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siniylev [52]
4 years ago
7

Which of the following is a factor of 7x2 − 12x − 4

Mathematics
1 answer:
nasty-shy [4]4 years ago
4 0
(7x + 2)(x - 2) are the factors
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A number is chosen at random from 1 to 50. Find the probability of not selecting a multiple of 2.
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Lets look at the number of numbers between 1 and 50 which is not a multiple of 2.  Its 1, 3, 5 ........... 47, 49.

That is 25 numbers.

So the required probability is 25/50 = 1/2 Answer


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What is the definite integral of log (tan x) with range from 90 to 0
nasty-shy [4]

Substituting <em>x</em> with <em>π</em>/2 - <em>x</em> gives the equivalent integral,

\displaystyle\int_0^{\frac\pi2}\log(\tan(x))\,\mathrm dx=-\int_{\frac\pi2}^0\log(\cot(x))(-\mathrm dx)=\int_0^{\frac\pi2}\log(\cot(x))\,\mathrm dx

So if we let <em>J</em> denote the value of the integral, we have

J=\displaystyle\int_0^{\frac\pi2}\log(\tan (x))\,\mathrm dx

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\implies 2J=\displaystyle\int_0^{\frac\pi2}\left(\log(\tan (x))+\log(\cot (x))\right)\,\mathrm dx

Condensing the logarithms, we have

log(tan(<em>x</em>)) + log(cot(<em>x</em>)) = log(tan(<em>x</em>) cot(<em>x</em>)) = log(1) = 0

since cot(<em>x</em>) = 1/tan(<em>x</em>), which means

2J=\displaystyle\int_0^{\frac\pi2}0\,\mathrm dx=0

and so the original integral has a value of <em>J</em> = 0.

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Step-by-step explanation:

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