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In space consider a point  Q and a plane which is 1 away from Q. The intersection between this plane and the sphere with center Q and radius 2 is

By simplifying the expression 



where a and b are two non-zero real numbers different from each other, we obtainDeselect Answer

The least common multiple of monomials 8x³y⁶, 6x²y⁶z², x⁴y³ isDeselect Answer

The prime factorization of the number (2⁵-2³)⁴3² isDeselect Answer

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Which of these equations represents a straight line passing through the point (-2,3)  and perpendicular to the bisector of the first quadrant?

A solution of the equation  is log₃(2+x)²=6 isDeselect Answer

The figure shows the graph of the function
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The equation (x-1)²+y²=0 defines in the Cartesian planeDeselect Answer

Only one of the following statements is correct; identify which one.

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The sum of the ages of two sisters is now 24 years. In eight years the age of the eldest will be equal to three times her current age minus twice the current age of the youngest. How old are the two sisters?

A new study conducted for the World Bank by Murdoch University's Institute for Science and Technology Policy (ISTP) has demonstrated that public transport is more efficient than cars. The study compared the proportion of money poured into transport by thirty-seven cities around the world. This included both the public and private costs of building, maintaining and using a transport system.

The study found that the Western Australian city of Perth is a good example of a city with minimal public transport. As a result, 17% of its wealth went into transport costs. Some European and Asian cities, on the other hand, spent as little as 5%. As a consequence, these more efficient cities were able to put the money saved into attracting industry and jobs or creating a better place to live.

Professor Newman, ISTP Director describes Melbourne as two cities: "A European city surrounded by a car-dependent one''. Melbourne's large tram network has greatly reduced car use in the inner city, but the outer suburbs have the same car-based structure as most other Australian cities. The increasing demand for accommodation in the inner suburbs of Melbourne suggests that people now prefer to live there.

Newman believes there is a new, more general way of considering public transport issues. In the past, environmental and social justice were considered before economics. Newman, however, thinks the study demonstrates that "the auto-dependent city model is inefficient and very inadequate in both economic and environmental terms''.

Supporters of the road networks often reject the models of cities with good public transport by saying that these systems would not work in their particular city. One objection is climate. Some people say their city could not make more use of public transport because it is either too hot or too cold. Newman rejects this, pointing out that public transport has been successful in both Toronto and Singapore and, in fact, checks have demonstrated no correlation between the use of cars and the climate.

When it comes to other physical characteristics, road lobbies are in a stronger position. For example, Newman accepts it would be hard for a city with a lot of hills like Auckland to develop a really good rail network. However, he points out that both Hong Kong and Zurich have managed to make a success of their rail systems, even if they have more hills than most cities in the world.

In fact, Newman believes the main reason for choosing one sort of transport instead of another is politics: "the more democratic the process, the more public transport is favored". He considers Portland, Oregon, a perfect example of this. Some years ago, the central government decided to finance the construction of a new road. However, local pressure groups called for a referendum and the money was spent on a railway instead, which worked extremely well. In the years that have followed, more and more rail systems have been put in, dramatically changing the nature of the city.

In the UK, travel times to work had been stable for at least six centuries, and people generally avoided spending more than half an hour travelling to work. Trains and cars initially allowed people to live at greater distances without taking longer to reach their destination. However, public infrastructure did not grow with the increase in urban areas, and this caused enormous congestion problems and much longer commuting times.

Many think that if people have more money they want to live further from the city centre where cars are the only practical means of transport. The example of European cities contradicts that. People are often wealthier than their American counterparts but do not use their cars as much. In Stockholm, car use has actually fallen in recent years as the city has become larger and wealthier. New studies show that developing cities in Asia, such as Jakarta and Bangkok, make more use of the car than wealthy Asian cities such as Tokyo and Singapore. In cities that developed later, the World bank and Asian Development Bank discouraged the building of public transport and people have been forced to depend on cars -- creating the massive traffic jams that characterize those cities.

An alternative proposal is to convert cities that have been built for cars to rail use, by creating urban villages at hundreds of sites, mostly around railway stations.

In the study Melbourne emerges as

The use of private transport

The ISTP report showed that cities with well-developed public transport

Some people who prefer travelling by car do not agree with an increase in public transport because

In the case of Portland, the most significant aspect governing the choice of trains was

Which of these diagrams illustrates the correct relationship between:

The product of 40 integer numbers is positive. From this information we can deduce that it is necessarily true that:

John doesn't believe that Anthony passed the professional certification exam, but he doesn't have any evidence to the contrary.
We can deduce that:

As it is true that:
- all sparrows are birds
- all sparrows are small
- all birds are animals
- some animals don't eat leaves
it can be deduced that:

Discussing their personal finances, four friends (Dilya, Gulzoda, Laziza e Tenkokuheya) state that:

- Dilya has less money than Laziza
- Gulzoda has less money than Laziza
- Laziza has more money than Tenkokuheya
- Gulzoda has more money than Dilya

Then, which of the following statements is NOT NECESSARILY correct?

At what depth must a diver immerse himself in water so that the pressure on his body is double that of the atmosphere? 
(atmospheric pressure =  10 ⁵ Pa  ; density of water = 10 ³ kg/m ³  ; acceleration of gravity = 10 m/s ² ) 

A point charge q = 3 ×10 ^-6 C, having a mass of 4 ×10 ^-3 kg, placed in a uniform electric field is subject to an acceleration equal in magnitude to 6 ×10 ^-3 m/s ² . What is the magnitude of the electric field?

A juggler throws an orange up the y-axis with an initial velocity of 10m/s. What will be the maximum height reached by the orange? Consider g= 10m/s ²    

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A mass m = 1 kg of water a 0⁰c  and an equal mass of ice a 0⁰c  are also placed in a container with perfectly insulating walls which is immediately sealed. If you reopen it after 1 hour, what do you find?

During a succession of thermodynamic transformations a gas absorbs from the outside a quantity of heat Q ₁ = 10000 J, it gives off a quantity of heat |Q ₂ | = 3000 J and does work L = 2000 J. In the end, how much has the internal energy of the gas changed?

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The specific heat of a body is defined by the relationship C=Q/(mΔT) where  Q is the heat exchanged by the body, m the mass of the body and ΔT its temperature variation. What is the SI unit of specific heat?

What force should we apply to lift an object off the ground?

Under Windows the command ipconfig /all

Which of the following instructions represents an assignment in languages such as C or Python?

Given the figure, which will be the value of b at the end of the program?

A real distance of 500 m in a 1:10,000 scale representation corresponds on the mapDeselect Answer

Given the front and right views of a solid, what is its correct three-dimensional representation?

Indicate in which historical period the descriptive geometry has been geometrically coded