Which fraction is closer to 1/2 than 1? 7/8 10/12 12/14 7/10

Mathematics

2 answers:

larisa [96]3 years ago

5 0

Answer:

7/10

Step-by-step explanation:

7/8 = .875

10/12 = .833

12/14 = .857

7/10 = .7

1/2 - .5

nevsk [136]3 years ago

4 0

Answer:

7/10

Step-by-step explanation:

Comparison of these three fractions is easier if you convert them so that all have the same denominator.

"Closer to 1/2 than to 1" implies that the fraction chosen lies between 1/2 and 3/4, that is, between 0.500 and 0.750.

7/8 = 0.875 must be rejected. It does not satisfy this criterion. 0.875 is NOT closer to 1/2 than it is to 1.

10/12 = 0.833 must be rejected for the same reason.

12/14 = 6/7 must be rejected for the same reason

7/10 = 0.700 satisfies the criterion (it lies closer to 1/2 than it does to 1).

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Notice that $x^3+x^2-4x-4=x^2(x+1)-4(x+1)=(x-2)(x+2)(x+1)$ . Decompose the integrand into partial fractions:

$\dfrac{x^2+x-3}{(x-2)^2(x+2)^2(x+1)^2}$
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Integrating term-by-term, you get

$\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx$
$=-\dfrac1{48(x-2)}+\dfrac1{3(x+1)}+\dfrac1{16(x+2)}+\dfrac1{96}\ln|x-2|+\dfrac13\ln|x+1|-\dfrac{11}{32}\ln|x+2|+C$