Mathematics
01.11.2020 15:25
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Which of the following represents the zeros of f(x) = x3 − 2x2 − 6x + 12? −2, −square

Which of the following represents the zeros of f(x) = x3 − 2x2 − 6x + 12?
−2, −square root of 6, −square root of 6
2, −square root of 6, −square root of 6
2, square root of 6, −square root of 6
−2, square root of 6, square root of 6
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tylercapozzoli
tylercapozzoli
4,5(75 marks)
f(x)=x^{3}-2x^{2}-6x+12 \\  \\ x^{3}-2x^{2}-6x+12=0 \\  \\ x^{2}(x-2)-6(x-2)=0 \\  \\ (x^{2}-6)(x-2)=0 \\  \\ (x- \sqrt{6})(x+ \sqrt{6})(x-2)=0 \\  \\ x- \sqrt{6}=0 \ \vee \ x+ \sqrt{6}=0 \ \vee \ x-2=0 \\  \\ x= \sqrt{6} \ \vee \ x=- \sqrt{6} \ \vee \ x=2 \\  \\ x\in \lbrace - \sqrt{6}, 2,  \sqrt{6} \rbrace

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skypeltier
skypeltier
4,4(7 marks)

75,000km  (kilometres)  converted from given 0.075 giga meters  gm

gm to km multiplies by 1 million

46 cs (centisecond) converted from given  0.00046 kilo second ks

ks x cs multiplies by 100,000

4.096 GB (Gigabyte)  converted from given 4096 Mega Byte MB

MB to GB divides by 1000

KB to GB divides by 1000

GB to MB multiplies by 1000

MB to KB multiplies by 1000  so that GB, MB, KB are all 1000 x each other.

0.0000002 mg (milligram) converted from 0.0002 Microgram ug

ug  microgram to mg milligram divides by 1000

Explanation of cs : seconds. siemens.

Language useful fact to know is the German name of kiloseconds and centiseconds is kilosiemens and centisiemens.

Which means Siemens means seconds.

The siemens (symbol: S) is the derived unit of electric conductance, electric susceptance, and electric admittance in the International System of Units (SI). Conductance, susceptance, and admittance are the reciprocals of resistance, reactance, and impedance respectively; hence one siemens is redundantly equal to the reciprocal of one ohm (Ω−1) and is also referred to as the mho. The 14th General Conference on Weights and Measures approved the addition of the siemens as a derived unit in 1971.[1]

The unit is named after Ernst Werner von Siemens. In English, the same word siemens is used both for the singular and plural

The unit siemens for the conductance G is defined by

{\displaystyle \mathrm {[S]} =[\Omega ^{-1}]=[\mathrm {A} /\mathrm {V} ]}{\displaystyle \mathrm {[S]} =[\Omega ^{-1}]=[\mathrm {A} /\mathrm {V} ]}

where Ω is the ohm, A is the ampere, and V is the volt.

For a device with a conductance of one siemens, the electric current through the device will increase by one ampere for every increase of one volt of electric potential difference across the device.

The conductance of a resistor with a resistance of five ohms, for example, is (5 Ω)−1, which is equal to 200 mS.

Another name for the siemens is the mho (/ˈmoʊ/). As the reciprocal of one ohm, it is the word ohm spelled backwards, at the suggestion of Sir William Thomson (Lord Kelvin) in 1883.[3] Its symbol is an inverted capital Greek letter omega: U+2127 ℧ INVERTED OHM SIGN.

NIST's Guide for the Use of the International System of Units (SI) refers to the mho as an "unaccepted special name for an SI unit", and indicates that it should be strictly avoided.[4]

The SI term siemens is used universally in science and often in electrical applications, while mho is still used in some electronic contexts.

The inverted capital omega symbol (℧), while not an official SI abbreviation, is less likely to be confused with a variable than the letter 'S' when writing on a blackboard or doing algebraic calculations by hand. The usual typographical distinctions (such as italic for variables and roman for units) are difficult to maintain. Likewise, it is difficult to distinguish the symbol 'S' (siemens) from the lower-case 's' (seconds), potentially causing confusion.[5] So, for example, a pentode’s transconductance of 2.2 mS might alternatively be written as 2.2 m℧ or 2200 μ℧ (most common in the 1930s) or 2.2 mA/V.

A handwritten 'S' can also be misread as the frequency-space variable 's', commonly used in transfer functions.

The ohm had officially replaced the old "siemens unit", a unit of resistance, at an international conference in 1881.[6]

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