Considere a_n e b_n os termos gerais de duas progressões geométricas, cujas razões são 4 e !$ { \large 1 \over 2} !$, respectivamente.

Tem-se, portanto, que c_n = a_n . b_n é o termo geral de uma progressão geométrica cuja razão é igual a

A estabilidade de um determinado processo industrial é avaliada a partir de um índice N, que é um número real positivo. O processo é considerado estável se, e somente se, 3 ≤ log3 (N) ≤ 4. O processo é dito instável se, e somente se, o mesmo não for estável.

Dessa forma, o referido processo industrial é considerado instável se, e somente se, o índice N pertence ao conjunto

Seja f: !$ \mathbb{R} \rightarrow \mathbb{R} !$ a função periódica definida por f(x) = sen(x), cujo gráfico é apresentado a seguir.

O período T de uma função periódica g é o menor número real, estritamente positivo, para o qual se tem g(x) = g(x + T), !$ \forall !$ x !$ \epsilon !$ !$ \mathbb{R} !$.

O período da função g: !$ \mathbb{R} \rightarrow \mathbb{R} !$ definida por g(x) = |f(x)| é

Natural gas waits for its moment

Paul Stenquist

Cars and trucks powered by natural gas make up a significant portion of the vehicle fleet in many parts of the world. Iran has more than two million natural gas vehicles on the road. As of 2009, Argentina had more than 1.8 million in operation and almost 2,000 natural gas filling stations. Brazil was not far behind. Italy and Germany have substantial natural gas vehicle fleets. Is America next?

With natural gas in plentiful supply at bargain prices in the United States, issues that have limited its use in cars are being rethought, and its market share could increase, perhaps substantially.

According to Energy Department Price Information from July, natural gas offers economic advantages over gasoline and diesel fuels. If a gasoline-engine vehicle can take you 40 miles on one gallon, the same vehicle running on compressed natural gas can do it for about $1.50 less at today’s prices. To that savings add lower maintenance costs. A study of New York City cabs running on natural gas found that oil changes need not be as frequent because of the clean burn of the fuel, and exhaustsystem parts last longer because natural gas is less corrosive than other fuels.

Today, those economic benefits are nullified by the initial cost of a natural gas vehicle — 20 to 30 percent more than a comparable gasoline-engine vehicle. But were production to increase significantly, economies of scale would bring prices down. In an interview by phone, Jon Coleman, fleet sustainability manager at the Ford Motor Company, said that given sufficient volume, the selling price of natural gas vehicles could be comparable to that of conventional vehicles.

It may be years before the economic benefits of natural gas vehicles can be realized, but the environmental benefits appear to be immediate. According to the Energy Department’s website, natural gas vehicles have smaller carbon footprints than gasoline or diesel automobiles, even when taking into account the natural gas production process, which releases carbon-rich methane into the atmosphere.

The United States government appears to favor natural gas as a motor vehicle fuel. To promote the production of vehicles with fewer carbon emissions, it has allowed automakers to count certain vehicle types more than once when calculating their Corporate Average Fuel Economy, under regulations mandating a fleet average of 54.5 miles per gallon by 2025. Plug-in hybrids and natural gas vehicles can be counted 1.6 times under the CAFE standards, and electric vehicles can be counted twice.

Adapting natural gas as a vehicle fuel introduces engineering challenges. While the fuel burns clean, it is less energy dense than gasoline, so if it is burned in an engine designed to run on conventional fuel, performance and efficiency are degraded.

But since natural gas has an octane rating of 130, compared with 93 for the best gasoline, an engine designed for it can run with very high cylinder pressure, which would cause a regular gasoline engine to knock from premature ignition. More cylinder pressure yields more power, and thus the energy-density advantage of gasoline can be nullified.[...]

Until the pressurized fuel tanks of natural gas vehicles can be easily and quickly refueled, the fleet cannot grow substantially. The number of commercial refueling stations for compressed natural gas has been increasing at a rate of 16 percent yearly, the Energy Department says. And, while the total is still small, advances in refueling equipment should increase the rate of expansion. Much of the infrastructure is already in place: America has millions of miles of natural gas pipeline. Connecting that network to refueling equipment is not difficult.

Although commercial refueling stations will be necessary to support a substantial fleet of natural gas vehicles, home refueling may be the magic bullet that makes the vehicles practical. Electric vehicles depend largely on home charging and most have less than half the range of a fully fueled natural gas vehicle. Somecompressed natural gas home refueling products are available, but they can cost as much as $5,000.

Seeking to change that, the Energy Department has awarded grants to a number of companies in an effort to develop affordable home-refueling equipment.

[...]

Available at: <http://www.nytimes.com/2013/10/30/automobiles/

natural-gas-waits-for-its-moment.html?page wanted=all&module=Search&mabReward=relbias%3A r%2C%7B%222%22%3A%22RI%3A18%22%7D>. Retrieved on: Sept 3rd, 2014. Adapted.

In the sentence of the text “Although commercial refueling stations will be necessary to support a substantial fleet of natural gas vehicles, home refueling may be the magic bullet that makes the vehicles practical”, the word although implies facts that are

Natural gas waits for its moment

Paul Stenquist

Cars and trucks powered by natural gas make up a significant portion of the vehicle fleet in many parts of the world. Iran has more than two million natural gas vehicles on the road. As of 2009, Argentina had more than 1.8 million in operation and almost 2,000 natural gas filling stations. Brazil was not far behind. Italy and Germany have substantial natural gas vehicle fleets. Is America next?

With natural gas in plentiful supply at bargain prices in the United States, issues that have limited its use in cars are being rethought, and its market share could increase, perhaps substantially.

According to Energy Department Price Information from July, natural gas offers economic advantages over gasoline and diesel fuels. If a gasoline-engine vehicle can take you 40 miles on one gallon, the same vehicle running on compressed natural gas can do it for about $1.50 less at today’s prices. To that savings add lower maintenance costs. A study of New York City cabs running on natural gas found that oil changes need not be as frequent because of the clean burn of the fuel, and exhaustsystem parts last longer because natural gas is less corrosive than other fuels.

Today, those economic benefits are nullified by the initial cost of a natural gas vehicle — 20 to 30 percent more than a comparable gasoline-engine vehicle. But were production to increase significantly, economies of scale would bring prices down. In an interview by phone, Jon Coleman, fleet sustainability manager at the Ford Motor Company, said that given sufficient volume, the selling price of natural gas vehicles could be comparable to that of conventional vehicles.

It may be years before the economic benefits of natural gas vehicles can be realized, but the environmental benefits appear to be immediate. According to the Energy Department’s website, natural gas vehicles have smaller carbon footprints than gasoline or diesel automobiles, even when taking into account the natural gas production process, which releases carbon-rich methane into the atmosphere.

The United States government appears to favor natural gas as a motor vehicle fuel. To promote the production of vehicles with fewer carbon emissions, it has allowed automakers to count certain vehicle types more than once when calculating their Corporate Average Fuel Economy, under regulations mandating a fleet average of 54.5 miles per gallon by 2025. Plug-in hybrids and natural gas vehicles can be counted 1.6 times under the CAFE standards, and electric vehicles can be counted twice.

Adapting natural gas as a vehicle fuel introduces engineering challenges. While the fuel burns clean, it is less energy dense than gasoline, so if it is burned in an engine designed to run on conventional fuel, performance and efficiency are degraded.

But since natural gas has an octane rating of 130, compared with 93 for the best gasoline, an engine designed for it can run with very high cylinder pressure, which would cause a regular gasoline engine to knock from premature ignition. More cylinder pressure yields more power, and thus the energy-density advantage of gasoline can be nullified.[...]

Until the pressurized fuel tanks of natural gas vehicles can be easily and quickly refueled, the fleet cannot grow substantially. The number of commercial refueling stations for compressed natural gas has been increasing at a rate of 16 percent yearly, the Energy Department says. And, while the total is still small, advances in refueling equipment should increase the rate of expansion. Much of the infrastructure is already in place: America has millions of miles of natural gas pipeline. Connecting that network to refueling equipment is not difficult.

Although commercial refueling stations will be necessary to support a substantial fleet of natural gas vehicles, home refueling may be the magic bullet that makes the vehicles practical. Electric vehicles depend largely on home charging and most have less than half the range of a fully fueled natural gas vehicle. Somecompressed natural gas home refueling products are available, but they can cost as much as $5,000.

Seeking to change that, the Energy Department has awarded grants to a number of companies in an effort to develop affordable home-refueling equipment.

[...]

Available at: <http://www.nytimes.com/2013/10/30/automobiles/

natural-gas-waits-for-its-moment.html?page wanted=all&module=Search&mabReward=relbias%3A r%2C%7B%222%22%3A%22RI%3A18%22%7D>. Retrieved on: Sept 3rd, 2014. Adapted.

According to the 6^th paragraph in the text (lines 43-52), one of the Corporate Average Fuel Economy goals for the fleet in the United States is average 54.5 miles per gallon

Natural gas waits for its moment

Paul Stenquist

Cars and trucks powered by natural gas make up a significant portion of the vehicle fleet in many parts of the world. Iran has more than two million natural gas vehicles on the road. As of 2009, Argentina had more than 1.8 million in operation and almost 2,000 natural gas filling stations. Brazil was not far behind. Italy and Germany have substantial natural gas vehicle fleets. Is America next?

With natural gas in plentiful supply at bargain prices in the United States, issues that have limited its use in cars are being rethought, and its market share could increase, perhaps substantially.

According to Energy Department Price Information from July, natural gas offers economic advantages over gasoline and diesel fuels. If a gasoline-engine vehicle can take you 40 miles on one gallon, the same vehicle running on compressed natural gas can do it for about $1.50 less at today’s prices. To that savings add lower maintenance costs. A study of New York City cabs running on natural gas found that oil changes need not be as frequent because of the clean burn of the fuel, and exhaustsystem parts last longer because natural gas is less corrosive than other fuels.

Today, those economic benefits are nullified by the initial cost of a natural gas vehicle — 20 to 30 percent more than a comparable gasoline-engine vehicle. But were production to increase significantly, economies of scale would bring prices down. In an interview by phone, Jon Coleman, fleet sustainability manager at the Ford Motor Company, said that given sufficient volume, the selling price of natural gas vehicles could be comparable to that of conventional vehicles.

It may be years before the economic benefits of natural gas vehicles can be realized, but the environmental benefits appear to be immediate. According to the Energy Department’s website, natural gas vehicles have smaller carbon footprints than gasoline or diesel automobiles, even when taking into account the natural gas production process, which releases carbon-rich methane into the atmosphere.

The United States government appears to favor natural gas as a motor vehicle fuel. To promote the production of vehicles with fewer carbon emissions, it has allowed automakers to count certain vehicle types more than once when calculating their Corporate Average Fuel Economy, under regulations mandating a fleet average of 54.5 miles per gallon by 2025. Plug-in hybrids and natural gas vehicles can be counted 1.6 times under the CAFE standards, and electric vehicles can be counted twice.

Adapting natural gas as a vehicle fuel introduces engineering challenges. While the fuel burns clean, it is less energy dense than gasoline, so if it is burned in an engine designed to run on conventional fuel, performance and efficiency are degraded.

But since natural gas has an octane rating of 130, compared with 93 for the best gasoline, an engine designed for it can run with very high cylinder pressure, which would cause a regular gasoline engine to knock from premature ignition. More cylinder pressure yields more power, and thus the energy-density advantage of gasoline can be nullified.[...]

Until the pressurized fuel tanks of natural gas vehicles can be easily and quickly refueled, the fleet cannot grow substantially. The number of commercial refueling stations for compressed natural gas has been increasing at a rate of 16 percent yearly, the Energy Department says. And, while the total is still small, advances in refueling equipment should increase the rate of expansion. Much of the infrastructure is already in place: America has millions of miles of natural gas pipeline. Connecting that network to refueling equipment is not difficult.

Although commercial refueling stations will be necessary to support a substantial fleet of natural gas vehicles, home refueling may be the magic bullet that makes the vehicles practical. Electric vehicles depend largely on home charging and most have less than half the range of a fully fueled natural gas vehicle. Somecompressed natural gas home refueling products are available, but they can cost as much as $5,000.

Seeking to change that, the Energy Department has awarded grants to a number of companies in an effort to develop affordable home-refueling equipment.

[...]

Available at: <http://www.nytimes.com/2013/10/30/automobiles/

natural-gas-waits-for-its-moment.html?page wanted=all&module=Search&mabReward=relbias%3A r%2C%7B%222%22%3A%22RI%3A18%22%7D>. Retrieved on: Sept 3rd, 2014. Adapted.

The sentence of the text “But were production to increase significantly, economies of scale would bring prices down” has the same meaning as: