field approximately the same as the 'straining flow' field described above?	1
An 'integrated' risk assessment, for simple risks such as everyday activities.	0
This problem leads you through an alternate derivation based on the invariance of the speed of light.	0
Force fields without potentials are called non-conservative.	0
The geometry is illustrated in the figure below, where we’ve assumed latex1 is odd (though the results will not depend on that).	0
Calculate the safety factor against buckling in the plane of the diagram**.	1
The general solution of the driven oscillator with light damping, where the driving force is latex0 , is the sum of the steady solution latex1 and the transient solution latex2 .	0
The combustion process in the real engine is to be modelled by a heat transfer latex6 to the air of latex7 .	0
Calculate the latex15 in a heat pump application.	1
A wide freshwater stream has a stream flow of latex0 at a uniform depth of latex1 .	0
Define a control volume in the reference frame moving with the compression front.	1
In the quantum picture, the power is dissipated by emitting photons, each one having energy latex11 .	0
The Reynolds number describes the ratio of inertial to viscous effects.	0
(You may assume throughout this question that all physical quantities are given in dimensionless units, and there are no external forces acting on the particle.)	0
The pressure is latex7 Pa, where latex8 is the distance parallel to the flow (measured in metres).	0
What is the maximum deflection angle for which a flow at latex2 will remain attached?	1
*** The centroid is the Cartesian point latex1 such that latex2 and latex3 where latex4 is the region of integration and latex5 is the area of that region.	0
By recognising: latex8 as a Fourier transform of a function from Question 3, evaluate the integral: latex9 through the use of Parseval’s theorem.	0
It branches in two repeatedly, and at each level, the volume of each daughter branch is one quarter that of its parent.	0
Find the acceleration of a disc of mass latex0 and radius latex1 , which has been released from rest, as it rolls (without slipping) down an inclined plane which is at an angle latex2 to the horizontal.	1
The sediment size at the river bed is described by latex2 .	0
If the planes intersect at a point, input the point of intersection.	1
Lubricant viscosity is VG32 (32 mPa.s).	0
Determine the dryness fraction latex6 at the final state of the steam	1
A crack of length latex0 has been found at the center of a large thin plate, with an end load of latex1 .	1
A passive contaminant or tracer.	0
The Navier latex0 Stokes equations describing the flow of an incompressible Newtonian fluid are as follows: latex36 latex37 latex38 In this part you will find the latex12 - and latex13 -components of the flow, latex9 and latex10 , in terms of the pressure field, latex43 .	1
Assume that advection is the only process of importance.	0
(Based on P3.164, White) The nozzle shown below ejects a jet of water into air at atmospheric pressure (101 kPa).	0
Why do these not hold?	1
Is the channel bed stable in terms of initiation of motion for this flow?	1
What is the highest frequency the card can sample without the danger of aliasing?	1
(Hint: find latex12 and latex13 from the fact that process latex14 is isentropic, then latex10 from the 1st Law, then latex11 from the equation of state.)	0
* You may wish to abbreviate that to latex41 for clarity.	0
(iii) Calculate the net specific work and hence the thermal efficiency of the cycle.	1
A constant force latex6 N acts for 5 s. Find the acceleration of the block and hence its final speed and final kinetic energy.	1
However, there is a simple classical model that works surprisingly well.	0
What is the probability of a randomly synthesised 6 nucleotide-long piece of DNA having the sequence AACCGT (assume all bases have equal probabilities of occurrence)?	1
Calculate the total resistance as measured between points a and b in the network below:	1
\[Riley 10.11] The hyperboloid latex0 is parameterised by latex1 , latex2 , latex3 .	0
Use Cramer's rule to find a solution to the following system of linear equations: latex0	1
Hint: Are there any symmetries that allow reduction of the spatial dimensions?	1
What is the deflection angle that will make the flow behind a shock at latex1 sonic?	1
You should assume that the conditions in the reservoir are steady.	0
Consider two infinitely narrow slits that are separated by a distance latex8 .	0
What is the total resultant force of the water on the dam?	1
Give its numerical value at ground level: Aircraft designers assume air to be a continuum medium.	1
A force of latex1 N acts on the mass for 4 seconds.	0
Assume acceleration is uniform up until the point of reaching maximum speed.	0
Assume the channel to be steady and uniform.	0
What is the pressure at the bottom of a (hypothetical) latex2 mm high column of mercury, latex3 kg/ latex4 ?	1
Find the pressures and temperatures at the end of the expansion process.	1
Hint: You may need to use the latex6 function in Matlab.	0
What is the critical bed shear stress, latex5 , for this channel?	1
Consider a river stream given by the specific flow rate latex0 , where the water depth is latex1 .	0
The water is present in both liquid and vapour phases, and has a total mass of latex3 .	0
Let’s write the frequencies of these normal modes in the form latex2 .	0
Answer the following questions.	1
If so - of what functions?	1
Find the net specific work of the cycle and then use this to find the power supplied by the engine if it is running at 5000 rev/min and the cylinder capacity is 2 litres ( latex1 ) Using the answer to part c, determine the thermal efficiency of the cycle, the Carnot efficiency, and the effective efficiency of the engine as a percentage of the Carnot.	1
Is the assumption of suspended sediment transport occurring in a small layer close to the bed valid?	1
Repeat this calculation for other time values.	1
Call this number of nuclei latex27 , and use it to obtain a particular solution to the ODE.	1
The phone has an internal resistance of latex2 and requires a latex3 input.	0
A snow plough starts at noon latex1 and moves along a road removing snow at a constant rate.	0
Now consider the burning of the log and describe the temperature latex5 as a convolution of the constant heat provided by the log with the temperature evolution latex6 from part (a).	1
The minus sign in the answer arises because the radial direction points out of the sphere while the flux is into the sphere.	0
(L13): A parallelogram latex0 (in latex1 ) anchored at the origin is defined by the sides with vectors with components latex2 and latex3 .	0
It can be shown that the mean-free path in the hard-sphere model is latex7 .	0
latex0 Which of the following is correct:- Select all that apply Does the function latex1 satisfy Laplace's equation?	1
You must choose your own unit normals --- do this with care regarding the signs.	1
the station.	0

Show that: latex9 Find latex1 for any positive value of latex3 .

1

Figures 1 and 2 are two views of a Formula 1 race.

0

Air, supplied by a reservoir at latex0 flows through a converging-diverging nozzle whose throat area is latex1 .

0

Figure 1 Figure 2 Figure 1 is consistent with: Figure 2 is consistent with:

0

Using experimental data given in the table, find the thrust generated by a geometrically similar propeller of diameter latex4 , spinning at latex5 at a forward velocity of latex6 , while operating at an altitude where the density is half that at sea level.

1

The following statements are true at *both* plates (1) and (2): o Plate area is latex0 .

0

Note that latex24 is the relative speed experienced by the cups, assumed constant for each half rotation of the anemometer.

0

Challenge yourself to answer this question with no further information.

0

Draw a circuit diagram of the system and select a suitable resistor value.

1

A square plate fixed along all four edges has a set of normal modes characterized by two integers latex0 and latex1 .

0

the latex5 component of latex23 .

0

By how much must the fracture toughness of the material be improved in order to tolerate a longer crack latex11 at the same fracture load?

1

In the lectures we looked at the interference pattern due to a pair of point sources with separation latex0 .

0

In this part of the question you will *begin* to find the latex22 component, latex11 , of the flow Given that the flow does not depend on latex12 or latex13 , simplify the continuity equation and solve it to find the dependency of latex11 upon latex12 , latex13 , latex29 and latex30 .

1

Use the cross product to find the angle between latex5 and latex6 .

1

The card can sample at latex3 .

0

Use a frame of reference fixed to the tank and assume no relative motion between the fluid particles in that frame of reference.

1

Find the values of latex2 and latex3 at latex4 .

1

Make use of Green's Theorem.

1

Consider the function latex0 , where latex1 , is analytic.

0

Using this figure, estimate the maximum operating temperature of a gas turbine blade made out of this material which is to withstand a stress of latex0 for a duration of latex1 hours.

1

The mass flow rate latex4 is the same on each side, so that the temperature difference latex5 between the hot and cold sides is constant throughout the heat exchanger.

0

The ratio of latex7 with latex1 is known as the Froude number (noted latex10 ).

0

It is often easier to understand where they come from and rederive them when needed.

0

Is the discrepancy in air-speed computations significant in this case?

1

There is damping in the system because the accelerating electron dissipates energy by radiation.

0

Show that the maximum value of latex2 is 	 latex3 , and that 	 latex4 The half-power frequencies are defined as the values of latex5 at which latex2 is half the maximum value.

1

Draw an element of material at the point of interest, and indicate the stresses acting on its faces.

1

In the channel flow pictured below, with water entering from the left, in which region (labelled A to F) is the flow field approximately the same as the 'straining flow' field described above?

1

An 'integrated' risk assessment, for simple risks such as everyday activities.

0

This problem leads you through an alternate derivation based on the invariance of the speed of light.

0

Force fields without potentials are called non-conservative.

0

The geometry is illustrated in the figure below, where we’ve assumed latex1 is odd (though the results will not depend on that).

0

** Calculate the safety factor against **buckling in the plane of the diagram**.

1

The general solution of the driven oscillator with light damping, where the driving force is latex0 , is the sum of the steady solution 	 latex1 and the transient solution 	 latex2 .

0

The combustion process in the real engine is to be modelled by a heat transfer latex6 to the air of latex7 .

0

Calculate the latex15 in a heat pump application.

1

A wide freshwater stream has a stream flow of latex0 at a uniform depth of latex1 .

0

Define a control volume in the reference frame moving with the compression front.

1

In the quantum picture, the power is dissipated by emitting photons, each one having energy latex11 .

0

The Reynolds number describes the ratio of inertial to viscous effects.

0

(You may assume throughout this question that all physical quantities are given in dimensionless units, and there are no external forces acting on the particle.)

0

The pressure is latex7 Pa, where latex8 is the distance parallel to the flow (measured in metres).

0

What is the maximum deflection angle for which a flow at latex2 will remain attached?

1

*** The centroid is the Cartesian point latex1 such that latex2 and latex3 where latex4 is the region of integration and latex5 is the area of that region.

0

By recognising: latex8 as a Fourier transform of a function from *Question 3*, evaluate the integral: latex9 through the use of Parseval’s theorem.

0

It branches in two repeatedly, and at each level, the volume of each daughter branch is one quarter that of its parent.

0

Find the acceleration of a disc of mass latex0 and radius latex1 , which has been released from rest, as it rolls (without slipping) down an inclined plane which is at an angle latex2 to the horizontal.

1

The sediment size at the river bed is described by latex2 .

0

If the planes intersect at a point, input the point of intersection.

1

Lubricant viscosity is VG32 (32 mPa.s).

0

Determine the dryness fraction latex6 at the final state of the steam

1

A crack of length latex0 has been found at the center of a large thin plate, with an end load of latex1 .

1

A passive contaminant or tracer.

0

The Navier latex0 Stokes equations describing the flow of an incompressible Newtonian fluid are as follows: latex36 latex37 latex38 In this part you will find the latex12 - and latex13 -components of the flow, latex9 and latex10 , in terms of the pressure field, latex43 .

1

Assume that advection is the only process of importance.

0

(Based on P3.164, White) The nozzle shown below ejects a jet of water into air at atmospheric pressure (101 kPa).

0

Why do these not hold?

1

Is the channel bed stable in terms of initiation of motion for this flow?

1

What is the highest frequency the card can sample without the danger of aliasing?

1

(*Hint: find* latex12 *and* latex13 *from the fact that process* latex14 *is isentropic, then* latex10 *from the 1st Law, then* latex11 *from the equation of state*.)

0

* You may wish to abbreviate that to latex41 for clarity.

0

(iii) Calculate the net specific work and hence the thermal efficiency of the cycle.

1

A constant force latex6 N acts for 5 s. Find the acceleration of the block and hence its final speed and final kinetic energy.

1

However, there is a simple classical model that works surprisingly well.

0

What is the probability of a randomly synthesised 6 nucleotide-long piece of DNA having the sequence AACCGT (assume all bases have equal probabilities of occurrence)?

1

Calculate the total resistance as measured between points **a** and **b** in the network below:

1

*\[Riley 10.11]* The hyperboloid latex0 is parameterised by latex1 , latex2 , latex3 .

0

Use Cramer's rule to find a solution to the following system of linear equations: latex0

1

Hint: Are there any symmetries that allow reduction of the spatial dimensions?

1

What is the deflection angle that will make the flow behind a shock at latex1 sonic?

1

You should assume that the conditions in the reservoir are steady.

0

Consider two infinitely narrow slits that are separated by a distance latex8 .

0

What is the total resultant force of the water on the dam?

1

Give its numerical value at ground level: Aircraft designers assume air to be a continuum medium.

1

A force of latex1 N acts on the mass for 4 seconds.

0

Assume acceleration is uniform up until the point of reaching maximum speed.

0

Assume the channel to be steady and uniform.

0

What is the pressure at the bottom of a (hypothetical) latex2 mm high column of mercury, latex3 kg/ latex4 ?

1

Find the pressures and temperatures at the end of the expansion process.

1

Hint: You may need to use the latex6 function in Matlab.

0

What is the critical bed shear stress, latex5 , for this channel?

1

Consider a river stream given by the specific flow rate latex0 , where the water depth is latex1 .

0

The water is present in both liquid and vapour phases, and has a total mass of latex3 .

0

Let’s write the frequencies of these normal modes in the form latex2 .

0

Answer the following questions.

1

If so - of what functions?

1

Find the net specific work of the cycle and then use this to find the power supplied by the engine if it is running at 5000 rev/min and the cylinder capacity is 2 litres ( latex1 ) Using the answer to part c, determine the thermal efficiency of the cycle, the Carnot efficiency, and the effective efficiency of the engine as a percentage of the Carnot.

1

Is the assumption of suspended sediment transport occurring in a small layer close to the bed valid?

1

Repeat this calculation for other time values.

1

Call this number of nuclei latex27 , and use it to obtain a particular solution to the ODE.

1

The phone has an internal resistance of latex2 and requires a latex3 input.

0

A snow plough starts at noon latex1 and moves along a road removing snow at a constant rate.

0

Now consider the burning of the log and describe the temperature latex5 as a convolution of the constant heat provided by the log with the temperature evolution latex6 from part (a).

1

The minus sign in the answer arises because the radial direction points out of the sphere while the flux is into the sphere.

0

**(L13)**: A parallelogram latex0 (in latex1 ) anchored at the origin is defined by the sides with vectors with components latex2 and latex3 .

0

It can be shown that the mean-free path in the hard-sphere model is latex7 .

0

latex0 Which of the following is correct:- Select all that apply Does the function latex1 satisfy Laplace's equation?

1

You must choose your own unit normals --- do this with care regarding the signs.

1

the station.

0