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数学 大学生・専門学校生・社会人

位置を2回微分すると、加速度になるんですか?

1OROY m m 0 0 9(t) 図1 単調和振動子。 復元力 F はF= ーky(t) であるとする.ここでk>0はバネ定数と呼ばれる与 えられた物理量である. ニュートンの法則(カ=質量× 加速度) を適用すると, ーky(t) =D my" (t) が得られる。ただしy" という記号でyのtに関する 2階導関数を表すものとす る。c= Vk/m とおくと, この2階常微分方程式は g"(t) +c9(t) =D0 となる。方程式(1) の一般解は, a, b を任意定数として 9(t) = a cos ct+bsinct により与えられる。明らかに, この形の関数はすべて方程式 (1) の解になってい る。そしてこの形の解のみがこの微分方程式の 2回微分可能な解になっている。 その証明の概略は練習6で述べる。 上述の y(t) を表す式のなかで, cは与えられた定数であるが, a, bはどのよ うな実数でもかまわない. この方程式の特別な解を決める場合, 二つの未知定数 a, b を考慮に入れた二つの初期条件を課さねばならない. たとえば物体の最初の 位置 y(0) と初期速度 y/'(0) が与えられれば, 物理的な問題の解は一意的となり, y(0) sin ct 9(t) = y(0) cos ct + C により与えられる. 容易にわかることであるが, ある定数 A>0と φERで, a cos ct + bsin ct = Acos (ct - 4) をみたすものが存在する. 上に述べた物理的な解釈に基づいて, A= Va? +6? をこの運動の「振幅」 cを「固有振動数」 (aを「位相| (これは ?Tの整数倍

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TOEIC・英語 大学生・専門学校生・社会人

問5 英語の長文問題です選択式です! よろしくお願いします。

【問5】 次の Global Warming の段落を読んで、その下の英文 (S) が True (正 い) か False (誤り) のどちらか、選びなさい。 AM Global Warmind: All over the world people are talking about global warming. Vorld leaders are meeting to discuss this problem. Why is it such an important ISSU@? f the temperature of the earth rises too much, the polar ice CapS will begin to melt, causing the water level in the oceans to rise. The Intergovernmental Panel on Climate Change (the IPCC) has made Studies which suggest that there could be a one-meter rise in sea levels by the year 2080. No one knows exactly how bad the effect of this rise could be. However, it is thought that roughly 1 billion people who live on coastal land could experience severe impacts. The places most likely to be badly affected by this rise in sea level are tropical and warmer zoness: these are places where the coasts are more highly populated. The most vulnerable regions are located along the southern coast of the Mediterranean Sea, the west coast of Africa, and southern Asian countries like India, Sri Lanka, and Bangladesh. These regions contain some of the poorest, most heavily populated, and highly fertile areas of the world. In these areas, there will be huge problems as people's homes are flooded and qood farming land becomes useless. In the Pacific and Indian Oceans there are many island nations that will cease to exist. About 5 million people will have to move to other countries as the rising seas ruin drinking water and severe storms destroy their homes. The consequences of global warming will be devastating for billions of people. This is not only their problem, but an issue for the world to discuss. Much has to be done before the oceans come ashore. (S): Because of global warming, the temperature of ice and snoW IS increasin9. 〇 A. TRUE (〇) B. FALSE

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TOEIC・英語 大学生・専門学校生・社会人

問5 英語の長文問題です 選択式です よろしくお願いします。

【問5】 次の Global Warming の段落を読んで、その下の英文 (S) が True (正 い) か False (誤り) のどちらか、選びなさい。 AM Global Warmind: All over the world people are talking about global warming. Vorld leaders are meeting to discuss this problem. Why is it such an important ISSU@? f the temperature of the earth rises too much, the polar ice CapS will begin to melt, causing the water level in the oceans to rise. The Intergovernmental Panel on Climate Change (the IPCC) has made Studies which suggest that there could be a one-meter rise in sea levels by the year 2080. No one knows exactly how bad the effect of this rise could be. However, it is thought that roughly 1 billion people who live on coastal land could experience severe impacts. The places most likely to be badly affected by this rise in sea level are tropical and warmer zoness: these are places where the coasts are more highly populated. The most vulnerable regions are located along the southern coast of the Mediterranean Sea, the west coast of Africa, and southern Asian countries like India, Sri Lanka, and Bangladesh. These regions contain some of the poorest, most heavily populated, and highly fertile areas of the world. In these areas, there will be huge problems as people's homes are flooded and qood farming land becomes useless. In the Pacific and Indian Oceans there are many island nations that will cease to exist. About 5 million people will have to move to other countries as the rising seas ruin drinking water and severe storms destroy their homes. The consequences of global warming will be devastating for billions of people. This is not only their problem, but an issue for the world to discuss. Much has to be done before the oceans come ashore. (S): Because of global warming, the temperature of ice and snoW IS increasin9. 〇 A. TRUE (〇) B. FALSE

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TOEIC・英語 大学生・専門学校生・社会人

問3 英語の長文問題です 選択式です よろしくお願いします

【問3】 次の Global Warming の段落を読んで、その下の英文 (S) が い) か False (誤り) のどちらか、選びなさい。 (S) が True (正し Global Warming: All over the world people are talking about global warming. World leaders are meeting to discuss this problem. Why is it Such an Important ISSUG? If the temperature of the earth rises too much, the polar ice capS will begin to melt, causing the water level in the oceans to rise. The Intergovernmental Panel on Climate Change (the IPCC) has made studies which suggest that there could be a one-meter rise In Se levels by the year 2080. No one knows exactly how bad the effect of this rise could be. However, it is thought that roughly 1 billion people who live on coastal land could experience severe impacts. The places most likely to be badly affected by this rise in sea level are tropical and warmer ZoneS: these are places where the coasts are Ore highly populated. The most vulnerable regions are located along the southern coast of the Mediterranean Sea, the west coast of Africa, and southerm Asian countries like India, Sri Lanka, and Bangladesh. These regions contain some of the poorest, most heavily populated, and highly fertlle areaS of the world. In these areas, there will be huge problems as people's homes are flooded and good farming land becomes useless. In the Pacific and Indian Oceans there are many jsland nations that will cease to exist. About 5 million people will have to move to other countries as the rising seas ruin drinking water and severe storms destroy their homes. The consequences Of global warming will be devastatind for billions of people. This is not only their problem, but an ISSue for the world to discuss. Much has to be done before the oceans come aShore. (S): As a result of global warmin9, farms and fertile lands throughout the world will be destroyed. 〇 A_ TRUE () B.FALSE

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TOEIC・英語 大学生・専門学校生・社会人

問2 長文の英語です。 選択式です よろしくお願いします。

【問2】 次の Global Warming の段落を読んで、その下の英文 (S) が True (正 い) か False (誤り) のどちらか、選びなさい> Il間 Global Warming: All over the world people are talking about global warming. World leaders are meeting to discuss this problem. Why is it such an important ISSUG? If the temperature of the earth rises too much, the polar ice caps will begin to melt, causing the water level in the oceans to rise. The Intergovernmental Panel on Climate Change (the IPCC) has made studies which suggest that there could be a one-meter rise in sea levels by the year 2080. No one knows exactly how bad the effect of this rise could be. However, it is thought that roughly 1 billion people who live on coastal land could experience severe impacts. The places most likely to be badly affected by this rise in sea level are tropical and warmer zones: these are places where the coasts are more highly populated. The most vulnerable regions are located along the southern coast of the Mediterranean Sea, the west coast of Africa, and southern Asian countries like India, Sri Lanka, and Bangladesh. These reqions contain some of the poorest, most heavily populated, and hiqhly fertile areas of the world. In these areas, there will be huge problems as people's homes are flooded and good farming land becomes useless. In the Pacific and Indian Oceans there are many island nations that will cease to exist. About 5 million people will have to move to other countries as the rising seas ruin drinking water and severe storms destroy their homes. The consequences of global warming wlll be devastating for billions of people. This is not only their problem, but an issue for the world to discuss. Much has to be done before the oceans come ashore. (S): Rising sea-levels will decrease acceSsSs to clean drinking water for hundreds of millions of people. (〇 A_ TRUE (〇) B. FALSE

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TOEIC・英語 大学生・専門学校生・社会人

5問目 英語の長文問題です。 選択式です。よろしくお願いします。

【問5】 次の Global Warming の段落を読んで、その下の英文 (S) が True (正 い) か False (誤り) のどちらか、選びなさい。 AM Global Warmind: All over the world people are talking about global warming. Vorld leaders are meeting to discuss this problem. Why is it such an important ISSU@? f the temperature of the earth rises too much, the polar ice CapS will begin to melt, causing the water level in the oceans to rise. The Intergovernmental Panel on Climate Change (the IPCC) has made Studies which suggest that there could be a one-meter rise in sea levels by the year 2080. No one knows exactly how bad the effect of this rise could be. However, it is thought that roughly 1 billion people who live on coastal land could experience severe impacts. The places most likely to be badly affected by this rise in sea level are tropical and warmer zoness: these are places where the coasts are more highly populated. The most vulnerable regions are located along the southern coast of the Mediterranean Sea, the west coast of Africa, and southern Asian countries like India, Sri Lanka, and Bangladesh. These regions contain some of the poorest, most heavily populated, and highly fertile areas of the world. In these areas, there will be huge problems as people's homes are flooded and qood farming land becomes useless. In the Pacific and Indian Oceans there are many island nations that will cease to exist. About 5 million people will have to move to other countries as the rising seas ruin drinking water and severe storms destroy their homes. The consequences of global warming will be devastating for billions of people. This is not only their problem, but an issue for the world to discuss. Much has to be done before the oceans come ashore. (S): Because of global warming, the temperature of ice and snoW IS increasin9. 〇 A. TRUE (〇) B. FALSE

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TOEIC・英語 大学生・専門学校生・社会人

3問目 英語の長文問題 選択式です、よろしくお願いします。

【問3】 次の Global Warming の段落を読んで、その下の英文 (S) が い) か False (誤り) のどちらか、選びなさい。 (S) が True (正し Global Warming: All over the world people are talking about global warming. World leaders are meeting to discuss this problem. Why is it Such an Important ISSUG? If the temperature of the earth rises too much, the polar ice capS will begin to melt, causing the water level in the oceans to rise. The Intergovernmental Panel on Climate Change (the IPCC) has made studies which suggest that there could be a one-meter rise In Se levels by the year 2080. No one knows exactly how bad the effect of this rise could be. However, it is thought that roughly 1 billion people who live on coastal land could experience severe impacts. The places most likely to be badly affected by this rise in sea level are tropical and warmer ZoneS: these are places where the coasts are Ore highly populated. The most vulnerable regions are located along the southern coast of the Mediterranean Sea, the west coast of Africa, and southerm Asian countries like India, Sri Lanka, and Bangladesh. These regions contain some of the poorest, most heavily populated, and highly fertlle areaS of the world. In these areas, there will be huge problems as people's homes are flooded and good farming land becomes useless. In the Pacific and Indian Oceans there are many jsland nations that will cease to exist. About 5 million people will have to move to other countries as the rising seas ruin drinking water and severe storms destroy their homes. The consequences Of global warming will be devastatind for billions of people. This is not only their problem, but an ISSue for the world to discuss. Much has to be done before the oceans come aShore. (S): As a result of global warmin9, farms and fertile lands throughout the world will be destroyed. 〇 A_ TRUE () B.FALSE

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TOEIC・英語 大学生・専門学校生・社会人

2問目 英語の長文問題です。選択式です。 よろしくお願いします。

【問2】 次の Global Warming の段落を読んで、その下の英文 (S) が True (正 い) か False (誤り) のどちらか、選びなさい> Il間 Global Warming: All over the world people are talking about global warming. World leaders are meeting to discuss this problem. Why is it such an important ISSUG? If the temperature of the earth rises too much, the polar ice caps will begin to melt, causing the water level in the oceans to rise. The Intergovernmental Panel on Climate Change (the IPCC) has made studies which suggest that there could be a one-meter rise in sea levels by the year 2080. No one knows exactly how bad the effect of this rise could be. However, it is thought that roughly 1 billion people who live on coastal land could experience severe impacts. The places most likely to be badly affected by this rise in sea level are tropical and warmer zones: these are places where the coasts are more highly populated. The most vulnerable regions are located along the southern coast of the Mediterranean Sea, the west coast of Africa, and southern Asian countries like India, Sri Lanka, and Bangladesh. These reqions contain some of the poorest, most heavily populated, and hiqhly fertile areas of the world. In these areas, there will be huge problems as people's homes are flooded and good farming land becomes useless. In the Pacific and Indian Oceans there are many island nations that will cease to exist. About 5 million people will have to move to other countries as the rising seas ruin drinking water and severe storms destroy their homes. The consequences of global warming wlll be devastating for billions of people. This is not only their problem, but an issue for the world to discuss. Much has to be done before the oceans come ashore. (S): Rising sea-levels will decrease acceSsSs to clean drinking water for hundreds of millions of people. (〇 A_ TRUE (〇) B. FALSE

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