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weqwewe [10]
4 years ago
5

Define plasma as a form of matter

Mathematics
1 answer:
natta225 [31]4 years ago
8 0

Plasma is a form of matter in which many of the electrons wander around freely among the nuclei of the atoms. Plasma has been called the fourth state of matter, the other three being solid, liquid and gas.

Normally, the electrons in a solid, liquid, or gaseous sample of matter stay with the same atomic nucleus. Some electrons can move from atom to atom if an electrical current flows in a solid or liquid, but the motion occurs as short jumps by individual electrons between adjacent nuclei. In a plasma, a significant number of electrons have such high energy levels that no nucleus can hold them.

An atom that has lost some of its electrons, thereby attaining an electric charge, is an ion. When a gas is subjected to heat or an electric field, some of its atoms become ions, and the gas is said to be ionized. An ionized gas, unlike a gas in its normal condition, can conduct electrical current to a limited extent. If the heat or electric field becomes extreme, many of the atoms become ions. The resulting super-ionized gas is a plasma, which can conduct a large and sustained electric current.

The behavior and properties of plasmas have aroused interest and creative work among scientists and engineers. Applications include electric lamps, lasers, medical devices, energy converters, water purifiers and flat-panel video displays. About 99% of the visible universe is formed of plasma.

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Please verify the following trigonometric identities.
Nina [5.8K]

Seems like there is a correction in the first question (RHS is tanx.tany)

(i) For convenience: let tanx = a ; tany = b

Thus, tanx + tany = a + b

Moreover, cotx = 1/tanx = 1/a ; coty = 1/b

Thus,

cotx + coty = 1/a + 1/b = (a + b)/ab

Hence,

=> (tanx + tany)/(cotx + coty)

=> (a + b) / { (a + b)/ab }

=> ab(a + b)/(a + b)

=> ab => tanx.tany , proved.

(ii) For convenience: let sinx = a ; cosx = b

As we know, sin²x + cos²x = 1 => a²+b²=1

=> (a³ + b³)/(a + b)

=> (a + b)(a² + b² - ab) / (a + b)

=> (a² + b² - ab)

=> 1 - ab => 1 - sinx.cosx , proved

(iii): let x/2 = A

=> tan(x/2) + cosx.tan(x/2)

=> tanA + cos2A.tanA

=> tanA [1 + cos2A]

=> tanA (2cos²A) {1+cos2A = 2cos²A}

=> (sinA/cosA) (2cos²A)

=> sinA (2cosA)

=> 2sinAcosA

=> sin2A

=> sin2(x/2)

=> sinx proved

Letting x/2 = A is not mandatory. I did it to decease words*(in a line).

<u>Indentities used</u>:

• sin²A + cos²A = 1

• (a³ + b³) = (a + b)(a² + b² - 1)

• 1 + cosA = 2 cos²(A/2)

• tanA = sinA/cosA.

• 2sinAcosA = sin2A

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lesya [120]

Answer:

$6,564.85

Step-by-step explanation:

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The diameter of a cylindrical construction pipe is 4ft If the pipe is 17ft long, what is its volume? Use the value 3.14 for /pi,
zvonat [6]

Answer:

214 ft^3

Step-by-step explanation:

Here, we are asked to calculate the volume of the cylindrical construction pipe.

Mathematically, the volume V

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r is radius = diameter/2 = 4/2 = 2 ft

h = 17ft

pi = 3.14

Putting these values, we have;

V = 3.14 * 2^2 * 17 = 213.52 which is 214 ft^3 to the nearest whole number

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Three fifths of a number is equal to twice the number minus sixty-three hundredths. What is the number?
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Answer:

That number is 0.45

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